Related papers: Maximum Likelihood Recursive State Estimation usin…
Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are…
This paper revisits the work of Rauch et al. (1965) and develops a novel method for recursive maximum likelihood particle filtering for general state-space models. The new method is based on statistical analysis of incomplete observations…
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…
We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…
Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known…
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…
We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence rate and features a simple adaptive…
We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…
Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we…
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…
We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…
This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…
Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…
Reinforcement learning is the method of choice to train models in sampling-based setups with binary outcome feedback, such as navigation, code generation, and mathematical problem solving. In such settings, models implicitly induce a…
In this contribution, we present an online method for joint state and parameter estimation in jump Markov non-linear systems (JMNLS). State inference is enabled via the use of particle filters which makes the method applicable to a wide…
Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…
Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…
Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum…