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Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by…

Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…

We propose a supervised learning approach for predicting an underlying graph from a set of graph signals. Our approach is based on linear regression. In the linear regression model, we predict edge-weights of a graph as the output, given a…

We consider the task of learning latent community structure from multiple correlated networks. First, we study the problem of learning the latent vertex correspondence between two edge-correlated stochastic block models, focusing on the…

We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…

Despite prior advances in PINNs, significant challenges remain in localized solid mechanics problems because of the limitations of single network formulations in simultaneous resolution of smooth global responses and near-tip singularities,…

The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…

Deep Learning (DL) is one of the most common subjects when Machine Learning and Data Science approaches are considered. There are clearly two movements related to DL: the first aggregates researchers in quest to outperform other algorithms…

Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…

Biological systems are driven by intricate interactions among the complex array of molecules that comprise the cell. Many methods have been developed to reconstruct network models of those interactions. These methods often draw on large…

Latent space models are frequently used for modeling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well-developed for more complex…

We propose a new way of thinking about deep neural networks, in which the linear and non-linear components of the network are naturally derived and justified in terms of principles in probability theory. In particular, the models…

We introduce learning to condition (L2C), a scalable, data-driven framework for accelerating Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs), a fundamentally intractable problem. L2C trains a neural…

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…

Deep neural networks have become very popular in modeling complex nonlinear processes due to their extraordinary ability to fit arbitrary nonlinear functions from data with minimal expert intervention. However, they are almost always…

Graphs have become pervasive tools to represent information and datasets with irregular support. However, in many cases, the underlying graph is either unavailable or naively obtained, calling for more advanced methods to its estimation.…

Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…

Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling…

Probabilistic graphical models (PGMs) provide a compact and flexible framework to model very complex real-life phenomena. They combine the probability theory which deals with uncertainty and logical structure represented by a graph which…