Related papers: Computing High-dimensional Confidence Sets for Arb…
We consider a fundamental problem in unsupervised learning called \emph{subspace recovery}: given a collection of $m$ points in $\mathbb{R}^n$, if many but not necessarily all of these points are contained in a $d$-dimensional subspace $T$…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
Despite rapid advances in AI, safety remains the main bottleneck to deploying machine-learning systems. A critical safety component is out-of-distribution detection: given an input, decide whether it comes from the same distribution as the…
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…
We consider the problem of learning uncertainty regions for parameter estimation problems. The regions are ellipsoids that minimize the average volumes subject to a prescribed coverage probability. As expected, under the assumption of…
Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization,…
Motivated by stochastic optimization, we introduce the problem of learning from samples of contextual value distributions. A contextual value distribution can be understood as a family of real-valued distributions, where each sample…
Distributionally robust reinforcement learning (DR-RL) has recently gained significant attention as a principled approach that addresses discrepancies between training and testing environments. To balance robustness, conservatism, and…
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…
The problem of constructing confidence sets that are adaptive in L^2-loss over a continuous scale of Sobolev classes of probability densities is considered. Adaptation holds, where possible, with respect to both the radius of the Sobolev…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
A set of vectors $S \subseteq \mathbb{R}^d$ is $(k_1,\varepsilon)$-clusterable if there are $k_1$ balls of radius $\varepsilon$ that cover $S$. A set of vectors $S \subseteq \mathbb{R}^d$ is $(k_2,\delta)$-far from being clusterable if…
Multi-distribution learning (MDL), which seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions, has emerged as a unified framework in response to the evolving demand for robustness,…
Models often need to be constrained to a certain size for them to be considered interpretable. For example, a decision tree of depth 5 is much easier to understand than one of depth 50. Limiting model size, however, often reduces accuracy.…
We consider the problem of learning a control policy that is robust against the parameter mismatches between the training environment and testing environment. We formulate this as a distributionally robust reinforcement learning (DR-RL)…
We present and analyze a finite volume scheme of arbitrary order for elliptic equations in the one-dimensional setting. In this scheme, the control volumes are constructed by using the Gauss points in subintervals of the underlying mesh. We…
Motivated by practical applications where stable long-term performance is critical-such as robotics, operations research, and healthcare-we study the problem of distributionally robust (DR) average-reward reinforcement learning. We propose…
In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…
We consider the task of certifying that a random $d$-dimensional subspace $X$ in $\mathbb{R}^n$ is well-spread - every vector $x \in X$ satisfies $c\sqrt{n} \|x\|_2 \leq \|x\|_1 \leq \sqrt{n}\|x\|_2$. In a seminal work, Barak et. al. showed…
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially…