Source code for pyro.distributions.diag_normal_mixture

from __future__ import absolute_import, division, print_function
import math

import torch
from torch.autograd import Function
from torch.autograd.function import once_differentiable
from torch.distributions import constraints, Categorical

from pyro.distributions.torch_distribution import TorchDistribution
from pyro.distributions.util import sum_leftmost


[docs]class MixtureOfDiagNormals(TorchDistribution): """ Mixture of Normal distributions with arbitrary means and arbitrary diagonal covariance matrices. That is, this distribution is a mixture with K components, where each component distribution is a D-dimensional Normal distribution with a D-dimensional mean parameter and a D-dimensional diagonal covariance matrix. The K different component means are gathered into the K x D dimensional parameter `locs` and the K different scale parameters are gathered into the K x D dimensional parameter `coord_scale`. The mixture weights are controlled by a K-dimensional vector of softmax logits, `component_logits`. This distribution implements pathwise derivatives for samples from the distribution. See reference [1] for details on the implementations of the pathwise derivative. Please consider citing this reference if you use the pathwise derivative in your research. Note that this distribution does not support dimension D = 1. [1] Pathwise Derivatives for Multivariate Distributions, Martin Jankowiak & Theofanis Karaletsos. arXiv:1806.01856 :param torch.Tensor locs: K x D mean matrix :param torch.Tensor coord_scale: K x D scale matrix :param torch.Tensor component_logits: K-dimensional vector of softmax logits """ has_rsample = True arg_constraints = {"locs": constraints.real, "coord_scale": constraints.positive, "component_logits": constraints.real} def __init__(self, locs, coord_scale, component_logits): self.batch_mode = (locs.dim() > 2) assert(coord_scale.shape == locs.shape) assert(self.batch_mode or locs.dim() == 2), \ "The locs parameter in MixtureOfDiagNormals should be K x D dimensional (or B x K x D if doing batches)" if not self.batch_mode: assert(coord_scale.dim() == 2), \ "The coord_scale parameter in MixtureOfDiagNormals should be K x D dimensional" assert(component_logits.dim() == 1), \ "The component_logits parameter in MixtureOfDiagNormals should be K dimensional" assert(component_logits.size(-1) == locs.size(-2)) batch_shape = () else: assert(coord_scale.dim() > 2), \ "The coord_scale parameter in MixtureOfDiagNormals should be B x K x D dimensional" assert(component_logits.dim() > 1), \ "The component_logits parameter in MixtureOfDiagNormals should be B x K dimensional" assert(component_logits.size(-1) == locs.size(-2)) batch_shape = tuple(locs.shape[:-2]) self.locs = locs self.coord_scale = coord_scale self.component_logits = component_logits self.dim = locs.size(-1) self.categorical = Categorical(logits=component_logits) self.probs = self.categorical.probs super(MixtureOfDiagNormals, self).__init__(batch_shape=torch.Size(batch_shape), event_shape=torch.Size((self.dim,)))
[docs] def expand(self, batch_shape, _instance=None): new = self._get_checked_instance(MixtureOfDiagNormals, _instance) new.batch_mode = True batch_shape = torch.Size(batch_shape) new.dim = self.dim new.locs = self.locs.expand(batch_shape + self.locs.shape[-2:]) new.coord_scale = self.coord_scale.expand(batch_shape + self.coord_scale.shape[-2:]) new.component_logits = self.component_logits.expand(batch_shape + self.component_logits.shape[-1:]) new.categorical = self.categorical.expand(batch_shape) new.probs = self.probs.expand(batch_shape + self.probs.shape[-1:]) super(MixtureOfDiagNormals, new).__init__(batch_shape, self.event_shape, validate_args=False) new._validate_args = self._validate_args return new
[docs] def log_prob(self, value): epsilon = (value.unsqueeze(-2) - self.locs) / self.coord_scale # L B K D eps_sqr = 0.5 * torch.pow(epsilon, 2.0).sum(-1) # L B K eps_sqr_min = torch.min(eps_sqr, -1)[0] # L B K coord_scale_prod = self.coord_scale.log().sum(-1).exp() # B K result = self.probs * torch.exp(-eps_sqr + eps_sqr_min.unsqueeze(-1)) / coord_scale_prod # L B K result = torch.log(result.sum(-1)) # L B result = result - 0.5 * math.log(2.0 * math.pi) * float(self.dim) result = result - eps_sqr_min return result
