Related papers: Convergence of the EM algorithm via proximal techn…
This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the…
This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal…
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…
Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
The Expectation-Maximization (EM) algorithm for mixture models often results in slow or invalid convergence. The popular convergence proof affirms that the likelihood increases with Q; Q is increasing in the M -step and non-decreasing in…
We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the…
Many practitioners who use the EM algorithm complain that it is sometimes slow. When does this happen, and what can be done about it? In this paper, we study the general class of bound optimization algorithms - including…
The purpose of this paper is to establish the almost sure weak ergodic convergence of a sequence of iterates $(x_n)$ given by $x_{n+1} = (I+\lambda_n A(\xi_{n+1},\,.\,))^{-1}(x_n)$ where $(A(s,\,.\,):s\in E)$ is a collection of maximal…
Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim,…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
The estimation of missing input vector elements in real time processing applications requires a system that possesses the knowledge of certain characteristics such as correlations between variables, which are inherent in the input space.…
Incremental gradient and incremental proximal methods are a fundamental class of optimization algorithms used for solving finite sum problems, broadly studied in the literature. Yet, without strong convexity, their convergence guarantees…
This work investigates the convergence behavior of augmented Lagrangian methods (ALMs) when applied to convex optimization problems that may be infeasible. ALMs are a popular class of algorithms for solving constrained optimization…
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…
We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
Mixture models of Plackett-Luce (PL) -- one of the most fundamental ranking models -- are an active research area of both theoretical and practical significance. Most previously proposed parameter estimation algorithms instantiate the EM…
We incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed for finding the zeros of a maximally monotone operator in real Hilbert…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…