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Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief…
This paper addresses the analysis and design of quadratic neural networks, which have been recently introduced in the literature, and their applications to regression, classification, system identification and control of dynamical systems.…
We analyze the complexity of learning directed acyclic graphical models from observational data in general settings without specific distributional assumptions. Our approach is information-theoretic and uses a local Markov boundary search…
In this work we explore encoding strategies learned by statistical models of sensory coding in noisy spiking networks. Early stages of sensory communication in neural systems can be viewed as encoding channels in the information-theoretic…
Learning the structure of Markov random fields (MRFs) plays an important role in multivariate analysis. The importance has been increasing with the recent rise of statistical relational models since the MRF serves as a building block of…
Training a classifier under non-convex constraints has gotten increasing attention in the machine learning community thanks to its wide range of applications such as algorithmic fairness and class-imbalanced classification. However, several…
Bayesian networks are basic graphical models, used widely both in statistics and artificial intelligence. These statistical models of conditional independence structure are described by acyclic directed graphs whose nodes correspond to…
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…
We present a novel approach to modelling and learning vector fields from physical systems using neural networks that explicitly satisfy known linear operator constraints. To achieve this, the target function is modelled as a linear…
Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem…
Optimal sensor scheduling with applications to networked estimation and control systems is considered. We model sensor measurement and transmission instances using jumps between states of a continuous-time Markov chain. We introduce a cost…
Humans are remarkably flexible when understanding new sentences that include combinations of concepts they have never encountered before. Recent work has shown that while deep networks can mimic some human language abilities when presented…
Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small…
Markov decision processes continue to gain in popularity for modeling a wide range of applications ranging from analysis of supply chains and queuing networks to cognitive science and control of autonomous vehicles. Nonetheless, they tend…
In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node…
Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…
The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…
A point-to-point wireless communication system in which the transmitter is equipped with an energy harvesting device and a rechargeable battery, is studied. Both the energy and the data arrivals at the transmitter are modeled as Markov…