Related papers: Maximum leave-one-out likelihood estimation for lo…
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…
We propose an inlier-based outlier detection method capable of both identifying the outliers and explaining why they are outliers, by identifying the outlier-specific features. Specifically, we employ an inlier-based outlier detection…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After…
A Maximum Likelihood recursive state estimator is derived for non-linear and non-Gaussian state-space models. The estimator combines a particle filter to generate the conditional density and the Expectation Maximization algorithm to compute…
The parameter estimation of unnormalized models is a challenging problem. The maximum likelihood estimation (MLE) is computationally infeasible for these models since normalizing constants are not explicitly calculated. Although some…
Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present…
We consider a semiparametric mixture of two univariate density functions where one of them is known while the weight and the other function are unknown. Such mixtures have a history of application to the problem of detecting differentially…
Opinion dynamics models such as the bounded confidence models (BCMs) describe how a population can reach consensus, fragmentation, or polarization, depending on a few parameters. Connecting such models to real-world data could help…
We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation…
In this paper, we consider maximum likelihood estimations of the degree of freedom parameter $\nu$, the location parameter $\mu$ and the scatter matrix $\Sigma$ of the multivariate Student-$t$ distribution. In particular, we are interested…
We consider covariance parameter estimation for a Gaussian process under inequality constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotics. We address the estimation of the variance parameter and the estimation of…
The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…
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…
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.…
The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to…
Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here…