We consider log-supermodular models on binary variables, which are probabilistic models with negative log-densities which are submodular. These models provide probabilistic interpretations of common combinatorial optimization tasks such as image segmentation. In this paper, we focus primarily on parameter estimation in the models from known upper-bounds on the intractable log-partition function. We show that the bound based on separable optimization on the base polytope of the submodular function is always inferior to a bound based on ``perturb-and-MAP'' ideas. Then, to learn parameters, given that our approximation of the log-partition function is an expectation (over our own randomization), we use a stochastic subgradient technique to maximize a lower-bound on the log-likelihood. This can also be extended to conditional maximum likelihood. We illustrate our new results in a set of experiments in binary image denoising, where we highlight the flexibility of a probabilistic model to learn with missing data.

We present a new type of probabilistic model which we call DISsimilarity COefficient Networks (DISCO Nets). DISCO Nets allow us to efficiently sample from a posterior distribution parametrised by a neural network. During training, DISCO Nets are learned by minimising the dissimilarity coefficient between the true distribution and the estimated distribution. This allows us to tailor the training to the loss related to the task at hand. We empirically show that (i) by modeling uncertainty on the output value, DISCO Nets outperform equivalent non-probabilistic predictive networks and (ii) DISCO Nets accurately model the uncertainty of the output, outperforming existing probabilistic models based on deep neural networks.

Code is available at https://github.com/wl-zhao/UniPC . In this paper, we propose a training-free framework for the fast sampling of DPMs called UniPC .

Variational Bayes (VB) is a scalable alternative to Markov chain Monte Carlo (MCMC)forBayesian posterior inference.

In recent years, convolutional neural networks (CNNs) are applied to various visual recognition tasks with great success [7, 8, 14].

These mechanisms typically retrieve items in a single step and are fixed after training.

Arya et al. suggest using either supervised or self-supervised learning techniques to train the NN; the former requires access to exact inference