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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…
We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on $\gamma$-divergence. A novel feature of the…
This paper studies inference for quadratic forms of linear regression coefficients with clustered data and many covariates. Our framework covers three important special cases: instrumental variables regression with many instruments and…
As with the advancement of geographical information systems, non-Gaussian spatial data sets are getting larger and more diverse. This study develops a general framework for fast and flexible non-Gaussian regression, especially for…
Multivariate linear regression is a fundamental statistical task, but classical estimators such as ordinary least squares are highly sensitive to outliers. These may occur as casewise outliers that affect entire observations, or as outlying…
In practical applications of regression analysis, it is not uncommon to encounter a multitude of values for each attribute. In such a situation, the univariate distribution, which is typically Gaussian, is suboptimal because the mean may be…
As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…
Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…
In medical studies, the collected covariates usually contain underlying outliers. For clustered /longitudinal data with censored observations, the traditional Gehan-type estimator is robust to outliers existing in response but sensitive to…
The mixture cure rate model is the most commonly used cure rate model in the literature. In the context of mixture cure rate model, the standard approach to model the effect of covariates on the cured or uncured probability is to use a…
Classical semiparametric inference with missing outcome data is not robust to contamination of the observed data and a single observation can have arbitrarily large influence on estimation of a parameter of interest. This sensitivity is…
Data analysis based on information from several sources is common in economic and biomedical studies. This setting is often referred to as the data fusion problem, which differs from traditional missing data problems since no complete data…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
The Best-Worst Method (BWM) is a well-known Multi-Criteria Decision-Making (MCDM) method. This article deals with the multiplicative model of BWM. We first formulate an optimization model that is equivalent to the existing multiplicative…
ProfileGLMM is an R package integrating Generalised Linear Mixed Models (GLMMs) as the outcome model for Bayesian profile regression. This statistical framework simultaneously i) explains the variation in the outcome and ii) clusters the…
We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…
In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness.…
We investigate statistical properties of Cluster-Weighted Modeling, which is a framework for supervised learning originally developed in order to recreate a digital violin with traditional inputs and realistic sound. The analysis is carried…
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…
Linear mixed models are widely used for analyzing hierarchically structured data involving missingness and unbalanced study designs. We consider a Bayesian clustering method that combines linear mixed models and predictive projections. For…