Related papers: Lower Bounds for Convexity Testing
In this paper we analyze the necessary number of samples to estimate the gradient of any multidimensional smooth (possibly non-convex) function in a zero-order stochastic oracle model. In this model, an estimator has access to noisy values…
Monotonicity testing of Boolean functions on the hypergrid, $f:[n]^d \to \{0,1\}$, is a classic topic in property testing. Determining the non-adaptive complexity of this problem is an important open question. For arbitrary $n$,…
Le Cam's two-point testing method yields perhaps the simplest lower bound for estimating the mean of a distribution: roughly, if it is impossible to well-distinguish a distribution centered at $\mu$ from the same distribution centered at…
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the…
This paper studies the problem of testing if an input (Gamma,*), where Gamma is a finite set of unknown size and * is a binary operation over Gamma given as an oracle, is close to a specified class of groups. Friedl et al. [Efficient…
We investigate the issue of model selection and the use of the nonconformity (strangeness) measure in batch learning. Using the nonconformity measure we propose a new training algorithm that helps avoid the need for Cross-Validation or…
We consider the Stochastic Boolean Function Evaluation (SBFE) problem where the task is to efficiently evaluate a known Boolean function $f$ on an unknown bit string $x$ of length $n$. We determine $f(x)$ by sequentially testing the…
In this paper, we derive mutual information based upper and lower bounds on the number of nonadaptive group tests required to identify a given number of "non defective" items from a large population containing a small number of "defective"…
Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
We study the problems of identity and closeness testing of $n$-dimensional product distributions. Prior works by Canonne, Diakonikolas, Kane and Stewart (COLT 2017) and Daskalakis and Pan (COLT 2017) have established tight sample complexity…
In a group testing scheme, a set of tests is designed to identify a small number $t$ of defective items that are present among a large number $N$ of items. Each test takes as input a group of items and produces a binary output indicating…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…
We consider testing for presence of a signal in Gaussian white noise with intensity 1/sqrt(n), when the alternatives are given by smoothness ellipsoids with an L2-ball of (squared) radius rho removed. It is known that, for a fixed Sobolev…
In recent years, the mathematical limits and algorithmic bounds for probabilistic group testing have become increasingly well-understood, with exact asymptotic thresholds now being known in general scaling regimes for the noiseless setting.…
We study the problem of estimating the number of edges in an $n$-vertex graph, accessed via the Bipartite Independent Set query model introduced by Beame et al. (ITCS '18). In this model, each query returns a Boolean, indicating the…
We consider the problem of proper learning a Boolean Halfspace with integer weights $\{0,1,\ldots,t\}$ from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks $n^{O(t^5)}$ membership…
The classic problems of testing uniformity of and learning a discrete distribution, given access to independent samples from it, are examined under general $\ell_p$ metrics. The intuitions and results often contrast with the classic…
Given samples from two distributions over an $n$-element set, we wish to test whether these distributions are statistically close. We present an algorithm which uses sublinear in $n$, specifically, $O(n^{2/3}\epsilon^{-8/3}\log n)$,…