Better support for missing labels (#2288)

* Fix prediction with NaN values in training labels

* Missing observation support for multitask and allow MultivariateMultitaskNormal indexing

* Fix error in MultitaskMultivariateNormal indexing on '...'

* Fix indexing with negative values

* Add tests

- Indexing MultitaskMultivariateNormal
- Missing data in single-task and multitask models

* Render docs for MultitaskMultivariateNormal indexing and missing observations

* Fix docs warning

* Fix docstring

* Finally fix docstring

* Change missing data handling to option flag

* Revamp missing value implementation

- Enable via gpytorch.settings
- Two modes: 'mask' and 'fill'
- Makes GaussianLikelihoodWithMissingObs obsolete
- Supports approximate GPs

* Fix Python version incompatibility

* Increase atol on variational tests

* Add ExactMarginalLogLikelihoodWithMissingObs back with deprecation warning

* Add warning if kernel matrix is made dense

* Fix docs

* Add quick path for noop slice indices

* Add test for noop slice indexing

* Fix docs

* Switch to MaskedLinearOperator

* Switch to MaskedLinearOperator from linear-operator 0.5.1

* Disable test_t_matmul_matrix() for LazyEvaluatedKernelTensor

The test fails because LazyEvaluatedKernelTensor only supports _matmul() with checkpointing, but checkpointing is deprecated.

* Fix merge conflict

Author: Turakar

docs/source/distributions.rst

@@ -44,6 +44,7 @@ MultitaskMultivariateNormal
 
 .. autoclass:: MultitaskMultivariateNormal
    :members:
+   :special-members: __getitem__
 
 
 Delta

docs/source/likelihoods.rst

@@ -34,7 +34,7 @@ reduce the variance when computing approximate GP objective functions.
    :members:
 
 :hidden:`GaussianLikelihoodWithMissingObs`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 .. autoclass:: GaussianLikelihoodWithMissingObs
    :members:

gpytorch/distributions/multitask_multivariate_normal.py

@@ -2,7 +2,12 @@
 
 import torch
 from linear_operator import LinearOperator, to_linear_operator
-from linear_operator.operators import BlockDiagLinearOperator, BlockInterleavedLinearOperator, CatLinearOperator
+from linear_operator.operators import (
+    BlockDiagLinearOperator,
+    BlockInterleavedLinearOperator,
+    CatLinearOperator,
+    DiagLinearOperator,
+)
 
 from .multivariate_normal import MultivariateNormal
 
@@ -18,7 +23,7 @@ class MultitaskMultivariateNormal(MultivariateNormal):
     :param torch.Tensor mean:  An `n x t` or batch `b x n x t` matrix of means for the MVN distribution.
     :param ~linear_operator.operators.LinearOperator covar: An `... x NT x NT` (batch) matrix.
         covariance matrix of MVN distribution.
-    :param bool validate_args: (default=False) If True, validate `mean` anad `covariance_matrix` arguments.
+    :param bool validate_args: (default=False) If True, validate `mean` and `covariance_matrix` arguments.
     :param bool interleaved: (default=True) If True, covariance matrix is interpreted as block-diagonal w.r.t.
         inter-task covariances for each observation. If False, it is interpreted as block-diagonal
         w.r.t. inter-observation covariance for each task.
@@ -276,5 +281,145 @@ def variance(self):
             return var.view(new_shape).transpose(-1, -2).contiguous()
         return var.view(self._output_shape)
 
+    def __getitem__(self, idx) -> MultivariateNormal:
+        """
+        Constructs a new MultivariateNormal that represents a random variable
+        modified by an indexing operation.
+
+        The mean and covariance matrix arguments are indexed accordingly.
+
+        :param Any idx: Index to apply to the mean. The covariance matrix is indexed accordingly.
+        :returns: If indices specify a slice for samples and tasks, returns a
+            MultitaskMultivariateNormal, else returns a MultivariateNormal.
+        """
+
+        # Normalize index to a tuple
+        if not isinstance(idx, tuple):
+            idx = (idx,)
+
+        if ... in idx:
+            # Replace ellipsis '...' with explicit indices
+            ellipsis_location = idx.index(...)
+            if ... in idx[ellipsis_location + 1 :]:
+                raise IndexError("Only one ellipsis '...' is supported!")
+            prefix = idx[:ellipsis_location]
+            suffix = idx[ellipsis_location + 1 :]
+            infix_length = self.mean.dim() - len(prefix) - len(suffix)
+            if infix_length < 0:
+                raise IndexError(f"Index {idx} has too many dimensions")
+            idx = prefix + (slice(None),) * infix_length + suffix
+        elif len(idx) == self.mean.dim() - 1:
+            # Normalize indices ignoring the task-index to include it
+            idx = idx + (slice(None),)
+
+        new_mean = self.mean[idx]
+
+        # We now create a covariance matrix appropriate for new_mean
+        if len(idx) <= self.mean.dim() - 2:
+            # We are only indexing the batch dimensions in this case
+            return MultitaskMultivariateNormal(
+                mean=new_mean,
+                covariance_matrix=self.lazy_covariance_matrix[idx],
+                interleaved=self._interleaved,
+            )
+        elif len(idx) > self.mean.dim():
+            raise IndexError(f"Index {idx} has too many dimensions")
+        else:
+            # We have an index that extends over all dimensions
+            batch_idx = idx[:-2]
+            if self._interleaved:
+                row_idx = idx[-2]
+                col_idx = idx[-1]
+                num_rows = self._output_shape[-2]
+                num_cols = self._output_shape[-1]
+            else:
+                row_idx = idx[-1]
+                col_idx = idx[-2]
+                num_rows = self._output_shape[-1]
+                num_cols = self._output_shape[-2]
+
+            if isinstance(row_idx, int) and isinstance(col_idx, int):
+                # Single sample with single task
+                row_idx = _normalize_index(row_idx, num_rows)
+                col_idx = _normalize_index(col_idx, num_cols)
+                new_cov = DiagLinearOperator(
+                    self.lazy_covariance_matrix.diagonal()[batch_idx + (row_idx * num_cols + col_idx,)]
+                )
+                return MultivariateNormal(mean=new_mean, covariance_matrix=new_cov)
+            elif isinstance(row_idx, int) and isinstance(col_idx, slice):
+                # A block of the covariance matrix
+                row_idx = _normalize_index(row_idx, num_rows)
+                col_idx = _normalize_slice(col_idx, num_cols)
+                new_slice = slice(
+                    col_idx.start + row_idx * num_cols,
+                    col_idx.stop + row_idx * num_cols,
+                    col_idx.step,
+                )
+                new_cov = self.lazy_covariance_matrix[batch_idx + (new_slice, new_slice)]
+                return MultivariateNormal(mean=new_mean, covariance_matrix=new_cov)
+            elif isinstance(row_idx, slice) and isinstance(col_idx, int):
+                # A block of the reversely interleaved covariance matrix
+                row_idx = _normalize_slice(row_idx, num_rows)
+                col_idx = _normalize_index(col_idx, num_cols)
+                new_slice = slice(row_idx.start + col_idx, row_idx.stop * num_cols + col_idx, row_idx.step * num_cols)
+                new_cov = self.lazy_covariance_matrix[batch_idx + (new_slice, new_slice)]
+                return MultivariateNormal(mean=new_mean, covariance_matrix=new_cov)
+            elif (
+                isinstance(row_idx, slice)
+                and isinstance(col_idx, slice)
+                and row_idx == col_idx == slice(None, None, None)
+            ):
+                new_cov = self.lazy_covariance_matrix[batch_idx]
+                return MultitaskMultivariateNormal(
+                    mean=new_mean,
+                    covariance_matrix=new_cov,
+                    interleaved=self._interleaved,
+                    validate_args=False,
+                )
+            elif isinstance(row_idx, slice) or isinstance(col_idx, slice):
+                # slice x slice or indices x slice or slice x indices
+                if isinstance(row_idx, slice):
+                    row_idx = torch.arange(num_rows)[row_idx]
+                if isinstance(col_idx, slice):
+                    col_idx = torch.arange(num_cols)[col_idx]
+                row_grid, col_grid = torch.meshgrid(row_idx, col_idx, indexing="ij")
+                indices = (row_grid * num_cols + col_grid).reshape(-1)
+                new_cov = self.lazy_covariance_matrix[batch_idx + (indices,)][..., indices]
+                return MultitaskMultivariateNormal(
+                    mean=new_mean, covariance_matrix=new_cov, interleaved=self._interleaved, validate_args=False
+                )
+            else:
+                # row_idx and col_idx have pairs of indices
+                indices = row_idx * num_cols + col_idx
+                new_cov = self.lazy_covariance_matrix[batch_idx + (indices,)][..., indices]
+                return MultivariateNormal(
+                    mean=new_mean,
+                    covariance_matrix=new_cov,
+                )
+
     def __repr__(self) -> str:
         return f"MultitaskMultivariateNormal(mean shape: {self._output_shape})"
+
+
+def _normalize_index(i: int, dim_size: int) -> int:
+    if i < 0:
+        return dim_size + i
+    else:
+        return i
+
+
+def _normalize_slice(s: slice, dim_size: int) -> slice:
+    start = s.start
+    if start is None:
+        start = 0
+    elif start < 0:
+        start = dim_size + start
+    stop = s.stop
+    if stop is None:
+        stop = dim_size
+    elif stop < 0:
+        stop = dim_size + stop
+    step = s.step
+    if step is None:
+        step = 1
+    return slice(start, stop, step)

