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We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Maximum entropy reinforcement learning (MaxEnt-RL) has become the standard approach to RL due to its beneficial exploration properties. Traditionally, policies are parameterized using Gaussian distributions, which significantly limits their…

Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing maximum likelihood estimate when dealing with Gaussian Mixture Model (GMM). When the sample size is smaller than the data dimension, this could lead…

The Expectation--Maximization Maximum Likelihood (EMML) algorithm belongs to the Expectation--Maximization family and is widely used for image reconstruction problems under Poisson noise.In this paper, we reinterpret EMML as a mirror…

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce…

Finite mixture models are among the most popular statistical models used in different data science disciplines. Despite their broad applicability, inference under these models typically leads to computationally challenging non-convex…

A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach…

Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not…

We propose a joint channel estimation and data detection algorithm for massive multilple-input multiple-output systems based on diffusion models. Our proposed method solves the blind inverse problem by sampling from the joint posterior…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

Diffusion models have recently shown remarkable results in magnetic resonance imaging reconstruction. However, the employed networks typically are black-box estimators of the (smoothed) prior score with tens of millions of parameters,…

The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…

In this work, we address the problem of estimating sparse communication channels in OFDM systems in the presence of carrier frequency offset (CFO) and unknown noise variance. To this end, we consider a convex optimization problem, including…

Unlike the ordinary least-squares (OLS) estimator for the linear model, a ridge regression linear model provides coefficient estimates via shrinkage, usually with improved mean-square and prediction error. This is true especially when the…

The horseshoe prior is known to possess many desirable properties for Bayesian estimation of sparse parameter vectors, yet its density function lacks an analytic form. As such, it is challenging to find a closed-form solution for the…

We present a reconstruction method involving maximum-likelihood expectation maximization (MLEM) to model Poisson noise as applied to fluorescence molecular tomography (FMT). MLEM is initialized with the output from a sparse…

Maximum likelihood (ML) learning for energy-based models (EBMs) is challenging, partly due to non-convergence of Markov chain Monte Carlo.Several variations of ML learning have been proposed, but existing methods all fail to achieve both…

In this paper, we investigate the diffusion least mean square (DLMS) algorithm over fading channel, where in addition to channel noise and path-loss the inter-node-interference (INI) among neighboring nodes of a host node is also taken into…

This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when…

In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…