Related papers: Computing High-dimensional Confidence Sets for Arb…
This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
Learning from data in the presence of outliers is a fundamental problem in statistics. In this work, we study robust statistics in the presence of overwhelming outliers for the fundamental problem of subspace recovery. Given a dataset where…
In the hypothesis selection problem, we are given sample and query access to finite set of candidate distributions (hypotheses), $\mathcal{H} = \{H_1, \ldots, H_n\}$, and samples from an unknown distribution $P$, both over a domain…
Existing learning from demonstration algorithms usually assume access to expert demonstrations. However, this assumption is limiting in many real-world applications since the collected demonstrations may be suboptimal or even consist of…
Multivariate histograms are difficult to construct due to the curse of dimensionality. Motivated by $k$-d trees in computer science, we show how to construct an efficient data-adaptive partition of Euclidean space that possesses the…
Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…
When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the…
We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most…
We investigate density estimation from a $n$-sample in the Euclidean space $\mathbb R^D$, when the data is supported by an unknown submanifold $M$ of possibly unknown dimension $d < D$ under a reach condition. We study nonparametric kernel…
We study the optimal sample complexity in large-scale Reinforcement Learning (RL) problems with policy space generalization, i.e. the agent has a prior knowledge that the optimal policy lies in a known policy space. Existing results show…
We study the problem of contextual search, a generalization of binary search in higher dimensions, in the adversarial noise model. Let $d$ be the dimension of the problem, $T$ be the time horizon and $C$ be the total amount of adversarial…
Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…
We revisit the online Unit Clustering and Unit Covering problems in higher dimensions: Given a set of $n$ points in a metric space, that arrive one by one, Unit Clustering asks to partition the points into the minimum number of clusters…
The construction of confidence intervals for the mean of a bounded random variable is a classical problem in statistics with numerous applications in machine learning and virtually all scientific fields. In particular, obtaining the…
We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…
We consider spatial voting where candidates are located in the Euclidean $d$-dimensional space, and each voter ranks candidates based on their distance from the voter's ideal point. We explore the case where information about the location…
We provide a systematic deterministic numerical scheme to approximate the volume (i.e. the Lebesgue measure) of a basic semi-algebraic set whose description follows a sparsity pattern. As in previous works (without sparsity), the underlying…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…