相关论文: Singularity, Misspecification, and the Convergence…
We study the approximation of expectations $\E(f(X))$ for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms,…
Though very popular, it is well known that the EM for GMM algorithm suffers from non-Gaussian distribution shapes, outliers and high-dimensionality. In this paper, we design a new robust clustering algorithm that can efficiently deal with…
Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction over fifty years ago, and is now commonly utilized within a family setting. Families of mixture models arise when the component…
Evidential-EM (E2M) algorithm is an effective approach for computing maximum likelihood estimations under finite mixture models, especially when there is uncertain information about data. In this paper we present an extension of the E2M…
We consider 1-dimensional location estimation, where we estimate a parameter $\lambda$ from $n$ samples $\lambda + \eta_i$, with each $\eta_i$ drawn i.i.d. from a known distribution $f$. For fixed $f$ the maximum-likelihood estimate (MLE)…
The EM-algorithm is a general procedure to get maximum likelihood estimates if part of the observations on the variables of a network are missing. In this paper a stochastic version of the algorithm is adapted to probabilistic neural…
Although the expectation maximisation (EM) algorithm was introduced in 1970, it remains somewhat inaccessible to machine learning practitioners due to its obscure notation, terse proofs and lack of concrete links to modern machine learning…
This paper addresses maximum likelihood (ML) estimation based model fitting in the context of extrasolar planet detection. This problem is featured by the following properties: 1) the candidate models under consideration are highly…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty…
Finite mixture of skew distributions have emerged as an effective tool in modelling heterogeneous data with asymmetric features. With various proposals appearing rapidly in the recent years, which are similar but not identical, the…
Dasgupta and Shulman showed that a two-round variant of the EM algorithm can learn mixture of Gaussian distributions with near optimal precision with high probability if the Gaussian distributions are well separated and if the dimension is…
We study estimation and clustering in Gaussian mixture models under variance misspecification. Observations are generated with true variance $\sigma^2$, while the component means are estimated using a likelihood with variance $\tau^2$,…
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…
Entity Matching (EM) is a critical task in numerous fields, such as healthcare, finance, and public administration, as it identifies records that refer to the same entity within or across different databases. EM faces considerable…
The EM algorithm is a generic tool that offers maximum likelihood solutions when datasets are incomplete with data values missing at random or completely at random. At least for its simplest form, the algorithm can be rewritten in terms of…
Cluster-weighted modeling (CWM) is a mixture approach for modeling the joint probability of a response variable and a set of explanatory variables. The parameters are estimated by means of the expectation-maximization algorithm according to…
This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with…
A key problem in the theory of meta-learning is to understand how the task distributions influence transfer risk, the expected error of a meta-learner on a new task drawn from the unknown task distribution. In this paper, focusing on fixed…
A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization…