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<div class="section" id="pai4sk-api">
<span id="pai4sk-api-documentation"></span><h1>pai4sk API<a class="headerlink" href="#pai4sk-api" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="pai4sk.linear_model.Ridge">
<em class="property">class </em><code class="descclassname">pai4sk.linear_model.</code><code class="descname">Ridge</code><span class="sig-paren">(</span><em>alpha=1.0</em>, <em>fit_intercept=True</em>, <em>normalize=False</em>, <em>copy_X=True</em>, <em>max_iter=None</em>, <em>tol=0.001</em>, <em>solver='auto'</em>, <em>random_state=None</em>, <em>dual=False</em>, <em>verbose=0</em>, <em>use_gpu=True</em>, <em>device_ids=[]</em>, <em>return_training_history=None</em>, <em>privacy=False</em>, <em>eta=0.3</em>, <em>batch_size=100</em>, <em>privacy_epsilon=10</em>, <em>grad_clip=1</em>, <em>num_threads=1</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.Ridge" title="Permalink to this definition">¶</a></dt>
<dd><p>Linear least squares with l2 regularization.</p>
<p>Minimizes the objective function:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">||</span><span class="n">y</span> <span class="o">-</span> <span class="n">Xw</span><span class="o">||^</span><span class="mi">2_2</span> <span class="o">+</span> <span class="n">alpha</span> <span class="o">*</span> <span class="o">||</span><span class="n">w</span><span class="o">||^</span><span class="mi">2_2</span>
</pre></div>
</div>
<p>This model solves a regression model where the loss function is
the linear least squares function and regularization is given by
the l2-norm. Also known as Ridge Regression or Tikhonov regularization.
This estimator has built-in support for multi-variate regression
(i.e., when y is a 2d-array of shape [n_samples, n_targets]).</p>
<p>Read more in the <span class="xref std std-ref">User Guide</span>.</p>
<p>For SnapML solver this supports both local and distributed(MPI) method of execution.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>alpha</strong> (<em>{float</em><em>, </em><em>array-like}</em><em>, </em><em>shape</em><em> (</em><em>n_targets</em><em>)</em>) – Regularization strength; must be a positive float. Regularization
improves the conditioning of the problem and reduces the variance of
the estimates. Larger values specify stronger regularization.
Alpha corresponds to <code class="docutils literal notranslate"><span class="pre">C^-1</span></code> in other linear models such as
LogisticRegression or LinearSVC. If an array is passed, penalties are
assumed to be specific to the targets. Hence they must correspond in
number.</li>
<li><strong>fit_intercept</strong> (<em>boolean</em>) – Whether to calculate the intercept for this model. If set
to false, no intercept will be used in calculations
(e.g. data is expected to be already centered).</li>
<li><strong>normalize</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default False</em>) – This parameter is ignored when <code class="docutils literal notranslate"><span class="pre">fit_intercept</span></code> is set to False.
If True, the regressors X will be normalized before regression by
subtracting the mean and dividing by the l2-norm.
If you wish to standardize, please use
<code class="xref py py-class docutils literal notranslate"><span class="pre">pai4sk.preprocessing.StandardScaler</span></code> before calling <code class="docutils literal notranslate"><span class="pre">fit</span></code>
on an estimator with <code class="docutils literal notranslate"><span class="pre">normalize=False</span></code>.</li>
<li><strong>copy_X</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default True</em>) – If True, X will be copied; else, it may be overwritten.</li>
<li><strong>max_iter</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>optional</em>) – Maximum number of iterations for conjugate gradient solver.
For ‘sparse_cg’ and ‘lsqr’ solvers, the default value is determined
by scipy.sparse.linalg. For ‘sag’ solver, the default value is 1000.</li>
<li><strong>tol</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a>) – Precision of the solution.</li>
<li><strong>regularizer</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default : 1.0</em>) – Regularization strength. It must be a positive float.
Larger regularization values imply stronger regularization.</li>
<li><strong>use_gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default : True</em>) – Flag for indicating the hardware platform used for training. If True, the training
is performed using the GPU. If False, the training is performed using the CPU.
The value of this parameter is subjected to changed based on the training data unless set explicitly.
Applicable only for snapml solver</li>
<li><strong>device_ids</strong> (<em>array-like of int</em><em>, </em><em>default :</em><em> [</em><em>]</em>) – If use_gpu is True, it indicates the IDs of the GPUs used for training.
For single GPU training, set device_ids to the GPU ID to be used for training, e.g., [0].
For multi-GPU training, set device_ids to a list of GPU IDs to be used for training, e.g., [0, 1].
Applicable only for snapml solver</li>
<li><strong>num_threads</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>default : 1</em>) – The number of threads used for running the training. The value of this parameter
should be a multiple of 32 if the training is performed on GPU (use_gpu=True)
(default value for GPU is 256). Applicable only for snapml solver</li>
<li><strong>return_training_history</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.7)"><em>str</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em>, </em><em>default : None</em>) – How much information about the training should be collected and returned by the fit function. By
default no information is returned (None), but this parameter can be set to “summary”, to obtain
summary statistics at the end of training, or “full” to obtain a complete set of statistics
for the entire training procedure. Note, enabling either option will result in slower training.
