Source code for pixyz.losses.entropy

import sympy

from .losses import Loss, SetLoss


[docs]class Entropy(SetLoss): r""" Entropy (Monte Carlo approximation). .. math:: H[p] = -\mathbb{E}_{p(x)}[\log p(x)] \approx -\frac{1}{L}\sum_{l=1}^L \log p(x_l), where :math:`x_l \sim p(x)`. Note: This class is a special case of the :attr:`Expectation` class. Examples -------- >>> import torch >>> from pixyz.distributions import Normal >>> p = Normal(loc=torch.tensor(0.), scale=torch.tensor(1.), var=["x"], features_shape=[64]) >>> loss_cls = Entropy(p) >>> print(loss_cls) - \mathbb{E}_{p(x)} \left[\log p(x) \right] >>> loss = loss_cls.eval() """ def __init__(self, p, input_var=None): if input_var is None: input_var = p.input_var loss = -p.log_prob().expectation(p, input_var) super().__init__(loss)
[docs]class AnalyticalEntropy(Loss): r""" Entropy (analytical). .. math:: H[p] = -\mathbb{E}_{p(x)}[\log p(x)] Examples -------- >>> import torch >>> from pixyz.distributions import Normal >>> p = Normal(loc=torch.tensor(0.), scale=torch.tensor(1.), var=["x"], features_shape=[64]) >>> loss_cls = AnalyticalEntropy(p) >>> print(loss_cls) - \mathbb{E}_{p(x)} \left[\log p(x) \right] >>> loss = loss_cls.eval() """ @property def _symbol(self): p_text = "{" + self.p.prob_text + "}" return sympy.Symbol("- \\mathbb{{E}}_{} \\left[{} \\right]".format(p_text, self.p.log_prob().loss_text)) def _get_eval(self, x_dict, **kwargs): if not hasattr(self.p, 'distribution_torch_class'): raise ValueError("Entropy of this distribution cannot be evaluated, " "got %s." % self.p.distribution_name) entropy = self.p.get_entropy(x_dict) return entropy, x_dict
[docs]class CrossEntropy(SetLoss): r""" Cross entropy, a.k.a., the negative expected value of log-likelihood (Monte Carlo approximation). .. math:: H[p||q] = -\mathbb{E}_{p(x)}[\log q(x)] \approx -\frac{1}{L}\sum_{l=1}^L \log q(x_l), where :math:`x_l \sim p(x)`. Note: This class is a special case of the :attr:`Expectation` class. Examples -------- >>> import torch >>> from pixyz.distributions import Normal >>> p = Normal(loc=torch.tensor(0.), scale=torch.tensor(1.), var=["x"], features_shape=[64], name="p") >>> q = Normal(loc=torch.tensor(0.), scale=torch.tensor(1.), var=["x"], features_shape=[64], name="q") >>> loss_cls = CrossEntropy(p, q) >>> print(loss_cls) - \mathbb{E}_{p(x)} \left[\log q(x) \right] >>> loss = loss_cls.eval() """ def __init__(self, p, q, input_var=None): if input_var is None: input_var = list(set(p.input_var + q.input_var) - set(p.var)) loss = -q.log_prob().expectation(p, input_var) super().__init__(loss)
[docs]class StochasticReconstructionLoss(SetLoss): r""" Reconstruction Loss (Monte Carlo approximation). .. math:: -\mathbb{E}_{q(z|x)}[\log p(x|z)] \approx -\frac{1}{L}\sum_{l=1}^L \log p(x|z_l), where :math:`z_l \sim q(z|x)`. Note: This class is a special case of the :attr:`Expectation` class. Examples -------- >>> import torch >>> from pixyz.distributions import Normal >>> q = Normal(loc="x", scale=torch.tensor(1.), var=["z"], cond_var=["x"], features_shape=[64], name="q") # q(z|x) >>> p = Normal(loc="z", scale=torch.tensor(1.), var=["x"], cond_var=["z"], features_shape=[64], name="p") # p(x|z) >>> loss_cls = StochasticReconstructionLoss(q, p) >>> print(loss_cls) - \mathbb{E}_{q(z|x)} \left[\log p(x|z) \right] >>> loss = loss_cls.eval({"x": torch.randn(1,64)}) """ def __init__(self, encoder, decoder, input_var=None): if input_var is None: input_var = encoder.input_var if not(set(decoder.var) <= set(input_var)): raise ValueError("Variable {} (in the `{}` class) is not included" " in `input_var` of the `{}` class.".format(decoder.var, decoder.__class__.__name__, encoder.__class__.__name__)) loss = -decoder.log_prob().expectation(encoder, input_var) super().__init__(loss)