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This work proposes new inference methods for a regression coefficient of interest in a (heterogeneous) quantile regression model. We consider a high-dimensional model where the number of regressors potentially exceeds the sample size but a…

Reweighting adversarial data during training has been recently shown to improve adversarial robustness, where data closer to the current decision boundaries are regarded as more critical and given larger weights. However, existing methods…

Under interpolation-type assumptions such as the strong growth condition, stochastic optimization methods can attain convergence rates comparable to full-batch methods, but their performance, particularly for SGD, remains highly sensitive…

We consider the problem of solving robust Markov decision process (MDP), which involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels. The goal of planning is to find a robust policy that…

Ordinal classification has been widely applied in many high-stakes applications, e.g., medical imaging and diagnosis, where reliable uncertainty quantification (UQ) is essential for decision making. Conformal prediction (CP) is a general UQ…

Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…

This paper presents a general theoretical framework of penalized quasi-maximum likelihood (PQML) estimation in stationary multiple time series models when the number of parameters possibly diverges. We show the oracle property of the PQML…

Model Predictive Control (MPC) is a versatile approach capable of accommodating diverse control requirements that holds significant promise for a broad spectrum of industrial applications. Noteworthy challenges associated with MPC include…

This study addresses the problem of off-policy evaluation (OPE) from dependent samples obtained via the bandit algorithm. The goal of OPE is to evaluate a new policy using historical data obtained from behavior policies generated by the…

We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…

We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset…

We propose a physics-informed machine learning method for uncertainty quantification in high-dimensional inverse problems. In this method, the states and parameters of partial differential equations (PDEs) are approximated with truncated…

We propose Bayesian Conformal Prediction (BCP), a framework that combines Bayesian posterior predictive distributions with PAC-style conformal risk control to produce prediction sets with finite-sample coverage guarantees. Standard…

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…

How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space $\mathcal{S}$ and the action space $\mathcal{A}$ are both finite, to obtain a nearly optimal policy with…

Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…

This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon…

We consider a distributionally robust Partially Observable Markov Decision Process (DR-POMDP), where the distribution of the transition-observation probabilities is unknown at the beginning of each decision period, but their realizations…