Applicable only for snapml solver</li>
<li><strong>solver</strong> (<em>{'auto'</em><em>, </em><em>'svd'</em><em>, </em><em>'cholesky'</em><em>, </em><em>'lsqr'</em><em>, </em><em>'sparse_cg'</em><em>, </em><em>'sag'</em><em>, </em><em>'saga'</em><em>, </em><em>'snapml'}</em>) – <p>Solver to use in the computational routines:</p>
<ul>
<li>’auto’ chooses the solver automatically based on the type of data.</li>
<li>’svd’ uses a Singular Value Decomposition of X to compute the Ridge
coefficients. More stable for singular matrices than
‘cholesky’.</li>
<li>’cholesky’ uses the standard scipy.linalg.solve function to
obtain a closed-form solution.</li>
<li>’sparse_cg’ uses the conjugate gradient solver as found in
scipy.sparse.linalg.cg. As an iterative algorithm, this solver is
more appropriate than ‘cholesky’ for large-scale data
(possibility to set <cite>tol</cite> and <cite>max_iter</cite>).</li>
<li>’lsqr’ uses the dedicated regularized least-squares routine
scipy.sparse.linalg.lsqr. It is the fastest and uses an iterative
procedure.</li>
<li>’sag’ uses a Stochastic Average Gradient descent, and ‘saga’ uses
its improved, unbiased version named SAGA. Both methods also use an
iterative procedure, and are often faster than other solvers when
both n_samples and n_features are large. Note that ‘sag’ and
‘saga’ fast convergence is only guaranteed on features with
approximately the same scale. You can preprocess the data with a
scaler from pai4sk.preprocessing.</li>
</ul>
<p>All last five solvers support both dense and sparse data. However,
only ‘sag’ and ‘saga’ supports sparse input when <cite>fit_intercept</cite> is
True.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.17: </span>Stochastic Average Gradient descent solver.</p>
</div>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.19: </span>SAGA solver.</p>
</div>
</li>
<li><strong>random_state</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>RandomState instance</em><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em>, </em><em>optional</em><em>, </em><em>default None</em>) – <p>The seed of the pseudo random number generator to use when shuffling
the data. If int, random_state is the seed used by the random number
generator; If RandomState instance, random_state is the random number
generator; If None, the random number generator is the RandomState
instance used by <cite>np.random</cite>. Used when <code class="docutils literal notranslate"><span class="pre">solver</span></code> == ‘sag’.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.17: </span><em>random_state</em> to support Stochastic Average Gradient.</p>
</div>
</li>
<li><strong>privacy</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default : False</em>) – Train the model using a differentially private algorithm.</li>
<li><strong>eta</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default : 0.3</em>) – Learning rate for the differentially private training algorithm.</li>
<li><strong>batch_size</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>default : 100</em>) – Mini-batch size for the differentially private training algorithm.</li>
<li><strong>privacy_epsilon</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default : 10.0</em>) – Target privacy gaurantee. Learned model will be (privacy_epsilon, 0.01)-private.</li>
<li><strong>grad_clip</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default: 1.0</em>) – Gradient clipping parameter for the differentially private training algorithm</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Variables:</th><td class="field-body"><ul class="first last simple">
<li><strong>coef</strong> (<em>array</em><em>, </em><em>shape</em><em> (</em><em>n_features</em><em>,</em><em>) or </em><em>(</em><em>n_targets</em><em>, </em><em>n_features</em><em>)</em>) – Weight vector(s).</li>
<li><strong>intercept</strong> (<em>float | array</em><em>, </em><em>shape =</em><em> (</em><em>n_targets</em><em>,</em><em>)</em>) – Independent term in decision function. Set to 0.0 if
<code class="docutils literal notranslate"><span class="pre">fit_intercept</span> <span class="pre">=</span> <span class="pre">False</span></code>.</li>
<li><strong>n_iter</strong> (<em>array</em><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em>, </em><em>shape</em><em> (</em><em>n_targets</em><em>,</em><em>)</em>) – Actual number of iterations for each target. Available only for
sag and lsqr solvers. Other solvers will return None.</li>
<li><strong>training_history</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.7)"><em>dict</em></a>) – <p>It returns a dictionary with the following keys : ‘epochs’, ‘t_elap_sec’, ‘train_obj’.
If ‘return_training_history’ is set to “summary”, ‘epochs’ contains the total number of
epochs performed, ‘t_elap_sec’ contains the total time for completing all of those epochs.
If ‘return_training_history’ is set to “full”, ‘epochs’ indicates the number of epochs
that have elapsed so far, and ‘t_elap_sec’ contains the time to do those epochs.
‘train_obj’ is the training loss.
Applicable only for snapml solver.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.17.</span></p>
</div>
</li>
</ul>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><code class="xref py py-class docutils literal notranslate"><span class="pre">RidgeClassifier</span></code></dt>
<dd>Ridge classifier</dd>
<dt><code class="xref py py-class docutils literal notranslate"><span class="pre">RidgeCV</span></code></dt>
<dd>Ridge regression with built-in cross validation</dd>
<dt><code class="xref py py-class docutils literal notranslate"><span class="pre">pai4sk.kernel_ridge.KernelRidge</span></code></dt>
<dd>Kernel ridge regression combines ridge regression with the kernel trick</dd>
</dl>
</div>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pai4sk.linear_model</span> <span class="k">import</span> <span class="n">Ridge</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span> <span class="o">=</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">5</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n_samples</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">clf</span> <span class="o">=</span> <span class="n">Ridge</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="mf">1.0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="c1"># doctest: +NORMALIZE_WHITESPACE</span>
<span class="go">Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,</span>
<span class="go"> normalize=False, random_state=None, solver='auto', tol=0.001)</span>
</pre></div>
</div>
<dl class="method">
<dt id="pai4sk.linear_model.Ridge.fit">
<code class="descname">fit</code><span class="sig-paren">(</span><em>X</em>, <em>y</em>, <em>sample_weight=None</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.Ridge.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit Ridge regression model</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>X</strong> (<em>{array-like</em><em>, </em><em>sparse matrix}</em><em>, </em><em>shape =</em><em> [</em><em>n_samples</em><em>, </em><em>n_features</em><em>]</em>) – Training data
For SnapML solver it also supports input of types SnapML data partition and DeviceNDArray.</li>
<li><strong>y</strong> (<em>array-like</em><em>, </em><em>shape =</em><em> [</em><em>n_samples</em><em>] or </em><em>[</em><em>n_samples</em><em>, </em><em>n_targets</em><em>]</em>) – Target values</li>
<li><strong>sample_weight</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em> or </em><em>numpy array of shape</em><em> [</em><em>n_samples</em><em>]</em>) – Individual weights for each sample</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>self</strong></p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">returns an instance of self.</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="pai4sk.linear_model.Ridge.predict">
<code class="descname">predict</code><span class="sig-paren">(</span><em>X</em>, <em>num_threads=0</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.Ridge.predict" title="Permalink to this definition">¶</a></dt>
<dd><blockquote>
<div><p>Class predictions
The returned class estimates.
Parameters
———-
X : sparse matrix (csr_matrix) or dense matrix (ndarray)</p>
<blockquote>
<div>Dataset used for predicting class estimates.
For SnapML solver it also supports input of type SnapML data partition.</div></blockquote>
</div></blockquote>
<dl class="docutils">
<dt>num_threads <span class="classifier-delimiter">:</span> <span class="classifier">int, default</span> <span class="classifier-delimiter">:</span> <span class="classifier">0</span></dt>
<dd><blockquote class="first">
<div>Number of threads used to run inference.