[docs] def rsample(self, sample_shape=torch.Size()): which = self.categorical.sample(sample_shape) return _MixDiagNormalSample.apply(self.locs, self.coord_scale, self.component_logits, self.categorical.probs, which, sample_shape + self.locs.shape[:-2] + (self.dim,))
class _MixDiagNormalSample(Function): @staticmethod def forward(ctx, locs, scales, component_logits, pis, which, noise_shape): dim = scales.size(-1) white = locs.new(noise_shape).normal_() n_unsqueezes = locs.dim() - which.dim() for _ in range(n_unsqueezes): which = which.unsqueeze(-1) which_expand = which.expand(tuple(which.shape[:-1] + (dim,))) loc = torch.gather(locs, -2, which_expand).squeeze(-2) sigma = torch.gather(scales, -2, which_expand).squeeze(-2) z = loc + sigma * white ctx.save_for_backward(z, scales, locs, component_logits, pis) return z @staticmethod @once_differentiable def backward(ctx, grad_output): z, scales, locs, logits, pis = ctx.saved_tensors dim = scales.size(-1) K = logits.size(-1) g = grad_output # l b i g = g.unsqueeze(-2) # l b 1 i batch_dims = locs.dim() - 2 locs_tilde = locs / scales # b j i sigma_0 = torch.min(scales, -2, keepdim=True)[0] # b 1 i z_shift = (z.unsqueeze(-2) - locs) / sigma_0 # l b j i z_tilde = z.unsqueeze(-2) / scales - locs_tilde # l b j i mu_cd = locs.unsqueeze(-2) - locs.unsqueeze(-3) # b c d i mu_cd_norm = torch.pow(mu_cd, 2.0).sum(-1).sqrt() # b c d mu_cd /= mu_cd_norm.unsqueeze(-1) # b c d i diagonals = z.new_empty((K,), dtype=torch.long) torch.arange(K, out=diagonals) mu_cd[..., diagonals, diagonals, :] = 0.0 mu_ll_cd = (locs.unsqueeze(-2) * mu_cd).sum(-1) # b c d z_ll_cd = (z.unsqueeze(-2).unsqueeze(-2) * mu_cd).sum(-1) # l b c d z_perp_cd = z.unsqueeze(-2).unsqueeze(-2) - z_ll_cd.unsqueeze(-1) * mu_cd # l b c d i z_perp_cd_sqr = torch.pow(z_perp_cd, 2.0).sum(-1) # l b c d shift_indices = z.new_empty((dim,), dtype=torch.long) torch.arange(dim, out=shift_indices) shift_indices = shift_indices - 1 shift_indices[0] = 0 z_shift_cumsum = torch.pow(z_shift, 2.0) z_shift_cumsum = z_shift_cumsum.sum(-1, keepdim=True) - torch.cumsum(z_shift_cumsum, dim=-1) # l b j i z_tilde_cumsum = torch.cumsum(torch.pow(z_tilde, 2.0), dim=-1) # l b j i z_tilde_cumsum = torch.index_select(z_tilde_cumsum, -1, shift_indices) z_tilde_cumsum[..., 0] = 0.0 r_sqr_ji = z_shift_cumsum + z_tilde_cumsum # l b j i log_scales = torch.log(scales) # b j i epsilons_sqr = torch.pow(z_tilde, 2.0) # l b j i log_qs = -0.5 * epsilons_sqr - 0.5 * math.log(2.0 * math.pi) - log_scales # l b j i log_q_j = log_qs.sum(-1, keepdim=True) # l b j 1 q_j = torch.exp(log_q_j) # l b j 1 q_tot = (pis * q_j.squeeze(-1)).sum(-1) # l b q_tot = q_tot.unsqueeze(-1) # l b 1 root_two = math.sqrt(2.0) shift_log_scales = log_scales[..., shift_indices] shift_log_scales[..., 0] = 0.0 sigma_products = torch.cumsum(shift_log_scales, dim=-1).exp() # b j i reverse_indices = z.new_tensor(range(dim - 1, -1, -1), dtype=torch.long) reverse_log_sigma_0 = sigma_0.log()[..., reverse_indices] # b 1 i sigma_0_products = torch.cumsum(reverse_log_sigma_0, dim=-1).exp()[..., reverse_indices - 1] # b 1 i sigma_0_products[..., -1] = 1.0 sigma_products *= sigma_0_products logits_grad = torch.erf(z_tilde / root_two) - torch.erf(z_shift / root_two) # l b j i logits_grad *= torch.exp(-0.5 * r_sqr_ji) # l b j i logits_grad = (logits_grad * g / sigma_products).sum(-1) # l b j logits_grad = sum_leftmost(logits_grad / q_tot, -1 - batch_dims) # b j logits_grad *= 0.5 * math.pow(2.0 * math.pi, -0.5 * (dim - 1)) logits_grad = -pis * logits_grad logits_grad = logits_grad - logits_grad.sum(-1, keepdim=True) * pis mu_ll_dc = torch.transpose(mu_ll_cd, -1, -2) v_cd = torch.erf((z_ll_cd - mu_ll_cd) / root_two) - torch.erf((z_ll_cd + mu_ll_dc) / root_two) v_cd *= torch.exp(-0.5 * z_perp_cd_sqr) # l b c d mu_cd_g = (g.unsqueeze(-2) * mu_cd).sum(-1) # l b c d v_cd *= -mu_cd_g * pis.unsqueeze(-2) * 0.5 * math.pow(2.0 * math.pi, -0.5 * (dim - 1)) # l b c d v_cd = pis * sum_leftmost(v_cd.sum(-1) / q_tot, -1 - batch_dims) logits_grad += v_cd prefactor = pis.unsqueeze(-1) * q_j * g / q_tot.unsqueeze(-1) locs_grad = sum_leftmost(prefactor, -2 - batch_dims) scales_grad = sum_leftmost(prefactor * z_tilde, -2 - batch_dims) return locs_grad, scales_grad, logits_grad, None, None, None