Related papers: An $\widetilde{O}(n)$ Queries Adaptive Tester for …
This papers considers the junta testing problem in a recently introduced ``relative error'' variant of the standard Boolean function property testing model. In relative-error testing we measure the distance from $f$ to $g$, where $f,g:…
Motivated by applications to goodness of fit testing, the empirical likelihood approach is generalized to allow for the number of constraints to grow with the sample size and for the constraints to use estimated criteria functions. The…
Testing to see whether a given data set comes from some specified distribution is among the oldest types of problems in Statistics. Many such tests have been developed and their performance studied. The general result has been that while a…
We study the problem of testing if a function depends on a small number of linear directions of its input data. We call a function $f$ a linear $k$-junta if it is completely determined by some $k$-dimensional subspace of the input space. In…
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends…
We provide two sufficient and necessary conditions to characterize any $n$-bit partial Boolean function with exact quantum 1-query complexity. Using the first characterization, we present all $n$-bit partial Boolean functions that depend on…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
$\newcommand{\F}{\mathbb{F}}$We study the Boolean function parameters sensitivity ($s$), block sensitivity ($bs$), and alternation ($alt$) under specially designed affine transforms. For a function $f:\F_2^n\to \{0,1\}$, and $A=Mx+b$ for $M…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
Let $\xi_0,\xi_1,...$ be independent identically distributed (i.i.d.) random variables such that $\E \log (1+|\xi_0|)<\infty$. We consider random analytic functions of the form $$ G_n(z)=\sum_{k=0}^{\infty} \xi_k f_{k,n} z^k, $$ where…
Given query access to a monotone function $f\colon\{0,1\}^n\to\{0,1\}$ with certificate complexity $C(f)$ and an input $x^{\star}$, we design an algorithm that outputs a size-$C(f)$ subset of $x^{\star}$ certifying the value of…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
Filters are fast, small and approximate set membership data structures. They are often used to filter out expensive accesses to a remote set S for negative queries (that is, a query x not in S). Filters have one-sided errors: on a negative…
A natural measure of smoothness of a Boolean function is its sensitivity (the largest number of Hamming neighbors of a point which differ from it in function value). The structure of smooth or equivalently low-sensitivity functions is still…
We construct an explicit distribution $\mathbf{D}$ over $\{0,1\}^N$ that exhibits an essentially optimal separation between adaptive and non-adaptive cell-probe sampling. The distribution can be sampled exactly when each output bit is…
Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…
For a permutation $\pi: [K]\rightarrow [K]$, a sequence $f: \{1,2,\cdots, n\}\rightarrow \mathbb R$ contains a $\pi$-pattern of size $K$, if there is a sequence of indices $(i_1, i_2, \cdots, i_K)$ ($i_1<i_2<\cdots<i_K$), satisfying that…
We show that, for almost all N-variable Boolean functions f, at least N/4-O(\sqrt{N} log N) queries are required to compute f in quantum black-box model with bounded error.
This paper provides some useful tests for fitting a parametric single-index regression model when covariates are measured with error and validation data is available. We propose two tests whose consistency rates do not depend on the…
This paper examines the problem of nonparametric testing for the no-effect of a random covariate (or predictor) on a functional response. This means testing whether the conditional expectation of the response given the covariate is almost…