gpytorch/distributions/multivariate_normal.py

@@ -343,16 +343,22 @@ def __getitem__(self, idx) -> MultivariateNormal:
 
         The mean and covariance matrix arguments are indexed accordingly.
 
-        :param idx: Index to apply.
+        :param idx: Index to apply to the mean. The covariance matrix is indexed accordingly.
         """
 
         if not isinstance(idx, tuple):
             idx = (idx,)
+        if len(idx) > self.mean.dim() and Ellipsis in idx:
+            idx = tuple(i for i in idx if i != Ellipsis)
+            if len(idx) < self.mean.dim():
+                raise IndexError("Multiple ambiguous ellipsis in index!")
+
         rest_idx = idx[:-1]
         last_idx = idx[-1]
         new_mean = self.mean[idx]
 
         if len(idx) <= self.mean.dim() - 1 and (Ellipsis not in rest_idx):
+            # We are only indexing the batch dimensions in this case
             new_cov = self.lazy_covariance_matrix[idx]
         elif len(idx) > self.mean.dim():
             raise IndexError(f"Index {idx} has too many dimensions")

gpytorch/likelihoods/gaussian_likelihood.py

@@ -1,15 +1,15 @@
 #!/usr/bin/env python3
-
 import math
 import warnings
 from copy import deepcopy
 from typing import Any, Optional, Tuple, Union
 
 import torch
-from linear_operator.operators import LinearOperator, ZeroLinearOperator
+from linear_operator.operators import LinearOperator, MaskedLinearOperator, ZeroLinearOperator
 from torch import Tensor
 from torch.distributions import Distribution, Normal
 
+from .. import settings
 from ..constraints import Interval
 from ..distributions import base_distributions, MultivariateNormal
 from ..priors import Prior
@@ -39,17 +39,39 @@ def _shaped_noise_covar(self, base_shape: torch.Size, *params: Any, **kwargs: An
         return self.noise_covar(*params, shape=base_shape, **kwargs)
 
     def expected_log_prob(self, target: Tensor, input: MultivariateNormal, *params: Any, **kwargs: Any) -> Tensor:
-        mean, variance = input.mean, input.variance
-        num_event_dim = len(input.event_shape)
 
-        noise = self._shaped_noise_covar(mean.shape, *params, **kwargs).diagonal(dim1=-1, dim2=-2)
+        noise = self._shaped_noise_covar(input.mean.shape, *params, **kwargs).diagonal(dim1=-1, dim2=-2)
         # Potentially reshape the noise to deal with the multitask case
         noise = noise.view(*noise.shape[:-1], *input.event_shape)
 
+        # Handle NaN values if enabled
+        nan_policy = settings.observation_nan_policy.value()
+        if nan_policy == "mask":
+            observed = settings.observation_nan_policy._get_observed(target, input.event_shape)
+            input = MultivariateNormal(
+                mean=input.mean[..., observed],
+                covariance_matrix=MaskedLinearOperator(
+                    input.lazy_covariance_matrix, observed.reshape(-1), observed.reshape(-1)
+                ),
+            )
+            noise = noise[..., observed]
+            target = target[..., observed]
+        elif nan_policy == "fill":
+            missing = torch.isnan(target)
+            target = settings.observation_nan_policy._fill_tensor(target)
+
+        mean, variance = input.mean, input.variance
         res = ((target - mean).square() + variance) / noise + noise.log() + math.log(2 * math.pi)
         res = res.mul(-0.5)
-        if num_event_dim > 1:  # Do appropriate summation for multitask Gaussian likelihoods
+
+        if nan_policy == "fill":
+            res = res * ~missing
+
+        # Do appropriate summation for multitask Gaussian likelihoods
+        num_event_dim = len(input.event_shape)
+        if num_event_dim > 1:
             res = res.sum(list(range(-1, -num_event_dim, -1)))
+
         return res
 
