Related papers: A Characterization of Constant-Sample Testable Pro…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
This paper develops a framework for the estimation of the functional mean and the functional principal components when the functions form a random field. More specifically, the data we study consist of curves $X(\mathbf{s}_k;t),t\in[0,T]$,…
Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
We study finite-sample inference for the trade-off function of two unknown probability distributions, the function that traces the optimal type I/type II error frontier in binary testing. Given samples from distributions $P$ and $Q$, we…
Let G be a graph with n vertices, and let k be an integer dividing n. G is said to be strongly k-colorable if for every partition of V(G) into disjoint sets V_1 \cup ... \cup V_r, all of size exactly k, there exists a proper vertex…
The graph and hypergraph container methods are powerful tools with a wide range of applications across combinatorics. Recently, Blais and Seth (FOCS 2023) showed that the graph container method is particularly well-suited for the analysis…
We initiate the study of property testing problems concerning relations between permutations. In such problems, the input is a tuple $(\sigma_1,\dotsc,\sigma_d)$ of permutations on $\{1,\dotsc,n\}$, and one wishes to determine whether this…
Random matrices like GUE, GOE and GSE have been studied for decades and have been shown that they possess a lot of nice properties. In 2005, a new property of independent GUE random matrices is discovered by Haagerup and Thorbj{\o}rnsen in…
A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the…
We characterize the model spaces $K_\Theta$ in which functions with smooth boundary extensions are dense. It is shown that such approximations are possible if and only if the singular measure associated to the singular inner factor of…
The normal distribution has the unique property that the cumulant generating function has only two terms, namely those involving the mean and the variance. This property is used to construct a simple by using the log of the modulus of the…
The problem of testing hypothesis that a density function has no more than $\mu$ derivatives versus it has more than $\mu$ derivatives is considered. For a solution, the $L^2$ norms of wavelet orthogonal projections on some orthogonal…
We investigate properties of a bootstrap-based methodology for testing hypotheses about equality of certain characteristics of the distributions between different populations in the context of functional data. The suggested testing…
The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…
A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…
A Boolean function $f:V \to \{-1,1\}$ on the vertex set of a graph $G=(V,E)$ is locally $p$-stable if for every vertex $v$ the proportion of neighbours $w$ of $v$ with $f(v)=f(w)$ is exactly $p$. This notion was introduced by Gross and…
For a permutation $\pi:[k] \to [k]$, a function $f:[n] \to \mathbb{R}$ contains a $\pi$-appearance if there exists $1 \leq i_1 < i_2 < \dots < i_k \leq n$ such that for all $s,t \in [k]$, $f(i_s) < f(i_t)$ if and only if $\pi(s) < \pi(t)$.…
We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the…