Discrete and especially binary random variables occur in many machine learning models, notably in variational autoencoders with binary latent states and in stochastic binary networks.
The importance of Variational Autoencoders reaches far beyond standalone generative models -- the approach is also used for learning latent representations and can be generalized to semi-supervised learning.
Training neural networks with binary weights and activations is a challenging problem due to the lack of gradients and difficulty of optimization over discrete weights.
In neural networks with binary activations and or binary weights the training by gradient descent is complicated as the model has piecewise constant response.
We consider the maximum-a-posteriori inference problem in discrete graphical models and study solvers based on the dual block-coordinate ascent rule.
Dense, discrete Graphical Models with pairwise potentials are a powerful class of models which are employed in state-of-the-art computer vision and bio-imaging applications.
It has been proposed by many researchers that combining deep neural networks with graphical models can create more efficient and better regularized composite models.
Probabilistic Neural Networks deal with various sources of stochasticity: input noise, dropout, stochastic neurons, parameter uncertainties modeled as random variables, etc.
Learning, taking into account full distribution of the data, referred to as generative, is not feasible with deep neural networks (DNNs) because they model only the conditional distribution of the outputs given the inputs.
We tackle the computation- and memory-intensive operations on the 4D cost volume by a min-projection which reduces memory complexity from quadratic to linear and binary descriptors for efficient matching.
Specifically, we show that general energy minimization, even in the 2-label pairwise case, and planar energy minimization with three or more labels are exp-APX-complete.
In particular, the joint M-best diverse labelings can be obtained by running a non-parametric submodular minimization (in the special case - max-flow) solver for M different values of $\gamma$ in parallel, for certain diversity measures.
Dense image matching is a fundamental low-level problem in Computer Vision, which has received tremendous attention from both discrete and continuous optimization communities.
For polyhedral relaxations of such problems it is generally not true that variables integer in the relaxed solution will retain the same values in the optimal discrete solution.
We propose a novel polynomial time algorithm to obtain a part of its optimal non-relaxed integral solution.
We propose a new sufficient condition for partial optimality which is: (1) verifiable in polynomial time (2) invariant to reparametrization of the problem and permutation of labels and (3) includes many existing sufficient conditions as special cases.