     def forward(self, function_samples: Tensor, *params: Any, **kwargs: Any) -> Normal:
@@ -60,12 +82,31 @@ def log_marginal(
         self, observations: Tensor, function_dist: MultivariateNormal, *params: Any, **kwargs: Any
     ) -> Tensor:
         marginal = self.marginal(function_dist, *params, **kwargs)
+
+        # Handle NaN values if enabled
+        nan_policy = settings.observation_nan_policy.value()
+        if nan_policy == "mask":
+            observed = settings.observation_nan_policy._get_observed(observations, marginal.event_shape)
+            marginal = MultivariateNormal(
+                mean=marginal.mean[..., observed],
+                covariance_matrix=MaskedLinearOperator(
+                    marginal.lazy_covariance_matrix, observed.reshape(-1), observed.reshape(-1)
+                ),
+            )
+            observations = observations[..., observed]
+        elif nan_policy == "fill":
+            missing = torch.isnan(observations)
+            observations = settings.observation_nan_policy._fill_tensor(observations)
+
         # We're making everything conditionally independent
         indep_dist = base_distributions.Normal(marginal.mean, marginal.variance.clamp_min(1e-8).sqrt())
         res = indep_dist.log_prob(observations)
 
+        if nan_policy == "fill":
+            res = res * ~missing
+
         # Do appropriate summation for multitask Gaussian likelihoods
-        num_event_dim = len(function_dist.event_shape)
+        num_event_dim = len(marginal.event_shape)
         if num_event_dim > 1:
             res = res.sum(list(range(-1, -num_event_dim, -1)))
         return res
@@ -150,13 +191,15 @@ class GaussianLikelihoodWithMissingObs(GaussianLikelihood):
     .. note::
         This likelihood can be used for exact or approximate inference.
 
+    .. warning::
+        This likelihood is deprecated in favor of :class:`gpytorch.settings.observation_nan_policy`.
+
     :param noise_prior: Prior for noise parameter :math:`\sigma^2`.
     :type noise_prior: ~gpytorch.priors.Prior, optional
     :param noise_constraint: Constraint for noise parameter :math:`\sigma^2`.
     :type noise_constraint: ~gpytorch.constraints.Interval, optional
     :param batch_shape: The batch shape of the learned noise parameter (default: []).
     :type batch_shape: torch.Size, optional
-
     :var torch.Tensor noise: :math:`\sigma^2` parameter (noise)
 
     .. note::
@@ -166,6 +209,10 @@ class GaussianLikelihoodWithMissingObs(GaussianLikelihood):
     MISSING_VALUE_FILL: float = -999.0
 
     def __init__(self, **kwargs: Any) -> None:
+        warnings.warn(
+            "GaussianLikelihoodWithMissingObs is replaced by gpytorch.settings.observation_nan_policy('fill').",
+            DeprecationWarning,
+        )
         super().__init__(**kwargs)
 
     def _get_masked_obs(self, x: Tensor) -> Tuple[Tensor, Tensor]:

gpytorch/mlls/exact_marginal_log_likelihood.py

@@ -1,5 +1,8 @@
 #!/usr/bin/env python3
 
+from linear_operator.operators import MaskedLinearOperator
+
+from .. import settings
 from ..distributions import MultivariateNormal
 from ..likelihoods import _GaussianLikelihoodBase
 from .marginal_log_likelihood import MarginalLogLikelihood
@@ -59,8 +62,23 @@ def forward(self, function_dist, target, *params):
         if not isinstance(function_dist, MultivariateNormal):
             raise RuntimeError("ExactMarginalLogLikelihood can only operate on Gaussian random variables")
 
-        # Get the log prob of the marginal distribution
+        # Determine output likelihood
         output = self.likelihood(function_dist, *params)
+
+        # Remove NaN values if enabled
+        if settings.observation_nan_policy.value() == "mask":
+            observed = settings.observation_nan_policy._get_observed(target, output.event_shape)
+            output = MultivariateNormal(
+                mean=output.mean[..., observed],
+                covariance_matrix=MaskedLinearOperator(
+                    output.lazy_covariance_matrix, observed.reshape(-1), observed.reshape(-1)
+                ),
+            )
+            target = target[..., observed]
+        elif settings.observation_nan_policy.value() == "fill":
+            raise ValueError("NaN observation policy 'fill' is not supported by ExactMarginalLogLikelihood!")
+
+        # Get the log prob of the marginal distribution
         res = output.log_prob(target)
         res = self._add_other_terms(res, params)