By default inference runs with maximum number of available threads.</div></blockquote>
<dl class="last docutils">
<dt>proba: array-like, shape = (n_samples,)</dt>
<dd>Returns the predicted class of the sample.</dd>
</dl>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="pai4sk.linear_model.Lasso">
<em class="property">class </em><code class="descclassname">pai4sk.linear_model.</code><code class="descname">Lasso</code><span class="sig-paren">(</span><em>alpha=1.0</em>, <em>fit_intercept=True</em>, <em>normalize=False</em>, <em>precompute=False</em>, <em>copy_X=True</em>, <em>max_iter=1000</em>, <em>tol=0.0001</em>, <em>warm_start=False</em>, <em>positive=False</em>, <em>random_state=None</em>, <em>selection='cyclic'</em>, <em>verbose=0</em>, <em>use_gpu=True</em>, <em>device_ids=[]</em>, <em>return_training_history=None</em>, <em>privacy=False</em>, <em>eta=0.3</em>, <em>batch_size=100</em>, <em>privacy_epsilon=10</em>, <em>grad_clip=1</em>, <em>num_threads=1</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.Lasso" title="Permalink to this definition">¶</a></dt>
<dd><p>Linear Model trained with L1 prior as regularizer (aka the Lasso)</p>
<p>The optimization objective for Lasso is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n_samples</span><span class="p">))</span> <span class="o">*</span> <span class="o">||</span><span class="n">y</span> <span class="o">-</span> <span class="n">Xw</span><span class="o">||^</span><span class="mi">2_2</span> <span class="o">+</span> <span class="n">alpha</span> <span class="o">*</span> <span class="o">||</span><span class="n">w</span><span class="o">||</span><span class="n">_1</span>
</pre></div>
</div>
<p>Technically the Lasso model is optimizing the same objective function as
the Elastic Net with <code class="docutils literal notranslate"><span class="pre">l1_ratio=1.0</span></code> (no L2 penalty).</p>
<p>Read more in the <span class="xref std std-ref">User Guide</span>.</p>
<p>For SnapML solver this supports both local and distributed(MPI) method of execution.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>alpha</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – Constant that multiplies the L1 term. Defaults to 1.0.
<code class="docutils literal notranslate"><span class="pre">alpha</span> <span class="pre">=</span> <span class="pre">0</span></code> is equivalent to an ordinary least square, solved
by the <code class="xref py py-class docutils literal notranslate"><span class="pre">LinearRegression</span></code> object. For numerical
reasons, using <code class="docutils literal notranslate"><span class="pre">alpha</span> <span class="pre">=</span> <span class="pre">0</span></code> with the <code class="docutils literal notranslate"><span class="pre">Lasso</span></code> object is not advised.
Given this, you should use the <code class="xref py py-class docutils literal notranslate"><span class="pre">LinearRegression</span></code> object.</li>
<li><strong>fit_intercept</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default True</em>) – Whether to calculate the intercept for this model. If set
to False, no intercept will be used in calculations
(e.g. data is expected to be already centered).</li>
<li><strong>normalize</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default False</em>) – This parameter is ignored when <code class="docutils literal notranslate"><span class="pre">fit_intercept</span></code> is set to False.
If True, the regressors X will be normalized before regression by
subtracting the mean and dividing by the l2-norm.
If you wish to standardize, please use
<code class="xref py py-class docutils literal notranslate"><span class="pre">pai4sk.preprocessing.StandardScaler</span></code> before calling <code class="docutils literal notranslate"><span class="pre">fit</span></code>
on an estimator with <code class="docutils literal notranslate"><span class="pre">normalize=False</span></code>.</li>
<li><strong>precompute</strong> (<em>True | False | array-like</em><em>, </em><em>default=False</em>) – Whether to use a precomputed Gram matrix to speed up
calculations. If set to <code class="docutils literal notranslate"><span class="pre">'auto'</span></code> let us decide. The Gram
matrix can also be passed as argument. For sparse input
this option is always <code class="docutils literal notranslate"><span class="pre">True</span></code> to preserve sparsity.</li>
<li><strong>copy_X</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default True</em>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, X will be copied; else, it may be overwritten.</li>
<li><strong>max_iter</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>optional</em>) – The maximum number of iterations</li>
<li><strong>tol</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em>) – The tolerance for the optimization: if the updates are
smaller than <code class="docutils literal notranslate"><span class="pre">tol</span></code>, the optimization code checks the
dual gap for optimality and continues until it is smaller
than <code class="docutils literal notranslate"><span class="pre">tol</span></code>.</li>
<li><strong>warm_start</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>optional</em>) – When set to True, reuse the solution of the previous call to fit as
initialization, otherwise, just erase the previous solution.
See <span class="xref std std-term">the Glossary</span>.</li>
<li><strong>positive</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>optional</em>) – When set to <code class="docutils literal notranslate"><span class="pre">True</span></code>, forces the coefficients to be positive.</li>
<li><strong>random_state</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>RandomState instance</em><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em>, </em><em>optional</em><em>, </em><em>default None</em>) – The seed of the pseudo random number generator that selects a random
feature to update. If int, random_state is the seed used by the random
number generator; If RandomState instance, random_state is the random
number generator; If None, the random number generator is the
RandomState instance used by <cite>np.random</cite>. Used when <code class="docutils literal notranslate"><span class="pre">selection</span></code> ==
‘random’.</li>
<li><strong>selection</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.7)"><em>str</em></a><em>, </em><em>default 'cyclic'</em>) – If set to ‘random’, a random coefficient is updated every iteration
rather than looping over features sequentially by default. This
(setting to ‘random’) often leads to significantly faster convergence
especially when tol is higher than 1e-4.</li>
<li><strong>verbose</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default : False</em>) – If True, it prints the training cost, one per iteration. Warning: this will increase the
training time. For performance evaluation, use verbose=False.</li>
<li><strong>use_gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default : True</em>) – Flag for indicating the hardware platform used for training. If True, the training
is performed using the GPU. If False, the training is performed using the CPU.
The value of this parameter is subjected to changed based on the training data unless set explicitly.
Applicable only for snapml solver</li>
<li><strong>device_ids</strong> (<em>array-like of int</em><em>, </em><em>default :</em><em> [</em><em>]</em>) – If use_gpu is True, it indicates the IDs of the GPUs used for training.
For single GPU training, set device_ids to the GPU ID to be used for training, e.g., [0].
For multi-GPU training, set device_ids to a list of GPU IDs to be used for training, e.g., [0, 1]. Applicable only for snapml solver</li>
<li><strong>num_threads</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>default : 1</em>) – The number of threads used for running the training. The value of this parameter
should be a multiple of 32 if the training is performed on GPU (use_gpu=True)
(default value for GPU is 256). Applicable only for snapml solver</li>
<li><strong>return_training_history</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.7)"><em>str</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em>, </em><em>default : None</em>) – How much information about the training should be collected and returned by the fit function. By
default no information is returned (None), but this parameter can be set to “summary”, to obtain
summary statistics at the end of training, or “full” to obtain a complete set of statistics
for the entire training procedure. Note, enabling either option will result in slower training.
