Related papers: Relative-error unateness testing
In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: - whose sample complexity…
A simple test is proposed for examining the correctness of a given completely specified response function against unspecified general alternatives in the context of univariate regression. The usual diagnostic tools based on residuals plots…
We initiate the study of property testing of submodularity on the boolean hypercube. Submodular functions come up in a variety of applications in combinatorial optimization. For a vast range of algorithms, the existence of an oracle to a…
We study the number of queries needed to identify a monotone Boolean function $f:\{0,1\}^n \rightarrow \{0,1\}$. A query consists of a 0-1-sequence, and the answer is the value of $f$ on that sequence. It is well-known that the number of…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
The problem of testing monotonicity for Boolean functions on the hypergrid, $f:[n]^d \to \{0,1\}$ is a classic topic in property testing. When $n=2$, the domain is the hypercube. For the hypercube case, a breakthrough result of…
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…
We study the extremal competitive ratio of Boolean function evaluation. We provide the first non-trivial lower and upper bounds for classes of Boolean functions which are not included in the class of monotone Boolean functions. For the…
We study the probability of Boolean functions with small max influence to become constant under random restrictions. Let $f$ be a Boolean function such that the variance of $f$ is $\Omega(1)$ and all its individual influences are bounded by…
This paper studies the problem of testing whether a function is monotone from a nonparametric Bayesian perspective. Two new families of tests are constructed. The first uses constrained smoothing splines, together with a hierarchical…
A sequence $f\colon\{1,\dots,n\}\to\mathbb{R}$ contains a permutation $\pi$ of length $k$ if there exist $i_1<\dots<i_k$ such that, for all $x,y$, $f(i_x)<f(i_y)$ if and only if $\pi(x)<\pi(y)$; otherwise, $f$ is said to be $\pi$-free. In…
Properties of Boolean functions can often be tested much faster than the functions can be learned. However, this advantage usually disappears when testers are limited to random samples of a function $f$--a natural setting for data…
A sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding. While sensitivity analyses in matched observational studies have been well addressed when there is a single outcome…
We present an adaptive algorithm with one-sided error for the problem of junta testing for Boolean function under the challenging distribution-free setting, the query complexity of which is $\widetilde O(k)/\epsilon$. This improves the…
We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noiseless, and the case when the measurements are…
The nonparametric estimators built by minimizing the mean squared relative error are gaining in popularity for their robustness in the presence of outliers in comparison to the Nadaraya Watson estimators. In this paper we build a relative…
Recently, there has been significant work studying distribution testing under the Conditional Sampling model. In this model, a query specifies a subset $S$ of the domain, and the output received is a sample drawn from the distribution…
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…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
We investigate the proximal map for the weighted mean absolute error function. An algorithm for its efficient and vectorized evaluation is presented. As a demonstration, this algorithm is applied as part of a checkerboard algorithm to solve…