Source code for gpytorch.mlls.gamma_robust_variational_elbo

#!/usr/bin/env python3

import math

import numpy as np
import torch

from ..likelihoods import _GaussianLikelihoodBase
from ._approximate_mll import _ApproximateMarginalLogLikelihood


[docs]class GammaRobustVariationalELBO(_ApproximateMarginalLogLikelihood): r""" An alternative to the variational evidence lower bound (ELBO), proposed by `Knoblauch, 2019`_. It is derived by replacing the log-likelihood term in the ELBO with a `\gamma` divergence: .. math:: \begin{align*} \mathcal{L}_{\gamma} &= \sum_{i=1}^N \mathbb{E}_{q( \mathbf u)} \left[ -\frac{\gamma}{\gamma - 1} \frac{ p( y_i \! \mid \! \mathbf u, x_i)^{\gamma - 1} }{ \int p(y \mid \mathbf u, x_i)^{\gamma} \: dy } \right] - \beta \: \text{KL} \left[ q( \mathbf u) \Vert p( \mathbf u) \right] \end{align*} where :math:`N` is the number of datapoints, :math:`\gamma` is a hyperparameter, :math:`q(\mathbf u)` is the variational distribution for the inducing function values, and :math:`p(\mathbf u)` is the prior distribution for the inducing function values. :math:`\beta` is a scaling constant for the KL divergence. .. note:: This module will only work with :obj:`~gpytorch.likelihoods.GaussianLikelihood`. :param ~gpytorch.likelihoods.GaussianLikelihood likelihood: The likelihood for the model :param ~gpytorch.models.ApproximateGP model: The approximate GP model :param int num_data: The total number of training data points (necessary for SGD) :param float beta: (optional, default=1.) A multiplicative factor for the KL divergence term. Setting it to anything less than 1 reduces the regularization effect of the model (similarly to what was proposed in `the beta-VAE paper`_). :param float gamma: (optional, default=1.03) The :math:`\gamma`-divergence hyperparameter. :param bool combine_terms: (default=True): Whether or not to sum the expected NLL with the KL terms (default True) Example: >>> # model is a gpytorch.models.ApproximateGP >>> # likelihood is a gpytorch.likelihoods.Likelihood >>> mll = gpytorch.mlls.GammaRobustVariationalELBO(likelihood, model, num_data=100, beta=0.5, gamma=1.03) >>> >>> output = model(train_x) >>> loss = -mll(output, train_y) >>> loss.backward() .. _Knoblauch, 2019: https://arxiv.org/pdf/1904.02303.pdf .. _Knoblauch, Jewson, Damoulas 2019: https://arxiv.org/pdf/1904.02063.pdf """ def __init__(self, likelihood, model, gamma=1.03, *args, **kwargs): if not isinstance(likelihood, _GaussianLikelihoodBase): raise RuntimeError("Likelihood must be Gaussian for exact inference") super().__init__(likelihood, model, *args, **kwargs) if gamma <= 1.0: raise ValueError("gamma should be > 1.0") self.gamma = gamma def _log_likelihood_term(self, variational_dist_f, target, *args, **kwargs): shifted_gamma = self.gamma - 1 muf, varf = variational_dist_f.mean, variational_dist_f.variance # Get noise from likelihood noise = self.likelihood._shaped_noise_covar(muf.shape, *args, **kwargs).diagonal(dim1=-1, dim2=-2) # Potentially reshape the noise to deal with the multitask case noise = noise.view(*noise.shape[:-1], *variational_dist_f.event_shape) # adapted from https://github.com/JeremiasKnoblauch/GVIPublic/ mut = shifted_gamma * target / noise + muf / varf sigmat = 1.0 / (shifted_gamma / noise + 1.0 / varf) log_integral = -0.5 * shifted_gamma * torch.log(2.0 * math.pi * noise) - 0.5 * np.log1p(shifted_gamma) log_tempered = ( -math.log(shifted_gamma) - 0.5 * shifted_gamma * torch.log(2.0 * math.pi * noise) - 0.5 * torch.log1p(shifted_gamma * varf / noise) - 0.5 * (shifted_gamma * target.pow(2.0) / noise) - 0.5 * muf.pow(2.0) / varf + 0.5 * mut.pow(2.0) * sigmat ) factor = log_tempered + shifted_gamma / self.gamma * log_integral factor = self.gamma * factor.exp() # Do appropriate summation for multitask Gaussian likelihoods num_event_dim = len(variational_dist_f.event_shape) if num_event_dim > 1: factor = factor.sum(list(range(-1, -num_event_dim, -1))) return factor.sum(-1)