Applicable only for snapml solver</li>
<li><strong>privacy</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default : False</em>) – Train the model using a differentially private algorithm.</li>
<li><strong>eta</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default : 0.3</em>) – Learning rate for the differentially private training algorithm.</li>
<li><strong>batch_size</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>default : 100</em>) – Mini-batch size for the differentially private training algorithm.</li>
<li><strong>privacy_epsilon</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default : 10.0</em>) – Target privacy gaurantee. Learned model will be (privacy_epsilon, 0.01)-private.</li>
<li><strong>grad_clip</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default: 1.0</em>) – Gradient clipping parameter for the differentially private training algorithm</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Variables:</th><td class="field-body"><ul class="first last simple">
<li><strong>coef</strong> (<em>array</em><em>, </em><em>shape</em><em> (</em><em>n_features</em><em>,</em><em>) </em><em>|</em><em> (</em><em>n_targets</em><em>, </em><em>n_features</em><em>)</em>) – parameter vector (w in the cost function formula)</li>
<li><strong>sparse_coef</strong> (<em>scipy.sparse matrix</em><em>, </em><em>shape</em><em> (</em><em>n_features</em><em>, </em><em>1</em><em>) </em><em>|</em><em> (</em><em>n_targets</em><em>, </em><em>n_features</em><em>)</em>) – <code class="docutils literal notranslate"><span class="pre">sparse_coef_</span></code> is a readonly property derived from <code class="docutils literal notranslate"><span class="pre">coef_</span></code></li>
<li><strong>intercept</strong> (<em>float | array</em><em>, </em><em>shape</em><em> (</em><em>n_targets</em><em>,</em><em>)</em>) – independent term in decision function.</li>
<li><strong>n_iter</strong> (<em>int | array-like</em><em>, </em><em>shape</em><em> (</em><em>n_targets</em><em>,</em><em>)</em>) – number of iterations run by the coordinate descent solver to reach
the specified tolerance.</li>
<li><strong>training_history</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.7)"><em>dict</em></a>) – It returns a dictionary with the following keys : ‘epochs’, ‘t_elap_sec’, ‘train_obj’.
If ‘return_training_history’ is set to “summary”, ‘epochs’ contains the total number of
epochs performed, ‘t_elap_sec’ contains the total time for completing all of those epochs.
If ‘return_training_history’ is set to “full”, ‘epochs’ indicates the number of epochs
that have elapsed so far, and ‘t_elap_sec’ contains the time to do those epochs.
‘train_obj’ is the training loss.
Applicable only for snapml solver.</li>
<li><strong>support</strong> (<em>array-like</em>) – Indices of the features that lie in the support ond contribute to the decision.</li>
<li><strong>model_sparsity</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a>) – Fraction of non-zeros in the model parameters.</li>
</ul>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pai4sk</span> <span class="k">import</span> <span class="n">linear_model</span>
<span class="gp">>>> </span><span class="n">clf</span> <span class="o">=</span> <span class="n">linear_model</span><span class="o">.</span><span class="n">Lasso</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="go">Lasso(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=1000,</span>
<span class="go"> normalize=False, positive=False, precompute=False, random_state=None,</span>
<span class="go"> selection='cyclic', tol=0.0001, warm_start=False)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">coef_</span><span class="p">)</span>
<span class="go">[0.85 0. ]</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">intercept_</span><span class="p">)</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="go">0.15...</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><code class="xref py py-class docutils literal notranslate"><span class="pre">lars_path</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">lasso_path</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">LassoLars</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">LassoCV</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">LassoLarsCV</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">pai4sk.decomposition.sparse_encode</span></code></p>
</div>
<p class="rubric">Notes</p>
<p>The algorithm used to fit the model is coordinate descent.</p>
<p>To avoid unnecessary memory duplication the X argument of the fit method
should be directly passed as a Fortran-contiguous numpy array.</p>
<dl class="method">
<dt id="pai4sk.linear_model.Lasso.fit">
<code class="descname">fit</code><span class="sig-paren">(</span><em>X</em>, <em>y</em>, <em>check_input=True</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.Lasso.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit model with coordinate descent.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>X</strong> (<em>ndarray</em><em> or </em><em>scipy.sparse matrix</em><em>, </em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – Data
For SnapML solver it also supports input of types SnapML data partition and DeviceNDArray.</li>
<li><strong>y</strong> (<em>ndarray</em><em>, </em><em>shape</em><em> (</em><em>n_samples</em><em>,</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>n_targets</em><em>)</em>) – Target. Will be cast to X’s dtype if necessary</li>
<li><strong>check_input</strong> (<em>boolean</em><em>, </em><em>(</em><em>default=True</em><em>)</em>) – Allow to bypass several input checking.
Don’t use this parameter unless you know what you do.</li>
</ul>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>Coordinate descent is an algorithm that considers each column of
data at a time hence it will automatically convert the X input
as a Fortran-contiguous numpy array if necessary.</p>
<p>To avoid memory re-allocation it is advised to allocate the
initial data in memory directly using that format.</p>
</dd></dl>
<dl class="method">
<dt id="pai4sk.linear_model.Lasso.predict">
<code class="descname">predict</code><span class="sig-paren">(</span><em>X</em>, <em>num_threads=0</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.Lasso.predict" title="Permalink to this definition">¶</a></dt>
<dd><blockquote>
<div><p>Class predictions
The returned class estimates.
Parameters
———-
X : sparse matrix (csr_matrix) or dense matrix (ndarray)</p>
<blockquote>
<div>Dataset used for predicting class estimates.
For SnapML solver it also supports input of type SnapML data partition.</div></blockquote>
</div></blockquote>
<dl class="docutils">
<dt>num_threads <span class="classifier-delimiter">:</span> <span class="classifier">int, default</span> <span class="classifier-delimiter">:</span> <span class="classifier">0</span></dt>
<dd><blockquote class="first">
<div>Number of threads used to run inference.
By default inference runs with maximum number of available threads.</div></blockquote>
<dl class="last docutils">
<dt>proba: array-like, shape = (n_samples,)</dt>
<dd>Returns the predicted class of the sample.</dd>
</dl>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="pai4sk.linear_model.LogisticRegression">
<em class="property">class </em><code class="descclassname">pai4sk.linear_model.</code><code class="descname">LogisticRegression</code><span class="sig-paren">(</span><em>penalty='l2'</em>, <em>dual=False</em>, <em>tol=0.0001</em>, <em>C=1.0</em>, <em>fit_intercept=True</em>, <em>intercept_scaling=1</em>, <em>class_weight=None</em>, <em>random_state=None</em>, <em>solver='warn'</em>, <em>max_iter=100</em>, <em>multi_class='warn'</em>, <em>verbose=0</em>, <em>warm_start=False</em>, <em>n_jobs=None</em>, <em>use_gpu=True</em>, <em>device_ids=[]</em>, <em>return_training_history=None</em>, <em>privacy=False</em>, <em>eta=0.3</em>, <em>batch_size=100</em>, <em>privacy_epsilon=10</em>, <em>grad_clip=1</em>, <em>num_threads=1</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.LogisticRegression" title="Permalink to this definition">¶</a></dt>
<dd><p>Logistic Regression (aka logit, MaxEnt) classifier.</p>
<p>In the multiclass case, the training algorithm uses the one-vs-rest (OvR)
scheme if the ‘multi_class’ option is set to ‘ovr’, and uses the cross-
entropy loss if the ‘multi_class’ option is set to ‘multinomial’.
