_vae.py

from __future__ import annotations

import logging
import warnings
from typing import TYPE_CHECKING

import numpy as np
import torch
from torch.nn.functional import one_hot

from scvi import REGISTRY_KEYS, settings
from scvi.data._constants import ADATA_MINIFY_TYPE
from scvi.module._constants import MODULE_KEYS
from scvi.module.base import (
    BaseMinifiedModeModuleClass,
    EmbeddingModuleMixin,
    LossOutput,
    auto_move_data,
)
from scvi.utils import unsupported_if_adata_minified

if TYPE_CHECKING:
    from collections.abc import Callable
    from typing import Literal

    from torch.distributions import Distribution

logger = logging.getLogger(__name__)


class VAE(EmbeddingModuleMixin, BaseMinifiedModeModuleClass):
    """Variational auto-encoder :cite:p:`Lopez18`.

    Parameters
    ----------
    n_input
        Number of input features.
    n_batch
        Number of batches. If ``0``, no batch correction is performed.
    n_labels
        Number of labels.
    n_hidden
        Number of nodes per hidden layer. Passed into :class:`~scvi.nn.Encoder` and
        :class:`~scvi.nn.DecoderSCVI`.
    n_latent
        Dimensionality of the latent space.
    n_layers
        Number of hidden layers. Passed into :class:`~scvi.nn.Encoder` and
        :class:`~scvi.nn.DecoderSCVI`.
    n_continuous_cov
        Number of continuous covariates.
    n_cats_per_cov
        A list of integers containing the number of categories for each categorical covariate.
    dropout_rate
        Dropout rate. Passed into :class:`~scvi.nn.Encoder` but not :class:`~scvi.nn.DecoderSCVI`.
    dispersion
        Flexibility of the dispersion parameter when ``gene_likelihood`` is either ``"nb"`` or
        ``"zinb"``. One of the following:

        * ``"gene"``: parameter is constant per gene across cells.
        * ``"gene-batch"``: parameter is constant per gene per batch.
        * ``"gene-label"``: parameter is constant per gene per label.
        * ``"gene-cell"``: parameter is constant per gene per cell.
    log_variational
        If ``True``, use :func:`~torch.log1p` on input data before encoding for numerical stability
        (not normalization).
    gene_likelihood
        Distribution to use for reconstruction in the generative process. One of the following:

        * ``"nb"``: :class:`~scvi.distributions.NegativeBinomial`.
        * ``"zinb"``: :class:`~scvi.distributions.ZeroInflatedNegativeBinomial`.
        * ``"poisson"``: :class:`~scvi.distributions.Poisson`.
        * ``"normal"``: :class:`~torch.distributions.Normal`.
    latent_distribution
        Distribution to use for the latent space. One of the following:

        * ``"normal"``: isotropic normal.
        * ``"ln"``: logistic normal with normal params N(0, 1).
    encode_covariates
        If ``True``, covariates are concatenated to gene expression prior to passing through
        the encoder(s). Else, only the gene expression is used.
    deeply_inject_covariates
        If ``True`` and ``n_layers > 1``, covariates are concatenated to the outputs of hidden
        layers in the encoder(s) (if ``encoder_covariates`` is ``True``) and the decoder prior to
        passing through the next layer.
    batch_representation
        ``EXPERIMENTAL`` Method for encoding batch information. One of the following:

        * ``"one-hot"``: represent batches with one-hot encodings.
        * ``"embedding"``: represent batches with continuously-valued embeddings using
          :class:`~scvi.nn.Embedding`.

        Note that batch representations are only passed into the encoder(s) if
        ``encode_covariates`` is ``True``.
    use_batch_norm
        Specifies where to use :class:`~torch.nn.BatchNorm1d` in the model. One of the following:

        * ``"none"``: don't use batch norm in either encoder(s) or decoder.
        * ``"encoder"``: use batch norm only in the encoder(s).
        * ``"decoder"``: use batch norm only in the decoder.
        * ``"both"``: use batch norm in both encoder(s) and decoder.

        Note: if ``use_layer_norm`` is also specified, both will be applied (first
        :class:`~torch.nn.BatchNorm1d`, then :class:`~torch.nn.LayerNorm`).
    use_layer_norm
        Specifies where to use :class:`~torch.nn.LayerNorm` in the model. One of the following:

        * ``"none"``: don't use layer norm in either encoder(s) or decoder.
        * ``"encoder"``: use layer norm only in the encoder(s).
        * ``"decoder"``: use layer norm only in the decoder.
        * ``"both"``: use layer norm in both encoder(s) and decoder.

