Multivariate distributions

src/probabilit/inspection.py

@@ -38,3 +38,11 @@ def plot(*variables, corr=None, **kwargs):
 
     plot(a, b)
     grid = plot(a)
+
+    from probabilit.modeling import MultivariateDistribution
+
+    cov = np.array([[1, 0.9], [0.9, 1]])
+    n1, n2 = MultivariateDistribution("multivariate_normal", mean=[1, 2], cov=cov)
+    from probabilit.inspection import plot
+
+    plot(n1, n2)

src/probabilit/modeling.py

@@ -114,8 +114,40 @@
        200.        , 200.        , 200.        , 273.23522915,
        235.11150117])
 
+Multivariate distributions
+--------------------------
+Support for multivariate distributions (MVD) is implemented, but with constraints:
+
+  1. MVD must be a leaf node (its arguments cannot be other distributions)
+  2. its return values *must* be unpacked as marginals (slices)
+  3. only pseudo-random sampling is possible (LHS, Sobol, etc is ignored)
+
+For instance, to create a Dirichlet distribution, we must unpack it as follows:
+
+>>> d1, d2 = MultivariateDistribution("dirichlet", alpha=[1, 2])
+>>> d1
+MarginalDistribution(Distribution("dirichlet", alpha=[1, 2]), d=0)
+
+Since the Direchlet distribution is defined on an (n-1) dimensional simplex,
+the sum of the marginals is always 1. We can check this by computing:
+
+>>> (d1 + d2).sample(5, random_state=0)
+array([1., 1., 1., 1., 1.])
+>>> d2.samples_.round(3)
+array([0.559, 0.324, 0.284, 0.524, 0.599])
+
+Here is an example with a multivariate normal distribution:
+
+>>> cov = np.array([[1, 0.5], [0.5, 1]])
+>>> n1, n2 = MultivariateDistribution("multivariate_normal", mean=[1, 2], cov=cov)
+>>> n1.sample(5, random_state=0)
+array([0.72058767, 3.13703525, 2.38930155, 1.50866787, 0.77018653])
+>>> (n1 + n2).sample(5, random_state=0)
+array([2.52848604, 5.31650094, 5.20076878, 4.06217341, 1.40748585])
+
 Samplers
 --------
+
 The default sampling uses pseudo-random numbers. To use e.g. latin hybercube
 sampling, pass the `method` argument into `.sample()`.
 
@@ -647,7 +679,13 @@ def unpack(arg):
 
         # Sample from the distribution with inverse CDF
         distribution = getattr(stats, self.distr)
-        return distribution(*args, **kwargs).ppf(q)
+        try:
+            return distribution(*args, **kwargs).ppf(q)
+        except AttributeError:
+            # Multivariate distributions do not have .ppf()
+            # isinstance(distribution, (multi_rv_generic, multi_rv_frozen))
+            seed = int(q[0] * 2**20)  # Seed based on q
+            return distribution(*args, **kwargs).rvs(size=len(q), random_state=seed)
 
     def get_parents(self):
         # A distribution only has parents if it has parameters that are Nodes
@@ -972,6 +1010,58 @@ def transformed_function(*args, **kwargs):
     return transformed_function
 
 
+class MarginalDistribution(Transform):
+    """A maginal distribution is a 'slice' of a multivariate distribution.
+
+    Examples
+    --------
+    >>> distr = Distribution("multinomial", n=10, p=[0.1, 0.2, 0.7])
+    >>> marginal_distr = MarginalDistribution(distr, d=0)
+    >>> marginal_distr
+    MarginalDistribution(Distribution("multinomial", n=10, p=[0.1, 0.2, 0.7]), d=0)
+    >>> marginal_distr.sample(5, random_state=0).astype(int)
+    array([2, 1, 2, 1, 1])
+    """
+
+    is_leaf = False
+
+    def __init__(self, distr, d):
+        self.distr = distr
+        self.d = d
+        super().__init__()
+
+    def _sample(self):
+        # Simply slice the parent
+        return np.atleast_2d(self.distr.samples_)[:, self.d]
+
+    def get_parents(self):
+        yield self.distr
+
+    def __repr__(self):
+        return f"{type(self).__name__}({self.distr}, d={self.d})"
+
+
+def MultivariateDistribution(distr, *args, **kwargs):
+    """Factory function that yields marginal distributions.
+
+    Examples
+    --------
+    >>> p = [0.2, 0.3, 0.5]  # Probability of each category
+    >>> m1, m2, m3 = MultivariateDistribution("multinomial", n=10, p=p)
+    >>> m1.sample(5, random_state=0).astype(int)
+    array([3, 2, 4, 2, 1])
+
+    Each category should sum to n=10:
+    >>> (m1 + m2 + m3).sample(5, random_state=0).astype(int)
+    array([10, 10, 10, 10, 10])
+    """
+    distr = Distribution(distr, *args, **kwargs)
+
+    # Get dimensionality by sampling once
+    d = len(distr._sample(q=[0.5]).squeeze())
+    yield from (MarginalDistribution(distr, d=i) for i in range(d))
+
+
 # ========================================================
 if __name__ == "__main__":
     import pytest
@@ -999,6 +1089,8 @@ def transformed_function(*args, **kwargs):
     plt.scatter(a.samples_, b.samples_, s=2)
     plt.show()
 
+    d1, d2, d3 = MultivariateDistribution("dirichlet", alpha=[1, 2, 3])
+
     # =========================
 
     cost = EmpiricalDistribution(data=[1, 2, 3, 3, 3, 3])