(Currently the ‘multinomial’ option is supported only by the ‘lbfgs’,
‘sag’ and ‘newton-cg’ solvers.)</p>
<p>This class implements regularized logistic regression using the
‘liblinear’ library, ‘newton-cg’, ‘sag’ and ‘lbfgs’ solvers. It can handle
both dense and sparse input. Use C-ordered arrays or CSR matrices
containing 64-bit floats for optimal performance; any other input format
will be converted (and copied).</p>
<p>The ‘newton-cg’, ‘sag’, and ‘lbfgs’ solvers support only L2 regularization
with primal formulation. The ‘liblinear’ solver supports both L1 and L2
regularization, with a dual formulation only for the L2 penalty.</p>
<p>Read more in the <span class="xref std std-ref">User Guide</span>.</p>
<p>For SnapML solver this supports both local and distributed(MPI) method of execution.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>penalty</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.7)"><em>str</em></a><em>, </em><em>'l1'</em><em> or </em><em>'l2'</em><em>, </em><em>default: 'l2'</em>) – <p>Used to specify the norm used in the penalization. The ‘newton-cg’,
‘sag’ and ‘lbfgs’ solvers support only l2 penalties.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.19: </span>l1 penalty with SAGA solver (allowing ‘multinomial’ + L1)</p>
</div>
</li>
<li><strong>dual</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default: False</em>) – Dual or primal formulation. Dual formulation is only implemented for
l2 penalty with liblinear solver. Prefer dual=False when
n_samples > n_features.</li>
<li><strong>tol</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default: 1e-4</em>) – Tolerance for stopping criteria.</li>
<li><strong>C</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default: 1.0</em>) – Inverse of regularization strength; must be a positive float.
Like in support vector machines, smaller values specify stronger
regularization.</li>
<li><strong>fit_intercept</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default: True</em>) – Specifies if a constant (a.k.a. bias or intercept) should be
added to the decision function.</li>
<li><strong>intercept_scaling</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default 1.</em>) – <p>Useful only when the solver ‘liblinear’ is used
and self.fit_intercept is set to True. In this case, x becomes
[x, self.intercept_scaling],
i.e. a “synthetic” feature with constant value equal to
intercept_scaling is appended to the instance vector.
The intercept becomes <code class="docutils literal notranslate"><span class="pre">intercept_scaling</span> <span class="pre">*</span> <span class="pre">synthetic_feature_weight</span></code>.</p>
<p>Note! the synthetic feature weight is subject to l1/l2 regularization
as all other features.
To lessen the effect of regularization on synthetic feature weight
(and therefore on the intercept) intercept_scaling has to be increased.</p>
</li>
<li><strong>class_weight</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.7)"><em>dict</em></a><em> or </em><em>'balanced'</em><em>, </em><em>default: None</em>) – <p>Weights associated with classes in the form <code class="docutils literal notranslate"><span class="pre">{class_label:</span> <span class="pre">weight}</span></code>.
If not given, all classes are supposed to have weight one.</p>
<p>The “balanced” mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as <code class="docutils literal notranslate"><span class="pre">n_samples</span> <span class="pre">/</span> <span class="pre">(n_classes</span> <span class="pre">*</span> <span class="pre">np.bincount(y))</span></code>.</p>
<p>Note that these weights will be multiplied with sample_weight (passed
through the fit method) if sample_weight is specified.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.17: </span><em>class_weight=’balanced’</em></p>
</div>
</li>
<li><strong>random_state</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>RandomState instance</em><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em>, </em><em>optional</em><em>, </em><em>default: None</em>) – The seed of the pseudo random number generator to use when shuffling
the data. If int, random_state is the seed used by the random number
generator; If RandomState instance, random_state is the random number
generator; If None, the random number generator is the RandomState
instance used by <cite>np.random</cite>. Used when <code class="docutils literal notranslate"><span class="pre">solver</span></code> == ‘sag’ or
‘liblinear’.</li>
<li><strong>solver</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.7)"><em>str</em></a><em>, </em><em>{'newton-cg'</em><em>, </em><em>'lbfgs'</em><em>, </em><em>'liblinear'</em><em>, </em><em>'sag'</em><em>, </em><em>'saga'</em><em>, </em><em>'snapml'}</em><em>, </em><em>default: 'snapml'</em><em>, </em><em>if 'snap_ml' library is in PYTHONPATH</em><em>, </em><em>else</em><em>,</em>) – <p>default: ‘liblinear’.</p>
<p>Algorithm to use in the optimization problem.</p>
<ul>
<li>For small datasets, ‘liblinear’ is a good choice, whereas ‘sag’ and
‘saga’ are faster for large ones.</li>
<li>For multiclass problems, only ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’
handle multinomial loss; ‘liblinear’ is limited to one-versus-rest
schemes.</li>
<li>’newton-cg’, ‘lbfgs’ and ‘sag’ only handle L2 penalty, whereas
‘liblinear’ and ‘saga’ handle L1 penalty.</li>
</ul>
<p>Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on
features with approximately the same scale. You can
preprocess the data with a scaler from pai4sk.preprocessing.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.17: </span>Stochastic Average Gradient descent solver.</p>
</div>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.19: </span>SAGA solver.</p>
</div>
<div class="versionchanged">
<p><span class="versionmodified">Changed in version 0.20: </span>Default will change from ‘liblinear’ to ‘lbfgs’ in 0.22.</p>
</div>
</li>
<li><strong>max_iter</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>default: 100</em>) – Useful only for the newton-cg, sag and lbfgs solvers.
Maximum number of iterations taken for the solvers to converge.</li>
<li><strong>multi_class</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.7)"><em>str</em></a><em>, </em><em>{'ovr'</em><em>, </em><em>'multinomial'</em><em>, </em><em>'auto'}</em><em>, </em><em>default: 'ovr'</em>) – <p>If the option chosen is ‘ovr’, then a binary problem is fit for each
label. For ‘multinomial’ the loss minimised is the multinomial loss fit
across the entire probability distribution, <em>even when the data is
binary</em>. ‘multinomial’ is unavailable when solver=’liblinear’.