        Note: if ``use_batch_norm`` is also specified, both will be applied (first
        :class:`~torch.nn.BatchNorm1d`, then :class:`~torch.nn.LayerNorm`).
    use_size_factor_key
        If ``True``, use the :attr:`~anndata.AnnData.obs` column as defined by the
        ``size_factor_key`` parameter in the model's ``setup_anndata`` method as the scaling
        factor in the mean of the conditional distribution. Takes priority over
        ``use_observed_lib_size``.
    use_observed_lib_size
        If ``True``, use the observed library size for RNA as the scaling factor in the mean of the
        conditional distribution.
    extra_payload_autotune
        If ``True``, will return extra matrices in the loss output to be used during autotune
    library_log_means
        :class:`~numpy.ndarray` of shape ``(1, n_batch)`` of means of the log library sizes that
        parameterize the prior on library size if ``use_size_factor_key`` is ``False`` and
        ``use_observed_lib_size`` is ``False``.
    library_log_vars
        :class:`~numpy.ndarray` of shape ``(1, n_batch)`` of variances of the log library sizes
        that parameterize the prior on library size if ``use_size_factor_key`` is ``False`` and
        ``use_observed_lib_size`` is ``False``.
    var_activation
        Callable used to ensure positivity of the variance of the variational distribution. Passed
        into :class:`~scvi.nn.Encoder`. Defaults to :func:`~torch.exp`.
    extra_encoder_kwargs
        Additional keyword arguments passed into :class:`~scvi.nn.Encoder`.
    extra_decoder_kwargs
        Additional keyword arguments passed into :class:`~scvi.nn.DecoderSCVI`.
    batch_embedding_kwargs
        Keyword arguments passed into :class:`~scvi.nn.Embedding` if ``batch_representation`` is
        set to ``"embedding"``.

    """

    def __init__(
        self,
        n_input: int,
        n_batch: int = 0,
        n_labels: int = 0,
        n_hidden: int = 128,
        n_latent: int = 10,
        n_layers: int = 1,
        n_continuous_cov: int = 0,
        n_cats_per_cov: list[int] | None = None,
        dropout_rate: float = 0.1,
        dispersion: Literal["gene", "gene-batch", "gene-label", "gene-cell"] = "gene",
        log_variational: bool = True,
        gene_likelihood: Literal["zinb", "nb", "poisson", "normal"] = "zinb",
        latent_distribution: Literal["normal", "ln"] = "normal",
        encode_covariates: bool = False,
        deeply_inject_covariates: bool = True,
        batch_representation: Literal["one-hot", "embedding"] = "one-hot",
        use_batch_norm: Literal["encoder", "decoder", "none", "both"] = "both",
        use_layer_norm: Literal["encoder", "decoder", "none", "both"] = "none",
        use_size_factor_key: bool = False,
        use_observed_lib_size: bool = True,
        extra_payload_autotune: bool = False,
        library_log_means: np.ndarray | None = None,
        library_log_vars: np.ndarray | None = None,
        var_activation: Callable[[torch.Tensor], torch.Tensor] = None,
        extra_encoder_kwargs: dict | None = None,
        extra_decoder_kwargs: dict | None = None,
        batch_embedding_kwargs: dict | None = None,
    ):
        from scvi.nn import DecoderSCVI, Encoder

        super().__init__()

        self.dispersion = dispersion
        self.n_latent = n_latent
        self.log_variational = log_variational
        self.gene_likelihood = gene_likelihood
        self.n_batch = n_batch
        self.n_input = n_input
        self.n_labels = n_labels
        self.n_hidden = n_hidden
        self.n_layers = n_layers
        self.latent_distribution = latent_distribution
        self.encode_covariates = encode_covariates
        self.use_size_factor_key = use_size_factor_key
        self.use_observed_lib_size = use_size_factor_key or use_observed_lib_size
        self.extra_payload_autotune = extra_payload_autotune

        if not self.use_observed_lib_size:
            if library_log_means is None or library_log_vars is None:
                raise ValueError(
                    "If not using observed_lib_size, "
                    "must provide library_log_means and library_log_vars."
                )

            self.register_buffer("library_log_means", torch.from_numpy(library_log_means).float())
            self.register_buffer("library_log_vars", torch.from_numpy(library_log_vars).float())

