Related papers: Mixture Proportion Estimation Beyond Irreducibilit…
Finite mixture models have been widely used for the modelling and analysis of data from heterogeneous populations. Maximum likelihood estimation of the parameters is typically carried out via the Expectation-Maximization (EM) algorithm. The…
This paper proposes a new approach to estimating the distribution of a response variable conditioned on observing some factors. The proposed approach possesses desirable properties of flexibility, interpretability, tractability and…
We consider the situation where the observed sample contains some observations whose class of origin is known (that is, they are classified with respect to the g underlying classes of interest), and where the remaining observations in the…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
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…
This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models.…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
Masked autoencoders (MAEs) have recently demonstrated effectiveness in tabular data imputation. However, due to the inherent heterogeneity of tabular data, the uniform random masking strategy commonly used in MAEs can disrupt the…
Understanding model's sensitivity to its training data is crucial but can also be challenging and costly, especially during training. To simplify such issues, we present the Memory-Perturbation Equation (MPE) which relates model's…
We propose Partially Interpretable Estimators (PIE) which attribute a prediction to individual features via an interpretable model, while a (possibly) small part of the PIE prediction is attributed to the interaction of features via a…
Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system…
Although by now the ensemble-based probabilistic forecasting is the most advanced approach to weather prediction, ensemble forecasts still might suffer from lack of calibration and/or display systematic bias, thus require some…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model…
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong…
The reasoning-based pose estimation (RPE) benchmark has emerged as a widely adopted evaluation standard for pose-aware multimodal large language models (MLLMs). Despite its significance, we identified critical reproducibility and…
We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We prove the existence of an optimal MAPE model and we show the universal consistency of Empirical…
In order to develop reliable services using machine learning, it is important to understand the uncertainty of the model outputs. Often the probability distribution that the prediction target follows has a complex shape, and a mixture…
We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate…
When estimating finite mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this work, we make no distributional assumptions on the mixture components and instead assume that…
We present alphaPDE, a new multivariate analysis technique for parameter estimation. The method is based on a direct construction of joint probability densities of known variables and the parameters to be estimated. We show how posterior…