‘auto’ selects ‘ovr’ if the data is binary, or if solver=’liblinear’,
and otherwise selects ‘multinomial’.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.18: </span>Stochastic Average Gradient descent solver for ‘multinomial’ case.</p>
</div>
<div class="versionchanged">
<p><span class="versionmodified">Changed in version 0.20: </span>Default will change from ‘ovr’ to ‘auto’ in 0.22.</p>
</div>
</li>
<li><strong>verbose</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>default: 0</em>) – For the liblinear and lbfgs solvers set verbose to any positive
number for verbosity.</li>
<li><strong>warm_start</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default: False</em>) – <p>When set to True, reuse the solution of the previous call to fit as
initialization, otherwise, just erase the previous solution.
Useless for liblinear solver. See <span class="xref std std-term">the Glossary</span>.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.17: </span><em>warm_start</em> to support <em>lbfgs</em>, <em>newton-cg</em>, <em>sag</em>, <em>saga</em> solvers.</p>
</div>
</li>
<li><strong>n_jobs</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em>, </em><em>optional</em><em> (</em><em>default=None</em><em>)</em>) – Number of CPU cores used when parallelizing over classes if
multi_class=’ovr’”. This parameter is ignored when the <code class="docutils literal notranslate"><span class="pre">solver</span></code> is
set to ‘liblinear’ regardless of whether ‘multi_class’ is specified or
not. <code class="docutils literal notranslate"><span class="pre">None</span></code> means 1 unless in a <code class="xref py py-obj docutils literal notranslate"><span class="pre">joblib.parallel_backend</span></code>
context. <code class="docutils literal notranslate"><span class="pre">-1</span></code> means using all processors.
See <span class="xref std std-term">Glossary</span> for more details.</li>
<li><strong>use_gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default : True</em>) – Flag for indicating the hardware platform used for training. If True, the training
is performed using the GPU. If False, the training is performed using the CPU.
The value of this parameter is subjected to changed based on the training data unless set explicitly.
Applicable only for snapml solver</li>
<li><strong>device_ids</strong> (<em>array-like of int</em><em>, </em><em>default :</em><em> [</em><em>]</em>) – If use_gpu is True, it indicates the IDs of the GPUs used for training.
For single-GPU training, set device_ids to the GPU ID to be used for training, e.g., [0].
For multi-GPU training, set device_ids to a list of GPU IDs to be used for training, e.g., [0, 1].
Applicable only for snapml solver</li>
<li><strong>num_threads</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>default : 1</em>) – The number of threads used for running the training. The value of this parameter
should be a multiple of 32 if the training is performed on GPU (use_gpu=True)
(default value for GPU is 256). Applicable only for snapml solver</li>
<li><strong>return_training_history</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.7)"><em>str</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em>, </em><em>default : None</em>) – How much information about the training should be collected and returned by the fit function. By
default no information is returned (None), but this parameter can be set to “summary”, to obtain
summary statistics at the end of training, or “full” to obtain a complete set of statistics
for the entire training procedure. Note, enabling either option will result in slower training.
Applicable only for snapml solver</li>
<li><strong>privacy</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default : False</em>) – Train the model using a differentially private algorithm.</li>
<li><strong>eta</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default : 0.3</em>) – Learning rate for the differentially private training algorithm.</li>
<li><strong>batch_size</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>default : 100</em>) – Mini-batch size for the differentially private training algorithm.</li>
<li><strong>privacy_epsilon</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default : 10.0</em>) – Target privacy gaurantee. Learned model will be (privacy_epsilon, 0.01)-private.</li>
<li><strong>grad_clip</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>default: 1.0</em>) – Gradient clipping parameter for the differentially private training algorithm</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Variables:</th><td class="field-body"><ul class="first last simple">
<li><strong>coef</strong> (<em>array</em><em>, </em><em>shape</em><em> (</em><em>1</em><em>, </em><em>n_features</em><em>) or </em><em>(</em><em>n_classes</em><em>, </em><em>n_features</em><em>)</em>) – <p>Coefficient of the features in the decision function.</p>
<p><cite>coef_</cite> is of shape (1, n_features) when the given problem is binary.
In particular, when <cite>multi_class=’multinomial’</cite>, <cite>coef_</cite> corresponds
to outcome 1 (True) and <cite>-coef_</cite> corresponds to outcome 0 (False).</p>
</li>
<li><strong>intercept</strong> (<em>array</em><em>, </em><em>shape</em><em> (</em><em>1</em><em>,</em><em>) or </em><em>(</em><em>n_classes</em><em>,</em><em>)</em>) – <p>Intercept (a.k.a. bias) added to the decision function.</p>
<p>If <cite>fit_intercept</cite> is set to False, the intercept is set to zero.
<cite>intercept_</cite> is of shape (1,) when the given problem is binary.
In particular, when <cite>multi_class=’multinomial’</cite>, <cite>intercept_</cite>
corresponds to outcome 1 (True) and <cite>-intercept_</cite> corresponds to
outcome 0 (False).</p>
</li>
<li><strong>n_iter</strong> (<em>array</em><em>, </em><em>shape</em><em> (</em><em>n_classes</em><em>,</em><em>) or </em><em>(</em><em>1</em><em>, </em><em>)</em>) – Actual number of iterations for all classes. If binary or multinomial,
it returns only 1 element. For liblinear solver, only the maximum
number of iteration across all classes is given.</li>
<li><strong>training_history</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.7)"><em>dict</em></a>) – It returns a dictionary with the following keys : ‘epochs’, ‘t_elap_sec’, ‘train_obj’.
If ‘return_training_history’ is set to “summary”, ‘epochs’ contains the total number of
epochs performed, ‘t_elap_sec’ contains the total time for completing all of those epochs.
If ‘return_training_history’ is set to “full”, ‘epochs’ indicates the number of epochs
that have elapsed so far, and ‘t_elap_sec’ contains the time to do those epochs.
‘train_obj’ is the training loss.
Applicable only for snapml solver.</li>
<li><strong>support</strong> (<em>array-like</em>) – Indices of the features that contribute to the decision. (only available for L1)</li>
<li><strong>model_sparsity</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a>) – <p>Fraction of non-zeros in the model parameters. (only available for L1)</p>
<div class="versionchanged">
<p><span class="versionmodified">Changed in version 0.20: </span>In SciPy <= 1.0.0 the number of lbfgs iterations may exceed
<code class="docutils literal notranslate"><span class="pre">max_iter</span></code>. <code class="docutils literal notranslate"><span class="pre">n_iter_</span></code> will now report at most <code class="docutils literal notranslate"><span class="pre">max_iter</span></code>.</p>
</div>
</li>
</ul>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pai4sk.datasets</span> <span class="k">import</span> <span class="n">load_iris</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pai4sk.linear_model</span> <span class="k">import</span> <span class="n">LogisticRegression</span>
<span class="gp">>>> </span><span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">load_iris</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">clf</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">solver</span><span class="o">=</span><span class="s1">'lbfgs'</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">multi_class</span><span class="o">=</span><span class="s1">'multinomial'</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="mi">2</span><span class="p">,</span> <span class="p">:])</span>
<span class="go">array([0, 0])</span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="mi">2</span><span class="p">,</span> <span class="p">:])</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="go">array([[9.8...e-01, 1.8...e-02, 1.4...e-08],</span>
<span class="go"> [9.7...e-01, 2.8...e-02, ...e-08]])</span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="go">0.97...</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><code class="xref py py-class docutils literal notranslate"><span class="pre">SGDClassifier</span></code></dt>
<dd>incrementally trained logistic regression (when given the parameter <code class="docutils literal notranslate"><span class="pre">loss="log"</span></code>).</dd>
<dt><code class="xref py py-class docutils literal notranslate"><span class="pre">LogisticRegressionCV</span></code></dt>
<dd>Logistic regression with built-in cross validation</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The underlying C implementation uses a random number generator to
select features when fitting the model. It is thus not uncommon,
to have slightly different results for the same input data. If
that happens, try with a smaller tol parameter.</p>
<p>Predict output may not match that of standalone liblinear in certain
cases. See <span class="xref std std-ref">differences from liblinear</span>
in the narrative documentation.</p>
<p class="rubric">References</p>
<dl class="docutils">
<dt>LIBLINEAR – A Library for Large Linear Classification</dt>
<dd><a class="reference external" href="http://www.csie.ntu.edu.tw/~cjlin/liblinear/">http://www.csie.ntu.edu.tw/~cjlin/liblinear/</a></dd>
<dt>SAG – Mark Schmidt, Nicolas Le Roux, and Francis Bach</dt>
<dd>Minimizing Finite Sums with the Stochastic Average Gradient
<a class="reference external" href="https://hal.inria.fr/hal-00860051/document">https://hal.inria.fr/hal-00860051/document</a></dd>
<dt>SAGA – Defazio, A., Bach F. & Lacoste-Julien S. (2014).</dt>
<dd>SAGA: A Fast Incremental Gradient Method With Support
for Non-Strongly Convex Composite Objectives
<a class="reference external" href="https://arxiv.org/abs/1407.0202">https://arxiv.org/abs/1407.0202</a></dd>
<dt>Hsiang-Fu Yu, Fang-Lan Huang, Chih-Jen Lin (2011). Dual coordinate descent</dt>
<dd>methods for logistic regression and maximum entropy models.
Machine Learning 85(1-2):41-75.
<a class="reference external" href="http://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf">http://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf</a></dd>
</dl>
<dl class="method">
<dt id="pai4sk.linear_model.LogisticRegression.fit">
<code class="descname">fit</code><span class="sig-paren">(</span><em>X</em>, <em>y</em>, <em>sample_weight=None</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.LogisticRegression.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit the model according to the given training data.
:param X: Training vector, where n_samples is the number of samples and</p>
<blockquote>
<div>n_features is the number of features.
For SnapML solver it also supports input of types SnapML data partition and DeviceNDArray.</div></blockquote>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>y</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_samples</em><em>,</em><em>) or </em><em>(</em><em>n_samples</em><em>, </em><em>n_targets</em><em>)</em>) – Target vector relative to X.</li>
<li><strong>sample_weight</strong> (<em>array-like</em><em>, </em><em>shape</em><em> (</em><em>n_samples</em><em>,</em><em>) </em><em>optional</em>) – <p>Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
.. versionadded:: 0.17</p>
<blockquote>
<div><em>sample_weight</em> support to LogisticRegression.</div></blockquote>
</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>self</strong></p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.7)">object</a></p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="pai4sk.linear_model.LogisticRegression.predict">
<code class="descname">predict</code><span class="sig-paren">(</span><em>X</em>, <em>num_threads=0</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.LogisticRegression.predict" title="Permalink to this definition">¶</a></dt>
<dd><p>Class predictions
The returned class estimates.
:param X: Dataset used for predicting class estimates.</p>
<blockquote>
<div>For SnapML solver it also supports input of type SnapML data partition.</div></blockquote>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>num_threads</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>default : 0</em>) – Number of threads used to run inference.
By default inference runs with maximum number of available threads.</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><strong>proba</strong> – Returns the predicted class of the sample.</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body">array-like, shape = (n_samples,)</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="pai4sk.linear_model.LogisticRegression.predict_log_proba">
<code class="descname">predict_log_proba</code><span class="sig-paren">(</span><em>X</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.LogisticRegression.predict_log_proba" title="Permalink to this definition">¶</a></dt>
<dd><p>Log of probability estimates.
The returned estimates for all classes are ordered by the
label of classes.
:param X: For SnapML solver it also supports input of type SnapML data partition.
:type X: array-like, shape = [n_samples, n_features]</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><strong>T</strong> – Returns the log-probability of the sample for each class in the
model, where classes are ordered as they are in <code class="docutils literal notranslate"><span class="pre">self.classes_</span></code>.</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body">array-like, shape = [n_samples, n_classes]</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="pai4sk.linear_model.LogisticRegression.predict_proba">
<code class="descname">predict_proba</code><span class="sig-paren">(</span><em>X</em>, <em>num_threads=0</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.linear_model.LogisticRegression.predict_proba" title="Permalink to this definition">¶</a></dt>
<dd><p>Probability estimates.
The returned estimates for all classes are ordered by the
label of classes.
For a multi_class problem, if multi_class is set to be “multinomial”
the softmax function is used to find the predicted probability of
each class.
Else use a one-vs-rest approach, i.e calculate the probability
of each class assuming it to be positive using the logistic function.
and normalize these values across all the classes.
:param X: For SnapML solver it also supports input of type SnapML data partition.
