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We study iterative methods for (two-stage) robust combinatorial optimization problems with discrete uncertainty. We propose a machine-learning-based heuristic to determine starting scenarios that provide strong lower bounds. To this end, we…

Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…

Model explainability is crucial for human users to be able to interpret how a proposed classifier assigns labels to data based on its feature values. We study generalized linear models constructed using sets of feature value rules, which…

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…

Expressive evaluation metrics are indispensable for informative experiments in all areas, and while several metrics are established in some areas, in others, such as feature selection, only indirect or otherwise limited evaluation metrics…

In this work, an adaptive predictive control scheme for linear systems with unknown parameters and bounded additive disturbances is proposed. In contrast to related adaptive control approaches that robustly consider the parametric…

Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly applied to them. Instead, feature maps (or representations)…

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…

This paper presents robust inference methods for general linear hypotheses in linear panel data models with latent group structure in the coefficients. We employ a selective conditional inference approach, deriving the conditional…

Feature selection in machine learning is subject to the intrinsic randomness of the feature selection algorithms (for example, random permutations during MDA). Stability of selected features with respect to such randomness is essential to…

This paper provides a semiparametric model of estimating states of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we…

The fixed-point analysis refers to the study of fixed-points that arise in the context of complex systems with many interacting entities. In this expository paper, we describe four levels of fixed-points in mean-field interacting particle…

We discuss recently developed methods that quantify the stability and generalizability of statistical findings under distributional changes. In many practical problems, the data is not drawn i.i.d. from the target population. For example,…

Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such…

We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…

We use Stein characterizations to obtain new moment-type estimators for the parameters of three classical spherical distributions (namely the Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the i.i.d. case. This leads…

We consider likelihood-based two-step estimation of latent variable models, in which just the measurement model is estimated in the first step and the measurement parameters are then fixed at their estimated values in the second step where…

The decay of unstable states when several metastable states are available for occupation is investigated using path-integral techniques. Specifically, a method is described which allows the probabilities with which the metastable states are…

Two-time-scale stochastic approximation is a popular iterative method for finding the solution of a system of two equations. Such methods have found broad applications in many areas, especially in machine learning and reinforcement…