        if self.dispersion == "gene":
            self.px_r = torch.nn.Parameter(torch.randn(n_input))
        elif self.dispersion == "gene-batch":
            self.px_r = torch.nn.Parameter(torch.randn(n_input, n_batch))
        elif self.dispersion == "gene-label":
            self.px_r = torch.nn.Parameter(torch.randn(n_input, n_labels))
        elif self.dispersion == "gene-cell":
            pass
        else:
            raise ValueError(
                "`dispersion` must be one of 'gene', 'gene-batch', 'gene-label', 'gene-cell'."
            )

        self.batch_representation = batch_representation
        if self.batch_representation == "embedding":
            self.init_embedding(REGISTRY_KEYS.BATCH_KEY, n_batch, **(batch_embedding_kwargs or {}))
            batch_dim = self.get_embedding(REGISTRY_KEYS.BATCH_KEY).embedding_dim
        elif self.batch_representation != "one-hot":
            raise ValueError("`batch_representation` must be one of 'one-hot', 'embedding'.")

        use_batch_norm_encoder = use_batch_norm == "encoder" or use_batch_norm == "both"
        use_batch_norm_decoder = use_batch_norm == "decoder" or use_batch_norm == "both"
        use_layer_norm_encoder = use_layer_norm == "encoder" or use_layer_norm == "both"
        use_layer_norm_decoder = use_layer_norm == "decoder" or use_layer_norm == "both"

        n_input_encoder = n_input + n_continuous_cov * encode_covariates
        if self.batch_representation == "embedding":
            n_input_encoder += batch_dim * encode_covariates
            cat_list = list([] if n_cats_per_cov is None else n_cats_per_cov)
        else:
            cat_list = [n_batch] + list([] if n_cats_per_cov is None else n_cats_per_cov)

        encoder_cat_list = cat_list if encode_covariates else None
        _extra_encoder_kwargs = extra_encoder_kwargs or {}
        z_encoder_kwargs = {
            "n_cat_list": encoder_cat_list,
            "n_layers": n_layers,
            "n_hidden": n_hidden,
            "dropout_rate": dropout_rate,
            "distribution": latent_distribution,
            "inject_covariates": deeply_inject_covariates,
            "use_batch_norm": use_batch_norm_encoder,
            "use_layer_norm": use_layer_norm_encoder,
            "var_activation": var_activation,
            "return_dist": True,
        }
        z_encoder_kwargs.update(_extra_encoder_kwargs)
        self.z_encoder = Encoder(
            n_input_encoder,
            n_latent,
            **z_encoder_kwargs,
        )
        # l encoder goes from n_input-dimensional data to 1-d library size
        # n_layers is fixed to 1 for the library encoder
        l_encoder_extra_kwargs = {
            k: v for k, v in _extra_encoder_kwargs.items() if k != "n_layers"
        }
        l_encoder_kwargs = {
            "n_layers": 1,
            "n_cat_list": encoder_cat_list,
            "n_hidden": n_hidden,
            "dropout_rate": dropout_rate,
            "inject_covariates": deeply_inject_covariates,
            "use_batch_norm": use_batch_norm_encoder,
            "use_layer_norm": use_layer_norm_encoder,
            "var_activation": var_activation,
            "return_dist": True,
        }
        l_encoder_kwargs.update(l_encoder_extra_kwargs)
        self.l_encoder = Encoder(
            n_input_encoder,
            1,
            **l_encoder_kwargs,
        )
        n_input_decoder = n_latent + n_continuous_cov
        if self.batch_representation == "embedding":
            n_input_decoder += batch_dim

        _extra_decoder_kwargs = extra_decoder_kwargs or {}
        decoder_kwargs = {
            "n_cat_list": cat_list,
            "n_layers": n_layers,
            "n_hidden": n_hidden,
            "inject_covariates": deeply_inject_covariates,
            "use_batch_norm": use_batch_norm_decoder,
            "use_layer_norm": use_layer_norm_decoder,
            "scale_activation": "softplus" if use_size_factor_key else "softmax",
        }
        decoder_kwargs.update(_extra_decoder_kwargs)
        self.decoder = DecoderSCVI(
            n_input_decoder,
            n_input,
            **decoder_kwargs,
        )

    def _get_inference_input(
        self,
        tensors: dict[str, torch.Tensor | None],
        full_forward_pass: bool = False,
    ) -> dict[str, torch.Tensor | None]:
        """Get input tensors for the inference process."""
        if full_forward_pass or self.minified_data_type is None:
            loader = "full_data"
        elif self.minified_data_type in [
            ADATA_MINIFY_TYPE.LATENT_POSTERIOR,
            ADATA_MINIFY_TYPE.LATENT_POSTERIOR_WITH_COUNTS,
        ]:
            loader = "minified_data"
        else:
            raise NotImplementedError(f"Unknown minified-data type: {self.minified_data_type}")

