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Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…

We study the problem of learning the topology of a directed Gaussian Graphical Model under the equal-variance assumption, where the graph has $n$ nodes and maximum in-degree $d$. Prior work has established that $O(d \log n)$ samples are…

Despite tremendous progress over the past decade, deep learning methods generally fall short of human-level systematic generalization. It has been argued that explicitly capturing the underlying structure of data should allow connectionist…

Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…

Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in…

A longstanding problem in machine learning is to find unsupervised methods that can learn the statistical structure of high dimensional signals. In recent years, GANs have gained much attention as a possible solution to the problem, and in…

We consider unsupervised estimation of mixtures of discrete graphical models, where the class variable corresponding to the mixture components is hidden and each mixture component over the observed variables can have a potentially different…

Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…

Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We give an algorithm for this problem that has a running time, and data requirement polynomial in the dimension and…

A method is presented for the rhythmic parsing problem: Given a sequence of observed musical note onset times, we estimate the corresponding notated rhythm and tempo process. A graphical model is developed that represents the simultaneous…

Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity…

Dynamic Bayesian networks have been well explored in the literature as discrete-time models: however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm…

We investigate the problem of learning undirected graphical models under Laplacian structural constraints from the point of view of financial market data. We show that Laplacian constraints have meaningful physical interpretations related…

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that…

The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we…

In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…

In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate…

Understanding large-scale patterns in student course enrollment is a problem of great interest to university administrators and educational researchers. Yet important decisions are often made without a good quantitative framework of the…

Graph Neural Networks (GNN) have recently gained popularity in the forecasting domain due to their ability to model complex spatial and temporal patterns in tasks such as traffic forecasting and region-based demand forecasting. Most of…

We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and…