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This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…
We investigate methods for parameter learning from incomplete data that is not missing at random. Likelihood-based methods then require the optimization of a profile likelihood that takes all possible missingness mechanisms into account.…
Estimators derived from an EM algorithm are not robust since they are based on the maximization of the likelihood function. We propose a proximal-point algorithm based on the EM algorithm which aim to minimize a divergence criterion.…
Expectation Maximization (EM) is the standard method to learn Gaussian mixtures. Yet its classic, centralized form is often infeasible, due to privacy concerns and computational and communication bottlenecks. Prior work dealt with data…
We systematically study various network Expectation-Maximization (EM) algorithms for the Gaussian mixture model within the framework of decentralized federated learning. Our theoretical investigation reveals that directly extending the…
The EM algorithm is a widely used methodology for penalized likelihood estimation. Provable monotonicity and convergence are the hallmarks of the EM algorithm and these properties are well established for smooth likelihood and smooth…
Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…
The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…
Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…
The deep-learning-based least squares method has shown successful results in solving high-dimensional non-linear partial differential equations (PDEs). However, this method usually converges slowly. To speed up the convergence of this…
Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning. In its original formulation it is limited to conservative systems, $\textit{i.e.}$ to…
We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i.i.d. samples are known to have lower accuracy than the classical $n^{- \frac{1}{2}}$ error. We investigate…
The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…
Pel-recursive motion estimation isa well-established approach. However, in the presence of noise, it becomes an ill-posed problem that requires regularization. In this paper, motion vectors are estimated in an iterative fashion by means of…
Probabilistic Latent Semantic Analysis is a novel statistical technique for the analysis of two-mode and co-occurrence data, which has applications in information retrieval and filtering, natural language processing, machine learning from…
Parameter estimation in logistic regression is a well-studied problem with the Newton-Raphson method being one of the most prominent optimization techniques used in practice. A number of monotone optimization methods including…
Future wireless networks are envisioned to provide ubiquitous sensing services, which also gives rise to a substantial demand for high-dimensional non-convex parameter estimation, i.e., the associated likelihood function is non-convex and…
When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by…
Non-homogeneous hidden Markov models (NHHMM) are a subclass of dependent mixture models used for semi-supervised learning, where both transition probabilities between the latent states and mean parameter of the probability distribution of…