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Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and…
Analyzing relational data consisting of multiple samples or layers involves critical challenges: How many networks are required to capture the variety of structures in the data? And what are the structures of these representative networks?…
This dissertation investigates integer linear programming (ILP) formulation of Bayesian Network structure learning problem. We review the definition and key properties of Bayesian network and explain score metrics used to measure how well…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
Bayesian networks are probabilistic graphical models with a wide range of application areas including gene regulatory networks inference, risk analysis and image processing. Learning the structure of a Bayesian network (BNSL) from discrete…
Bayesian methods have been successfully applied to sparsify weights of neural networks and to remove structure units from the networks, e. g. neurons. We apply and further develop this approach for gated recurrent architectures.…
We uncover a strong correspondence between Bayesian Networks and (Multiplicative) Linear Logic Proof-Nets, relating the two as a representation of a joint probability distribution and at the level of computation, so yielding a…
We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…
We introduce a pruning algorithm that provably sparsifies the parameters of a trained model in a way that approximately preserves the model's predictive accuracy. Our algorithm uses a small batch of input points to construct a data-informed…
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…
We present a systematic and detailed study of the robustness of directed networks under random and targeted removal of links. We work with a set of network models of random and scale free type, generated with specific features of clustering…
Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replacement of their…
Algorithms for learning the conditional probabilities of Bayesian networks with hidden variables typically operate within a high-dimensional search space and yield only locally optimal solutions. One way of limiting the search space and…
This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that…
We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems,…
Data-driven optimization of sampling patterns in MRI has recently received a significant attention.Following recent observations on the combinatorial number of minimizers in off-the-grid optimization, we propose a framework to globally…
Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an…