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In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the…

Pearson's $\rho$ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a…

We study statistical properties of the k-nearest neighbors algorithm for multiclass classification, with a focus on settings where the number of classes may be large and/or classes may be highly imbalanced. In particular, we consider a…

There has been a wide interest to extend univariate and multivariate nonparametric procedures to clustered and hierarchical data. Traditionally, parametric mixed models have been used to account for the correlation structures among the…

Nearest Neighbors Algorithm is a Lazy Learning Algorithm, in which the algorithm tries to approximate the predictions with the help of similar existing vectors in the training dataset. The predictions made by the K-Nearest Neighbors…

We present a new notion of probabilistic duality for random variables involving mixture distributions. Using this notion, we show how to implement a highly-parallelizable Gibbs sampler for weakly coupled discrete pairwise graphical models…

Covariate adjustment can improve precision in analyzing randomized experiments. With fully observed data, regression adjustment and propensity score weighting are asymptotically equivalent in improving efficiency over unadjusted analysis.…

Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a…

In this paper we show that the negative sample distance covariance function is a quasi-concave set function of samples of random variables that are not statistically independent. We use these properties to propose greedy algorithms to…

Meta-analysis is a statistical method to combine results from multiple clinical or genomic studies with the same or similar research problems. It has been widely use to increase statistical power in finding clinical or genomic differences…

In contrastive self-supervised learning, positive samples are typically drawn from the same image but in different augmented views, resulting in a relatively limited source of positive samples. An effective way to alleviate this problem is…

Imbalances in covariates between treatment groups are frequent in observational studies and can lead to biased comparisons. Various adjustment methods can be employed to correct these biases in the context of multi-level treatments ($>$ 2).…

This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…

Nearest neighbor is a popular class of classification methods with many desirable properties. For a large data set which cannot be loaded into the memory of a single machine due to computation, communication, privacy, or ownership…

A default assumption in many machine learning scenarios is that the training and test samples are drawn from the same probability distribution. However, such an assumption is often violated in the real world due to non-stationarity of the…

Randomized controlled trials are the gold standard for measuring causal effects. However, they are often not always feasible, and causal treatment effects must be estimated from observational data. Observational studies do not allow robust…

In this paper, we present a novel approach to fitting mixture models based on estimating first the posterior distribution of the auxiliary variables that assign each observation to a group in the mixture. The posterior distributions of the…

Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…

Forecast combination and model averaging have become popular tools in forecasting and prediction, both of which combine a set of candidate estimates with certain weights and are often shown to outperform single estimates. A data-driven…

In observational studies of treatment effects, matched samples are created so treated and control groups are similar in terms of observable covariates. Traditionally such matched samples consist of matched pairs. If a pair match fails to…