        if loader == "full_data":
            return {
                MODULE_KEYS.X_KEY: tensors[REGISTRY_KEYS.X_KEY],
                MODULE_KEYS.BATCH_INDEX_KEY: tensors[REGISTRY_KEYS.BATCH_KEY],
                MODULE_KEYS.CONT_COVS_KEY: tensors.get(REGISTRY_KEYS.CONT_COVS_KEY, None),
                MODULE_KEYS.CAT_COVS_KEY: tensors.get(REGISTRY_KEYS.CAT_COVS_KEY, None),
            }
        else:
            return {
                MODULE_KEYS.QZM_KEY: tensors[REGISTRY_KEYS.LATENT_QZM_KEY],
                MODULE_KEYS.QZV_KEY: tensors[REGISTRY_KEYS.LATENT_QZV_KEY],
                REGISTRY_KEYS.OBSERVED_LIB_SIZE: tensors[REGISTRY_KEYS.OBSERVED_LIB_SIZE],
            }

    def _get_generative_input(
        self,
        tensors: dict[str, torch.Tensor],
        inference_outputs: dict[str, torch.Tensor | Distribution | None],
    ) -> dict[str, torch.Tensor | None]:
        """Get input tensors for the generative process."""
        size_factor = tensors.get(REGISTRY_KEYS.SIZE_FACTOR_KEY, None)
        if size_factor is not None:
            size_factor = torch.log(size_factor)

        return {
            MODULE_KEYS.Z_KEY: inference_outputs[MODULE_KEYS.Z_KEY],
            MODULE_KEYS.LIBRARY_KEY: inference_outputs[MODULE_KEYS.LIBRARY_KEY],
            MODULE_KEYS.BATCH_INDEX_KEY: tensors[REGISTRY_KEYS.BATCH_KEY],
            MODULE_KEYS.Y_KEY: tensors[REGISTRY_KEYS.LABELS_KEY],
            MODULE_KEYS.CONT_COVS_KEY: tensors.get(REGISTRY_KEYS.CONT_COVS_KEY, None),
            MODULE_KEYS.CAT_COVS_KEY: tensors.get(REGISTRY_KEYS.CAT_COVS_KEY, None),
            MODULE_KEYS.SIZE_FACTOR_KEY: size_factor,
        }

    def _compute_local_library_params(
        self,
        batch_index: torch.Tensor,
    ) -> tuple[torch.Tensor, torch.Tensor]:
        """Computes local library parameters.

        Compute two tensors of shape (batch_index.shape[0], 1) where each
        element corresponds to the mean and variances, respectively, of the
        log library sizes in the batch the cell corresponds to.
        """
        from torch.nn.functional import linear

        n_batch = self.library_log_means.shape[1]
        local_library_log_means = linear(
            one_hot(batch_index.squeeze(-1), n_batch).float(), self.library_log_means
        )

        local_library_log_vars = linear(
            one_hot(batch_index.squeeze(-1), n_batch).float(), self.library_log_vars
        )

        return local_library_log_means, local_library_log_vars

    @auto_move_data
    def _regular_inference(
        self,
        x: torch.Tensor,
        batch_index: torch.Tensor,
        cont_covs: torch.Tensor | None = None,
        cat_covs: torch.Tensor | None = None,
        n_samples: int = 1,
    ) -> dict[str, torch.Tensor | Distribution | None]:
        """Run the regular inference process."""
        x_ = x
        if self.use_observed_lib_size:
            library = torch.log(x.sum(1)).unsqueeze(1)
        if self.log_variational:
            x_ = torch.log1p(x_)

        if cont_covs is not None and self.encode_covariates:
            encoder_input = torch.cat((x_, cont_covs), dim=-1)
        else:
            encoder_input = x_
        if cat_covs is not None and self.encode_covariates:
            categorical_input = torch.split(cat_covs, 1, dim=1)
        else:
            categorical_input = ()

        if self.batch_representation == "embedding" and self.encode_covariates:
            batch_rep = self.compute_embedding(REGISTRY_KEYS.BATCH_KEY, batch_index)
            encoder_input = torch.cat([encoder_input, batch_rep], dim=-1)
            qz, z = self.z_encoder(encoder_input, *categorical_input)
        else:
            qz, z = self.z_encoder(encoder_input, batch_index, *categorical_input)

        ql = None
        if not self.use_observed_lib_size:
            if self.batch_representation == "embedding":
                ql, library_encoded = self.l_encoder(encoder_input, *categorical_input)
            else:
                ql, library_encoded = self.l_encoder(
                    encoder_input, batch_index, *categorical_input
                )
            library = library_encoded

        if n_samples > 1:
            untran_z = qz.sample((n_samples,))
            z = self.z_encoder.z_transformation(untran_z)
            if self.use_observed_lib_size:
                library = library.unsqueeze(0).expand(
                    (n_samples, library.size(0), library.size(1))
                )
            else:
                library = ql.sample((n_samples,))

        return {
            MODULE_KEYS.Z_KEY: z,
            MODULE_KEYS.QZ_KEY: qz,
            MODULE_KEYS.QL_KEY: ql,
            MODULE_KEYS.LIBRARY_KEY: library,
        }

    @auto_move_data
    def _cached_inference(
        self,
        qzm: torch.Tensor,
        qzv: torch.Tensor,
        observed_lib_size: torch.Tensor,
        n_samples: int = 1,
    ) -> dict[str, torch.Tensor | None]:
        """Run the cached inference process."""
        from torch.distributions import Normal

        qz = Normal(qzm, qzv.sqrt())
        # use dist.sample() rather than rsample because we aren't optimizing the z here
        untran_z = qz.sample() if n_samples == 1 else qz.sample((n_samples,))
        z = self.z_encoder.z_transformation(untran_z)
        library = torch.log(observed_lib_size)
        if n_samples > 1:
            library = library.unsqueeze(0).expand((n_samples, library.size(0), library.size(1)))

        return {
            MODULE_KEYS.Z_KEY: z,
            MODULE_KEYS.QZ_KEY: qz,
            MODULE_KEYS.QL_KEY: None,
            MODULE_KEYS.LIBRARY_KEY: library,
        }

    @auto_move_data
    def generative(
        self,
        z: torch.Tensor,
        library: torch.Tensor,
        batch_index: torch.Tensor,
        cont_covs: torch.Tensor | None = None,
        cat_covs: torch.Tensor | None = None,
        size_factor: torch.Tensor | None = None,
        y: torch.Tensor | None = None,
        transform_batch: torch.Tensor | None = None,
    ) -> dict[str, Distribution | None]:
        """Run the generative process."""
        from torch.nn.functional import linear

        from scvi.distributions import (
            NegativeBinomial,
            Normal,
            Poisson,
            ZeroInflatedNegativeBinomial,
        )

        # TODO: refactor forward function to not rely on y
        # Likelihood distribution
        if cont_covs is None:
            decoder_input = z
        elif z.dim() != cont_covs.dim():
            decoder_input = torch.cat(
                [z, cont_covs.unsqueeze(0).expand(z.size(0), -1, -1)], dim=-1
            )
        else:
            decoder_input = torch.cat([z, cont_covs], dim=-1)

        if cat_covs is not None:
            categorical_input = torch.split(cat_covs, 1, dim=1)
        else:
            categorical_input = ()

        if transform_batch is not None:
            batch_index = torch.ones_like(batch_index) * transform_batch

        if not self.use_size_factor_key:
            size_factor = library

        if self.batch_representation == "embedding":
            batch_rep = self.compute_embedding(REGISTRY_KEYS.BATCH_KEY, batch_index)
            decoder_input = torch.cat([decoder_input, batch_rep], dim=-1)
            px_scale, px_r, px_rate, px_dropout = self.decoder(
                self.dispersion,
                decoder_input,
                size_factor,
                *categorical_input,
                y,
            )
        else:
            px_scale, px_r, px_rate, px_dropout = self.decoder(
                self.dispersion,
                decoder_input,
                size_factor,
                batch_index,
                *categorical_input,
                y,
            )

        if self.dispersion == "gene-label":
            px_r = linear(
                one_hot(y.squeeze(-1), self.n_labels).float(), self.px_r
            )  # px_r gets transposed - last dimension is nb genes
        elif self.dispersion == "gene-batch":
            px_r = linear(one_hot(batch_index.squeeze(-1), self.n_batch).float(), self.px_r)
        elif self.dispersion == "gene":
            px_r = self.px_r

        px_r = torch.exp(px_r)

        if self.gene_likelihood == "zinb":
            px = ZeroInflatedNegativeBinomial(
                mu=px_rate,
                theta=px_r,
                zi_logits=px_dropout,
                scale=px_scale,
            )
        elif self.gene_likelihood == "nb":
            px = NegativeBinomial(mu=px_rate, theta=px_r, scale=px_scale)
        elif self.gene_likelihood == "poisson":
            px = Poisson(rate=px_rate, scale=px_scale)
        elif self.gene_likelihood == "normal":
            px = Normal(px_rate, px_r, normal_mu=px_scale)

        # Priors
        if self.use_observed_lib_size:
            pl = None
        else:
            (
                local_library_log_means,
                local_library_log_vars,
            ) = self._compute_local_library_params(batch_index)
            pl = Normal(local_library_log_means, local_library_log_vars.sqrt())
        pz = Normal(torch.zeros_like(z), torch.ones_like(z))

        return {
            MODULE_KEYS.PX_KEY: px,
            MODULE_KEYS.PL_KEY: pl,
            MODULE_KEYS.PZ_KEY: pz,
        }

    @unsupported_if_adata_minified
    def loss(
        self,
        tensors: dict[str, torch.Tensor],
        inference_outputs: dict[str, torch.Tensor | Distribution | None],
        generative_outputs: dict[str, Distribution | None],
        kl_weight: torch.tensor | float = 1.0,
    ) -> LossOutput:
        """Compute the loss."""
        from torch.distributions import kl_divergence

        x = tensors[REGISTRY_KEYS.X_KEY]
        kl_divergence_z = kl_divergence(
            inference_outputs[MODULE_KEYS.QZ_KEY], generative_outputs[MODULE_KEYS.PZ_KEY]
        ).sum(dim=-1)
        if not self.use_observed_lib_size:
            kl_divergence_l = kl_divergence(
                inference_outputs[MODULE_KEYS.QL_KEY], generative_outputs[MODULE_KEYS.PL_KEY]
            ).sum(dim=1)
        else:
            kl_divergence_l = torch.zeros_like(kl_divergence_z)

        reconst_loss = -generative_outputs[MODULE_KEYS.PX_KEY].log_prob(x).sum(-1)

        kl_local_for_warmup = kl_divergence_z
        kl_local_no_warmup = kl_divergence_l

        weighted_kl_local = kl_weight * kl_local_for_warmup + kl_local_no_warmup

        loss = torch.mean(reconst_loss + weighted_kl_local)

        # a payload to be used during autotune
        if self.extra_payload_autotune:
            extra_metrics_payload = {
                "z": inference_outputs["z"],
                "batch": tensors[REGISTRY_KEYS.BATCH_KEY],
                "labels": tensors[REGISTRY_KEYS.LABELS_KEY],
            }
        else:
            extra_metrics_payload = {}

        return LossOutput(
            loss=loss,
            reconstruction_loss=reconst_loss,
            kl_local={
                MODULE_KEYS.KL_L_KEY: kl_divergence_l,
                MODULE_KEYS.KL_Z_KEY: kl_divergence_z,
            },
            extra_metrics=extra_metrics_payload,
        )

    @torch.inference_mode()
    def sample(
        self,
        tensors: dict[str, torch.Tensor],
        n_samples: int = 1,
        max_poisson_rate: float = 1e8,
        generative_kwargs: dict | None = None,
    ) -> torch.Tensor:
        r"""Generate predictive samples from the posterior predictive distribution.

        The posterior predictive distribution is denoted as :math:`p(\hat{x} \mid x)`, where
        :math:`x` is the input data and :math:`\hat{x}` is the sampled data.

        We sample from this distribution by first sampling ``n_samples`` times from the posterior
        distribution :math:`q(z \mid x)` for a given observation, and then sampling from the
        likelihood :math:`p(\hat{x} \mid z)` for each of these.

        Parameters
        ----------
        tensors
            Dictionary of tensors passed into ``VAE.forward``.
        n_samples
            Number of Monte Carlo samples to draw from the distribution for each observation.
        max_poisson_rate
            The maximum value to which to clip the ``rate`` parameter of
            :class:`~scvi.distributions.Poisson`. Avoids numerical sampling issues when the
            parameter is very large due to the variance of the distribution.
        generative_kwargs
            Keyword args for ``generative()`` in fwd pass

        Returns
        -------
        Tensor on CPU with shape ``(n_obs, n_vars)`` if ``n_samples == 1``, else
        ``(n_obs, n_vars,)``.
        """
        from scvi.distributions import Poisson

        inference_kwargs = {"n_samples": n_samples}
        _, generative_outputs = self.forward(
            tensors,
            inference_kwargs=inference_kwargs,
            generative_kwargs=generative_kwargs,
            compute_loss=False,
        )

        dist = generative_outputs[MODULE_KEYS.PX_KEY]
        if self.gene_likelihood == "poisson":
            # TODO: NEED TORCH MPS FIX for 'aten::poisson'
            dist = (
                Poisson(torch.clamp(dist.rate.to("cpu"), max=max_poisson_rate))
                if self.device.type == "mps"
                else Poisson(torch.clamp(dist.rate, max=max_poisson_rate))
            )

        # (n_obs, n_vars) if n_samples == 1, else (n_samples, n_obs, n_vars)
        samples = dist.sample()
        # (n_samples, n_obs, n_vars) -> (n_obs, n_vars, n_samples)
        samples = torch.permute(samples, (1, 2, 0)) if n_samples > 1 else samples

        return samples.cpu()

    @torch.inference_mode()
    @auto_move_data
    def marginal_ll(
        self,
        tensors: dict[str, torch.Tensor],
        n_mc_samples: int,
        return_mean: bool = False,
        n_mc_samples_per_pass: int = 1,
    ):
        """Compute the marginal log-likelihood of the data under the model.

        Parameters
        ----------
        tensors
            Dictionary of tensors passed into ``VAE.forward``.
        n_mc_samples
            Number of Monte Carlo samples to use for the estimation of the marginal log-likelihood.
        return_mean
            Whether to return the mean of marginal likelihoods over cells.
        n_mc_samples_per_pass
            Number of Monte Carlo samples to use per pass. This is useful to avoid memory issues.
        """
        from torch import logsumexp
        from torch.distributions import Normal

        batch_index = tensors[REGISTRY_KEYS.BATCH_KEY]

        to_sum = []
        if n_mc_samples_per_pass > n_mc_samples:
            warnings.warn(
                "Number of chunks is larger than the total number of samples, setting it to the "
                "number of samples",
                RuntimeWarning,
                stacklevel=settings.warnings_stacklevel,
            )
            n_mc_samples_per_pass = n_mc_samples
        n_passes = int(np.ceil(n_mc_samples / n_mc_samples_per_pass))
        for _ in range(n_passes):
            # Distribution parameters and sampled variables
            inference_outputs, _, losses = self.forward(
                tensors,
                inference_kwargs={"n_samples": n_mc_samples_per_pass},
                get_inference_input_kwargs={"full_forward_pass": True},
            )
            qz = inference_outputs[MODULE_KEYS.QZ_KEY]
            ql = inference_outputs[MODULE_KEYS.QL_KEY]
            z = inference_outputs[MODULE_KEYS.Z_KEY]
            library = inference_outputs[MODULE_KEYS.LIBRARY_KEY]

            # Reconstruction Loss
            reconst_loss = losses.dict_sum(losses.reconstruction_loss)

            # Log-probabilities
            p_z = (
                Normal(torch.zeros_like(qz.loc), torch.ones_like(qz.scale)).log_prob(z).sum(dim=-1)
            )
            p_x_zl = -reconst_loss
            q_z_x = qz.log_prob(z).sum(dim=-1)
            log_prob_sum = p_z + p_x_zl - q_z_x

            if not self.use_observed_lib_size:
                (
                    local_library_log_means,
                    local_library_log_vars,
                ) = self._compute_local_library_params(batch_index)

                p_l = (
                    Normal(local_library_log_means, local_library_log_vars.sqrt())
                    .log_prob(library)
                    .sum(dim=-1)
                )
                q_l_x = ql.log_prob(library).sum(dim=-1)

                log_prob_sum += p_l - q_l_x
            if n_mc_samples_per_pass == 1:
                log_prob_sum = log_prob_sum.unsqueeze(0)

            to_sum.append(log_prob_sum)
        to_sum = torch.cat(to_sum, dim=0)
        batch_log_lkl = logsumexp(to_sum, dim=0) - np.log(n_mc_samples)
        if return_mean:
            batch_log_lkl = torch.mean(batch_log_lkl).item()
        else:
            batch_log_lkl = batch_log_lkl.cpu()
        return batch_log_lkl


class LDVAE(VAE):
    """Linear-decoded Variational auto-encoder model.

    Implementation of :cite:p:`Svensson20`.

    This model uses a linear decoder, directly mapping the latent representation
    to gene expression levels. It still uses a deep neural network to encode
    the latent representation.

    Compared to standard VAE, this model is less powerful but can be used to
    inspect which genes contribute to variation in the dataset. It may also be used
    for all scVI tasks, like differential expression, batch correction, imputation, etc.
    However, batch correction may be less powerful as it assumes a linear model.

    Parameters
    ----------
    n_input
        Number of input genes
    n_batch
        Number of batches
    n_labels
        Number of labels
    n_hidden
        Number of nodes per hidden layer (for encoder)
    n_latent
        Dimensionality of the latent space
    n_layers_encoder
        Number of hidden layers used for encoder NNs
    dropout_rate
        Dropout rate for neural networks
    dispersion
        One of the following

        * ``'gene'`` - dispersion parameter of NB is constant per gene across cells
        * ``'gene-batch'`` - dispersion can differ between different batches
        * ``'gene-label'`` - dispersion can differ between different labels
        * ``'gene-cell'`` - dispersion can differ for every gene in every cell
    log_variational
        Log(data+1) prior to encoding for numerical stability. Not normalization.
    gene_likelihood
        One of

        * ``'nb'`` - Negative binomial distribution
        * ``'zinb'`` - Zero-inflated negative binomial distribution
        * ``'poisson'`` - Poisson distribution
    use_batch_norm
        Bool whether to use batch norm in decoder
    bias
        Bool whether to have bias term in linear decoder
    latent_distribution
        One of

        * ``'normal'`` - Isotropic normal
        * ``'ln'`` - Logistic normal with normal params N(0, 1)
    use_observed_lib_size
        Use observed library size for RNA as scaling factor in mean of conditional distribution.
    **kwargs
    """

    def __init__(
        self,
        n_input: int,
        n_batch: int = 0,
        n_labels: int = 0,
        n_hidden: int = 128,
        n_latent: int = 10,
        n_layers_encoder: int = 1,
        dropout_rate: float = 0.1,
        dispersion: str = "gene",
        log_variational: bool = True,
        gene_likelihood: str = "nb",
        use_batch_norm: bool = True,
        bias: bool = False,
        latent_distribution: str = "normal",
        use_observed_lib_size: bool = False,
        **kwargs,
    ):
        from scvi.nn import Encoder, LinearDecoderSCVI

        super().__init__(
            n_input=n_input,
            n_batch=n_batch,
            n_labels=n_labels,
            n_hidden=n_hidden,
            n_latent=n_latent,
            n_layers=n_layers_encoder,
            dropout_rate=dropout_rate,
            dispersion=dispersion,
            log_variational=log_variational,
            gene_likelihood=gene_likelihood,
            latent_distribution=latent_distribution,
            use_observed_lib_size=use_observed_lib_size,
            **kwargs,
        )
        self.use_batch_norm = use_batch_norm
        self.z_encoder = Encoder(
            n_input,
            n_latent,
            n_layers=n_layers_encoder,
            n_hidden=n_hidden,
            dropout_rate=dropout_rate,
            distribution=latent_distribution,
            use_batch_norm=True,
            use_layer_norm=False,
            return_dist=True,
        )
        self.l_encoder = Encoder(
            n_input,
            1,
            n_layers=1,
            n_hidden=n_hidden,
            dropout_rate=dropout_rate,
            use_batch_norm=True,
            use_layer_norm=False,
            return_dist=True,
        )
        self.decoder = LinearDecoderSCVI(
            n_latent,
            n_input,
            n_cat_list=[n_batch],
            use_batch_norm=use_batch_norm,
            use_layer_norm=False,
            bias=bias,
        )

    @torch.inference_mode()
    def get_loadings(self) -> np.ndarray:
        """Extract per-gene weights in the linear decoder."""
        # This is BW, where B is diag(b) batch norm, W is the weight matrix
        if self.use_batch_norm is True:
            w = self.decoder.factor_regressor.fc_layers[0][0].weight
            bn = self.decoder.factor_regressor.fc_layers[0][1]
            sigma = torch.sqrt(bn.running_var + bn.eps)
            gamma = bn.weight
            b = gamma / sigma
            b_identity = torch.diag(b)
            loadings = torch.matmul(b_identity, w)
        else:
            loadings = self.decoder.factor_regressor.fc_layers[0][0].weight
        loadings = loadings.detach().cpu().numpy()
        if self.n_batch > 1:
            loadings = loadings[:, : -self.n_batch]

        return loadings