Related papers: Sigma-Point Filtering and Smoothing Based Paramete…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…
The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…
(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…
In this manuscript, we consider a finite multivariate nonparametric mixture model where the dependence between the marginal densities is modeled using the copula device. Pseudo EM stochastic algorithms were recently proposed to estimate all…
We consider a linear model which can have a large number of explanatory variables, the errors with an asymmetric distribution or some values of the explained variable are missing at random. In order to take in account these several…
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…
Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used…
Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters - show performance degradation when applied to nonlinear systems whose uncertainty follows…
Fast Incremental Expectation Maximization (FIEM) is a version of the EM framework for large datasets. In this paper, we first recast FIEM and other incremental EM type algorithms in the {\em Stochastic Approximation within EM} framework.…
In this paper, we describe a novel application of sigma-point methods to continuous-discrete filtering. In principle, the nonlinear continuous- discrete filtering problem can be solved exactly. In practice, the solution contains terms that…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…
We propose a two-step pseudo-maximum likelihood procedure for semiparametric single-index regression models where the conditional variance is a known function of the regression and an additional parameter. The Poisson single-index…
We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for…