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Stochastic Maximum Likelihood (SML) is a popular direction of arrival (DOA) estimation technique in array signal processing. It is a parametric method that jointly estimates signal and instrument noise by maximum likelihood, achieving…
The Expectation-Maximization algorithm is perhaps the most broadly used algorithm for inference of latent variable problems. A theoretical understanding of its performance, however, largely remains lacking. Recent results established that…
Evolutionary algorithms (EA) have been widely accepted as efficient solvers for complex real world optimization problems, including engineering optimization. However, real world optimization problems often involve uncertain environment…
Multi-agent distributed consensus optimization problems arise in many signal processing applications. Recently, the alternating direction method of multipliers (ADMM) has been used for solving this family of problems. ADMM based distributed…
This paper presents a novel Bayesian strategy for the estimation of smooth signals corrupted by Gaussian noise. The method assumes a smooth evolution of a succession of continuous signals that can have a numerical or an analytical…
We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a…
In this paper, a novel method based on the entropy estimation of the observation space eigenvalues is proposed to estimate the number of the sources in Gaussian and Non-Gaussian noise. In this method, the eigenvalues of correlation matrix…
We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
ADMM is a popular algorithm for solving convex optimization problems. Applying this algorithm to distributed consensus optimization problem results in a fully distributed iterative solution which relies on processing at the nodes and…
In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…
The purpose of this research work is to employ the Optimal Auxiliary Function Method (OAFM) for obtaining numerical approximations of time-dependent nonlinear partial differential equations (PDEs) that arise in many disciplines of science…
We study the convergence of the Expectation-Maximization (EM) algorithm for mixtures of linear regressions with an arbitrary number $k$ of components. We show that as long as signal-to-noise ratio (SNR) is $\tilde{\Omega}(k)$,…
We study the Nonparametric Maximum Likelihood Estimator (NPMLE) for estimating Gaussian location mixture densities in $d$-dimensions from independent observations. Unlike usual likelihood-based methods for fitting mixtures, NPMLEs are based…
Most classification algorithms used in high energy physics fall under the category of supervised machine learning. Such methods require a training set containing both signal and background events and are prone to classification errors…
In the context of the Internet of Things (IoT), sound sensing applications are required to run on embedded platforms where notions of product pricing and form factor impose hard constraints on the available computing power. Whereas…
We deal with the combinatorial problem of learning directed acyclic graph (DAG) structure from observational data adhering to a linear structural equation model (SEM). Leveraging advances in differentiable, nonconvex characterizations of…
We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher order schemes for SDEs based on It\^o-Taylor expansion and…
Stochastic version of alternating direction method of multiplier (ADMM) and its variants (linearized ADMM, gradient-based ADMM) plays a key role for modern large scale machine learning problems. One example is the regularized empirical risk…
This paper develops a probabilistic anticipation algorithm for dynamic objects observed by an autonomous robot in an urban environment. Predictive Gaussian mixture models are used due to their ability to probabilistically capture continuous…
In this paper, we present the discrete-time unbiased extremum seeking (ES) algorithm for n-dimensional (nD) static quadratic maps in the presence of unknown time-varying measurement delays bounded by known constants which can be large. The…