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It is shown in [10] that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to operate on effective intervals to obtain regular Dirichlet…

Time series forecasting in real-world applications requires both high predictive accuracy and interpretable uncertainty quantification. Traditional point prediction methods often fail to capture the inherent uncertainty in time series data,…

Multiple regression has been the go-to method for data analysis for generations of scholars due to its transparency, interpretability, and desirable theoretical properties. However, the method's simplicity precludes the discovery of complex…

This paper introduces new empirical process tools for analyzing a broad class of statistical learning models under heavy-tailed noise and complex function classes. Our primary contribution is the derivation of two Dudley-type maximal…

While there is a rich literature on robust methodologies for contamination in continuously distributed data, contamination in categorical data is largely overlooked. This is regrettable because many datasets are categorical and oftentimes…

Dynamic Item Response Models extend the standard Item Response Theory (IRT) to capture temporal dynamics in learner ability. While these models have the potential to allow instructional systems to actively monitor the evolution of learner…

The median absolute deviation (MAD) is a robust measure of scale that is simple to implement and easy to interpret. Motivated by this, we introduce interval estimators of the MAD to make reliable inferences for dispersion for a single…

Human-generated categorical annotations frequently produce empirical response distributions (soft labels) that reflect ambiguity rather than simple annotator error. We introduce an ambiguity measure that maps a discrete response…

Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust…

We propose a general optimization-based framework for computing differentially private M-estimators and a new method for constructing differentially private confidence regions. Firstly, we show that robust statistics can be used in…

Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…

Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…

Handling missing data is a central challenge in data-driven analysis. Modern imputation methods not only aim for accurate reconstruction but also differ in how they represent and quantify uncertainty. Yet, the reliability and calibration of…

Missingness in categorical data is a common problem in various real applications. Traditional approaches either utilize only the complete observations or impute the missing data by some ad hoc methods rather than the true conditional…

Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in…

The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown…

We consider the estimation of Dirichlet Process Mixture Models (DPMMs) in distributed environments, where data are distributed across multiple computing nodes. A key advantage of Bayesian nonparametric models such as DPMMs is that they…

The integrated conditional moment (ICM) test is a classical and widely used method for assessing the adequacy of regression models. Although it performs well in fixed-dimension settings, its behavior changes dramatically when the predictor…

A crucial step in fitting a regression model to data is determining the model's structure, i.e., the subset of explanatory variables to be included. However, the uncertainty in this step is often overlooked due to a lack of satisfactory…