PairwiseGP modularization and PairwiseLogitLikelihood (#1193)

Summary:
Pull Request resolved: #1193

Modularize PairwiseGP's likelihood and add logit likelihood support in addition to the original probit likelihood. Fixed PairwiseGP's conditioning gradient issue.

Reviewed By: Balandat

Differential Revision: D35921953

fbshipit-source-id: ff121f654b7e0e2fabb67ec002b2e88481a575c9

botorch/models/likelihoods/__init__.py

@@ -0,0 +1,16 @@
+#!/usr/bin/env python3
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
+
+from botorch.models.likelihoods.pairwise import (
+    PairwiseProbitLikelihood,
+    PairwiseLogitLikelihood,
+)
+
+
+__all__ = [
+    "PairwiseProbitLikelihood",
+    "PairwiseLogitLikelihood",
+]

botorch/models/likelihoods/pairwise.py

@@ -0,0 +1,204 @@
+#!/usr/bin/env python3
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
+
+r"""
+Pairwise likelihood for pairwise preference model (e.g., PairwiseGP).
+"""
+
+from __future__ import annotations
+
+import math
+from abc import ABC, abstractmethod
+from typing import Tuple, Any
+
+import torch
+from gpytorch.likelihoods import Likelihood
+from torch import Tensor
+from torch.distributions import Bernoulli
+
+
+class PairwiseLikelihood(Likelihood, ABC):
+    """Pairwise likelihood base class for pairwise preference GP (e.g., PairwiseGP)"""
+
+    def forward(self, utility: Tensor, D: Tensor, **kwargs: Any) -> Bernoulli:
+        """Given the difference in (estimated) utility util_diff = f(v) - f(u),
+        return a Bernoulli distribution object representing the likelihood of
+        the user prefer v over u.
+
+        Note that this is not used by the `PairwiseGP` model,
+        """
+        return Bernoulli(probs=self.p(utility=utility, D=D))
+
+    @abstractmethod
+    def p(self, utility: Tensor, D: Tensor) -> Tensor:
+        """Given the difference in (estimated) utility util_diff = f(v) - f(u),
+        return the probability of the user prefer v over u.
+
+        Args:
+            utility: A Tensor of shape `(batch_size) x n`, the utility at MAP point
+            D: D is `(batch_size x) m x n` matrix with all elements being zero in last
+                dimension except at two positions D[..., i] = 1 and D[..., j] = -1
+                respectively, representing item i is preferred over item j.
+            log: if true, return log probability
+        """
+
+    def log_p(self, utility: Tensor, D: Tensor) -> Tensor:
+        """return the log of p"""
+        return torch.log(self.p(utility=utility, D=D))
+
+    def negative_log_gradient_sum(self, utility: Tensor, D: Tensor) -> Tensor:
+        """Calculate the sum of negative log gradient with respect to each item's latent
+            utility values. Useful for models using laplace approximation.
+
+        Args:
+            utility: A Tensor of shape `(batch_size x) n`, the utility at MAP point
+            D: D is `(batch_size x) m x n` matrix with all elements being zero in last
+                dimension except at two positions D[..., i] = 1 and D[..., j] = -1
+                respectively, representing item i is preferred over item j.
+
+        Returns:
+            A `(batch_size x) n` Tensor representing the sum of negative log gradient
+            values of the likelihood over all comparisons (i.e., the m dimension)
+            with respect to each item.
+        """
+        raise NotImplementedError
+
+    def negative_log_hessian_sum(self, utility: Tensor, D: Tensor) -> Tensor:
+        """Calculate the sum of negative log hessian with respect to each item's latent
+            utility values. Useful for models using laplace approximation.
+
+        Args:
+            utility: A Tensor of shape `(batch_size) x n`, the utility at MAP point
+            D: D is `(batch_size x) m x n` matrix with all elements being zero in last
+                dimension except at two positions D[..., i] = 1 and D[..., j] = -1
+                respectively, representing item i is preferred over item j.
+
+        Returns:
+            A `(batch_size x) n x n` Tensor representing the sum of negative log hessian
+            values of the likelihood over all comparisons (i.e., the m dimension) with
+            respect to each item.
+        """
+        raise NotImplementedError
+
+
+class PairwiseProbitLikelihood(PairwiseLikelihood):
+    """Pairwise likelihood using probit function
+
+    Given two items v and u with utilities f(v) and f(u), the probability that we
+    prefer v over u with probability std_normal_cdf((f(v) - f(u))/sqrt(2)). Note
+    that this formulation implicitly assume the noise term is fixed at 1.
+    """
+
+    # Clamping z values for better numerical stability. See self._calc_z for detail
+    # norm_cdf(z=3) ~= 0.999, top 0.1% percent
+    _zlim = 3
+
+    def _calc_z(self, utility: Tensor, D: Tensor) -> Tensor:
+        """Calculate the z score given estimated utility values and
+        the comparison matrix D.
+        """
+        scaled_util = (utility / math.sqrt(2)).unsqueeze(-1)
+        z = D.to(scaled_util) @ scaled_util
+        z = z.clamp(-self._zlim, self._zlim).squeeze(-1)
+        return z
+
+    def _calc_z_derived(self, z: Tensor) -> Tuple[Tensor, Tensor, Tensor]:
+        """Calculate auxiliary statistics derived from z, including log pdf,
+        log cdf, and the hazard function (pdf divided by cdf)"""
+        std_norm = torch.distributions.normal.Normal(
+            torch.zeros(1, dtype=z.dtype, device=z.device),
+            torch.ones(1, dtype=z.dtype, device=z.device),
+        )
+        z_logpdf = std_norm.log_prob(z)
+        z_cdf = std_norm.cdf(z)
+        z_logcdf = torch.log(z_cdf)
+        hazard = torch.exp(z_logpdf - z_logcdf)
+        return z_logpdf, z_logcdf, hazard
+
+    def p(self, utility: Tensor, D: Tensor, log: bool = False) -> Tensor:
+        z = self._calc_z(utility=utility, D=D)
+        std_norm = torch.distributions.normal.Normal(
+            torch.zeros(1, dtype=z.dtype, device=z.device),
+            torch.ones(1, dtype=z.dtype, device=z.device),
+        )
+        return std_norm.cdf(z)
+
+    def negative_log_gradient_sum(self, utility: Tensor, D: Tensor) -> Tensor:
+        # Compute the sum over of grad. of negative Log-LH wrt utility f.
+        # Original grad should be of dimension m x n, as in (6) from
+        # [Chu2005preference]_. The sum over the m dimension of grad. of
+        # negative log likelihood with respect to the utility
+        z = self._calc_z(utility, D)
+        _, _, h = self._calc_z_derived(z)
+        h_factor = h / math.sqrt(2)
+        grad = (h_factor.unsqueeze(-2) @ (-D)).squeeze(-2)
+
+        return grad
+
+    def negative_log_hessian_sum(self, utility: Tensor, D: Tensor) -> Tensor:
+        # Original hess should be of dimension m x n x n, as in (7) from
+        # [Chu2005preference]_ Sum over the first dimension and return a tensor of
+        # shape n x n.
+        # The sum over the m dimension of hessian of negative log likelihood
+        # with respect to the utility
+        DT = D.transpose(-1, -2)
+        z = self._calc_z(utility, D)
+        _, _, h = self._calc_z_derived(z)
+        mul_factor = h * (h + z) / 2
+        mul_factor = mul_factor.unsqueeze(-2).expand(*DT.size())
+        # multiply the hessian value by preference signs
+        # (+1 if preferred or -1 otherwise) and sum over the m dimension
+        hess = DT * mul_factor @ D
+        return hess
+
+
+class PairwiseLogitLikelihood(PairwiseLikelihood):
+    """Pairwise likelihood using logistic (i.e., sigmoid) function
+
+    Given two items v and u with utilities f(v) and f(u), the probability that we
+    prefer v over u with probability sigmoid(f(v) - f(u)). Note
+    that this formulation implicitly assume the beta term in logistic function is
+    fixed at 1.
+    """
+
+    # Clamping logit values for better numerical stability.
+    # See self._calc_logit for detail logistic(8) ~= 0.9997, top 0.03% percent
+    _logit_lim = 8
+
+    def _calc_logit(self, utility: Tensor, D: Tensor) -> Tensor:
+        logit = D.to(utility) @ utility.unsqueeze(-1)
+        logit = logit.clamp(-self._logit_lim, self._logit_lim).squeeze(-1)
+        return logit
+
+    def log_p(self, utility: Tensor, D: Tensor) -> Tensor:
+        logit = self._calc_logit(utility=utility, D=D)
+        return torch.nn.functional.logsigmoid(logit)
+
+    def p(self, utility: Tensor, D: Tensor) -> Tensor:
+        logit = self._calc_logit(utility=utility, D=D)
+        return torch.sigmoid(logit)
+
+    def negative_log_gradient_sum(self, utility: Tensor, D: Tensor) -> Tensor:
+        indices_shape = utility.shape[:-1] + (-1,)
+        winner_indices = (D == 1).nonzero(as_tuple=True)[-1].reshape(indices_shape)
+        loser_indices = (D == -1).nonzero(as_tuple=True)[-1].reshape(indices_shape)
+        ex = torch.exp(torch.gather(utility, -1, winner_indices))
+        ey = torch.exp(torch.gather(utility, -1, loser_indices))
+        unsigned_grad = ey / (ex + ey)
+        grad = (unsigned_grad.unsqueeze(-2) @ (-D)).squeeze(-2)
+        return grad
+
+    def negative_log_hessian_sum(self, utility: Tensor, D: Tensor) -> Tensor:
+        DT = D.transpose(-1, -2)
+        # calculating f(v) - f(u) given u > v information in D
+        neg_logit = -(D @ utility.unsqueeze(-1)).squeeze(-1)
+        term = torch.sigmoid(neg_logit)
+        mul_factor = term - (term) ** 2
+        mul_factor = mul_factor.unsqueeze(-2).expand(*DT.size())
+        # multiply the hessian value by preference signs
+        # (+1 if preferred or -1 otherwise) and sum over the m dimension
+        hess = DT * mul_factor @ D
+        return hess