:type X: array-like, shape = [n_samples, n_features]
:param num_threads: Number of threads used to run inference.</p>
<blockquote>
<div>By default inference runs with maximum number of available threads.</div></blockquote>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><strong>T</strong> – Returns the probability of the sample for each class in the model,
where classes are ordered as they are in <code class="docutils literal notranslate"><span class="pre">self.classes_</span></code>.</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body">array-like, shape = [n_samples, n_classes]</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="pai4sk.svm.LinearSVC">
<em class="property">class </em><code class="descclassname">pai4sk.svm.</code><code class="descname">LinearSVC</code><span class="sig-paren">(</span><em>penalty='l2'</em>, <em>loss='squared_hinge'</em>, <em>dual=True</em>, <em>tol=0.0001</em>, <em>C=1.0</em>, <em>multi_class='ovr'</em>, <em>fit_intercept=True</em>, <em>intercept_scaling=1</em>, <em>class_weight=None</em>, <em>verbose=0</em>, <em>random_state=None</em>, <em>max_iter=1000</em>, <em>use_gpu=True</em>, <em>device_ids=[]</em>, <em>num_threads=1</em>, <em>return_training_history=None</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.svm.LinearSVC" title="Permalink to this definition">¶</a></dt>
<dd><p>Linear Support Vector Classification.</p>
<p>Similar to SVC with parameter kernel=’linear’, but implemented in terms of
liblinear rather than libsvm, so it has more flexibility in the choice of
penalties and loss functions and should scale better to large numbers of
samples.</p>
<p>This class supports both dense and sparse input and the multiclass support
is handled according to a one-vs-the-rest scheme.</p>
<p>Read more in the <span class="xref std std-ref">User Guide</span>.</p>
<p>For SnapML solver this supports both local and distributed(MPI) method of execution.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>penalty</strong> (<em>string</em><em>, </em><em>'l1'</em><em> or </em><em>'l2'</em><em> (</em><em>default='l2'</em><em>)</em>) – Specifies the norm used in the penalization. The ‘l2’
penalty is the standard used in SVC. The ‘l1’ leads to <code class="docutils literal notranslate"><span class="pre">coef_</span></code>
vectors that are sparse.</li>
<li><strong>loss</strong> (<em>string</em><em>, </em><em>'hinge'</em><em> or </em><em>'squared_hinge'</em><em> (</em><em>default='squared_hinge'</em><em>)</em>) – Specifies the loss function. ‘hinge’ is the standard SVM loss
(used e.g. by the SVC class) while ‘squared_hinge’ is the
square of the hinge loss.</li>
<li><strong>dual</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>(</em><em>default=True</em><em>)</em>) – Select the algorithm to either solve the dual or primal
optimization problem. Prefer dual=False when n_samples > n_features.</li>
<li><strong>tol</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=1e-4</em><em>)</em>) – Tolerance for stopping criteria.</li>
<li><strong>C</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=1.0</em><em>)</em>) – Penalty parameter C of the error term.</li>
<li><strong>multi_class</strong> (<em>string</em><em>, </em><em>'ovr'</em><em> or </em><em>'crammer_singer'</em><em> (</em><em>default='ovr'</em><em>)</em>) – Determines the multi-class strategy if <cite>y</cite> contains more than
two classes.
<code class="docutils literal notranslate"><span class="pre">"ovr"</span></code> trains n_classes one-vs-rest classifiers, while
<code class="docutils literal notranslate"><span class="pre">"crammer_singer"</span></code> optimizes a joint objective over all classes.
While <cite>crammer_singer</cite> is interesting from a theoretical perspective
as it is consistent, it is seldom used in practice as it rarely leads
to better accuracy and is more expensive to compute.
If <code class="docutils literal notranslate"><span class="pre">"crammer_singer"</span></code> is chosen, the options loss, penalty and dual
will be ignored.</li>
<li><strong>fit_intercept</strong> (<em>boolean</em><em>, </em><em>optional</em><em> (</em><em>default=True</em><em>)</em>) – Whether to calculate the intercept for this model. If set
to false, no intercept will be used in calculations
(i.e. data is expected to be already centered).</li>
<li><strong>intercept_scaling</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><em>optional</em><em> (</em><em>default=1</em><em>)</em>) – When self.fit_intercept is True, instance vector x becomes
<code class="docutils literal notranslate"><span class="pre">[x,</span> <span class="pre">self.intercept_scaling]</span></code>,
i.e. a “synthetic” feature with constant value equals to
intercept_scaling is appended to the instance vector.
The intercept becomes intercept_scaling * synthetic feature weight
Note! the synthetic feature weight is subject to l1/l2 regularization
as all other features.
To lessen the effect of regularization on synthetic feature weight
(and therefore on the intercept) intercept_scaling has to be increased.</li>
<li><strong>class_weight</strong> (<em>{dict</em><em>, </em><em>'balanced'}</em><em>, </em><em>optional</em>) – Set the parameter C of class i to <code class="docutils literal notranslate"><span class="pre">class_weight[i]*C</span></code> for
SVC. If not given, all classes are supposed to have
weight one.
The “balanced” mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as <code class="docutils literal notranslate"><span class="pre">n_samples</span> <span class="pre">/</span> <span class="pre">(n_classes</span> <span class="pre">*</span> <span class="pre">np.bincount(y))</span></code></li>
<li><strong>verbose</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>(</em><em>default=0</em><em>)</em>) – Enable verbose output. Note that this setting takes advantage of a
per-process runtime setting in liblinear that, if enabled, may not work
properly in a multithreaded context.</li>
<li><strong>random_state</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>RandomState instance</em><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em>, </em><em>optional</em><em> (</em><em>default=None</em><em>)</em>) – The seed of the pseudo random number generator to use when shuffling
the data for the dual coordinate descent (if <code class="docutils literal notranslate"><span class="pre">dual=True</span></code>). When
<code class="docutils literal notranslate"><span class="pre">dual=False</span></code> the underlying implementation of <a class="reference internal" href="svcdoc.html#pai4sk.svm.LinearSVC" title="pai4sk.svm.LinearSVC"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinearSVC</span></code></a>
is not random and <code class="docutils literal notranslate"><span class="pre">random_state</span></code> has no effect on the results. If
int, random_state is the seed used by the random number generator; If
RandomState instance, random_state is the random number generator; If
None, the random number generator is the RandomState instance used by
<cite>np.random</cite>.</li>
<li><strong>max_iter</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>(</em><em>default=1000</em><em>)</em>) – The maximum number of iterations to be run.</li>
<li><strong>use_gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>default : True</em>) – Flag for indicating the hardware platform used for training. If True, the training
is performed using the GPU. If False, the training is performed using the CPU.
The value of this parameter is subjected to changed based on the training data unless set explicitly.
Applicable only for snapml solver</li>
<li><strong>device_ids</strong> (<em>array-like of int</em><em>, </em><em>default :</em><em> [</em><em>]</em>) – If use_gpu is True, it indicates the IDs of the GPUs used for training.
For single GPU training, set device_ids to the GPU ID to be used for training,
e.g., [0]. For multi-GPU training, set device_ids to a list of GPU IDs to be used