Related papers: Quantum Measurements for Hidden Subgroup Problems …
The hidden subgroup problem (HSP) provides a unified framework to study problems of group-theoretical nature in quantum computing such as order finding and the discrete logarithm problem. While it is known that Fourier sampling provides an…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…
We consider the problem of best subset selection (BSS) under high-dimensional sparse linear regression model. Recently, Guo et al. (2020) showed that the model selection performance of BSS depends on a certain identifiability margin, a…
The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive…
Financial fraud detection poses a typical challenge characterized by class imbalance, where instances of fraud are extremely rare but can lead to unpredictable economic losses if misidentified. Precisely classifying these critical minority…
In classical statistics and distribution testing, it is often assumed that elements can be sampled from some distribution $P$, and that when an element $x$ is sampled, the probability $P$ of sampling $x$ is also known. Recent work in…
We study the problem of differentially private query release assisted by access to public data. In this problem, the goal is to answer a large class $\mathcal{H}$ of statistical queries with error no more than $\alpha$ using a combination…
The sample complexity of simple binary hypothesis testing is the smallest number of i.i.d.\ samples required to distinguish between two distributions $p$ and $q$ in either: (i) the prior-free setting, with type-I error at most $\alpha$ and…
A geometrically uniform (GU) ensemble is a uniformly weighted quantum state ensemble generated from a fixed state by a unitary representation of a finite group $G$. In this work we analyze the problem of discriminating GU ensembles from…
We study the sample complexity of learning an $\epsilon$-optimal policy in the Stochastic Shortest Path (SSP) problem. We first derive sample complexity bounds when the learner has access to a generative model. We show that there exists a…
The group testing problem is concerned with identifying a small set of infected individuals in a large population. At our disposal is a testing procedure that allows us to test several individuals together. In an idealized setting, a test…
We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, consider the symmetric stochastic block model with $q$ groups, average degree $d$, and connection…
We give new upper and lower bounds on the minimax sample complexity of differentially private mean estimation of distributions with bounded $k$-th moments. Roughly speaking, in the univariate case, we show that $n =…
We show a new lower bound on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer statistical queries on high-dimensional databases. The novelty of our bound is that it depends optimally…
Scenario decision making offers a flexible way of making decision in an uncertain environment while obtaining probabilistic guarantees on the risk of failure of the decision. The idea of this approach is to draw samples of the uncertainty…
We consider a broad class of permutation invariant statistical problems by extending the standard decision theoretic definition to allow also selective inference tasks, where the target is specified only after seeing the data. For any such…
One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this…
This work considers the problem of selective-sampling for best-arm identification. Given a set of potential options $\mathcal{Z}\subset\mathbb{R}^d$, a learner aims to compute with probability greater than $1-\delta$, $\arg\max_{z\in…
Consider the problem of finding a population or a probability distribution amongst many with the largest mean when these means are unknown but population samples can be simulated or otherwise generated. Typically, by selecting largest…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…