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Models of discrete-valued outcomes are easily misspecified if the data exhibit zero-inflation, overdispersion or contamination. Without additional knowledge about the existence and nature of this misspecification, model inference and…
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. This problem is magnified in high-dimensional settings where the number of variables $p$ diverges with the sample size $n$, as well…
The study of model bias and variance with respect to decision boundaries is critically important in supervised classification. There is generally a tradeoff between the two, as fine-tuning of the decision boundary of a classification model…
The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…
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…
Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for…
Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…
The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between centre and surround classes. Discriminant power of features for the classification is measured as mutual…
In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and in particular consider unbalanced settings. First, the problem of estimating multiple negative multinomial parameter vectors…
We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…
We explore why many recently proposed robust estimation problems are efficiently solvable, even though the underlying optimization problems are non-convex. We study the loss landscape of these robust estimation problems, and identify the…
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…
Regression depth, introduced by Rousseeuw and Hubert in 1999, is a notion that measures how good of a regression hyperplane a given query hyperplane is with respect to a set of data points. Under projective duality, this can be interpreted…
Distribution shifts are ubiquitous in real-world machine learning applications, posing a challenge to the generalization of models trained on one data distribution to another. We focus on scenarios where data distributions vary across…
Sensitivity and specificity evaluated at an optimal diagnostic cut-off are fundamental measures of classification accuracy when continuous biomarkers are used for disease diagnosis. Joint inference for these quantities is challenging…
In numerous regular statistical models, median bias reduction (Kenne Pagui et al., 2017) has proven to be a noteworthy improvement over maximum likelihood, alternative to mean bias reduction. The estimator is obtained as solution to a…
In this article, we introduce the concept of model confidence bounds (MCB) for variable selection in the context of nested models. Similarly to the endpoints in the familiar confidence interval for parameter estimation, the MCB identifies…
The sample mean is among the most well studied estimators in statistics, having many desirable properties such as unbiasedness and consistency. However, when analyzing data collected using a multi-armed bandit (MAB) experiment, the sample…