Related papers: Sample-based high-dimensional convexity testing
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
We study the minimax sample complexity of multicalibration in the batch setting. A learner observes $n$ i.i.d. samples from an unknown distribution and must output a (possibly randomized) predictor whose population multicalibration error,…
Hypothesis testing is a statistical inference approach used to determine whether data supports a specific hypothesis. An important type is the two-sample test, which evaluates whether two sets of data points are from identical…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…
One popular trend in meta-learning is to learn from many training tasks a common initialization for a gradient-based method that can be used to solve a new task with few samples. The theory of meta-learning is still in its early stages,…
A hypothesis testing algorithm is replicable if, when run on two different samples from the same distribution, it produces the same output with high probability. This notion, defined by by Impagliazzo, Lei, Pitassi, and Sorell [STOC'22],…
This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
We give nearly optimal bounds on the sample complexity of $(\widetilde{\Omega}(\epsilon),\epsilon)$-tolerant testing the $\rho$-independent set property in the dense graph setting. In particular, we give an algorithm that inspects a random…
We initiate a systematic study of tolerant testers of image properties or, equivalently, algorithms that approximate the distance from a given image to the desired property (that is, the smallest fraction of pixels that need to change in…
Given a sample of size $N$, it is often useful to select a subsample of smaller size $n<N$ to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the…
We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…
Consider a pair of cumulative distribution functions $F$ and $G$, where $F$ is unknown and $G$ is a known reference distribution. Given a sample from $F$, we propose tests to detect the convexity or the concavity of $G^{-1}\circ F$ versus…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
In this paper, we consider lower bounds on the query complexity for testing CSPs in the bounded-degree model. First, for any ``symmetric'' predicate $P:{0,1}^{k} \to {0,1}$ except \equ where $k\geq 3$, we show that every (randomized)…
A set $S \subset \mathbb{Z}^d$ is digital convex if $conv(S) \cap \mathbb{Z}^d = S$, where $conv(S)$ denotes the convex hull of $S$. In this paper, we consider the algorithmic problem of testing whether a given set $S$ of $n$ lattice points…
The standard paired-sample testing approach in the multidimensional setting applies multiple univariate tests on the individual features, followed by p-value adjustments. Such an approach suffers when the data carry numerous features. A…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…