Related papers: Optimal Boolean Locality-Sensitive Hashing
In the problem of minimal perfect hashing, we are given a size $k$ subset $\mathcal{A}$ of a universe of keys $[n] = \{1,2, \cdots, n\}$, for which we wish to construct a hash function $h: [n] \to [k]$ such that $h(\cdot)$ maps…
Hierarchical classification offers an approach to incorporate the concept of mistake severity by leveraging a structured, labeled hierarchy. However, decoding in such settings frequently relies on heuristic decision rules, which may not…
We show that under minimal assumptions on a class of functions $\mathcal{H}$ defined on a probability space $(\mathcal{X},\mu)$, there is a threshold $\Delta_0$ satisfying the following: for every $\Delta\geq\Delta_0$, with probability at…
Suppose $X$ is a uniformly distributed $n$-dimensional binary vector and $Y$ is obtained by passing $X$ through a binary symmetric channel with crossover probability $\alpha$. A recent conjecture by Courtade and Kumar postulates that…
The optimal receiver operating characteristic (ROC) curve, giving the maximum probability of detection as a function of the probability of false alarm, is a key information-theoretic indicator of the difficulty of a binary hypothesis…
This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…
We present new algorithms for estimating and testing \emph{collision probability}, a fundamental measure of the spread of a discrete distribution that is widely used in many scientific fields. We describe an algorithm that satisfies…
We study distributed (strongly convex) optimization problems over a network of agents, with no centralized nodes. The loss functions of the agents are assumed to be \textit{similar}, due to statistical data similarity or otherwise. In order…
In this paper, we show a construction of locality-sensitive hash functions without false negatives, i.e., which ensure collision for every pair of points within a given radius $R$ in $d$ dimensional space equipped with $l_p$ norm when $p…
In the misspecified spectral algorithms problem, researchers usually assume the underground true function $f_{\rho}^{*} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ for…
We establish local boundedness and local H\"older continuity of weak solutions to the following prototype problem: $$ -\operatorname{div}\left(|x|^{-2 \beta}|\nabla u|^{\mathbf{q}-2} \nabla u\right)+(-\Delta)_{p(\cdot, \cdot),…
We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the alphabet size $S$ is…
The area under the ROC curve is widely used as a measure of performance of classification rules. However, it has recently been shown that the measure is fundamentally incoherent, in the sense that it treats the relative severities of…
Let $f: T\to \{ 0,1 \}$ be a Boolean function on the Boolean half-slice, $T$, \ie elements of $\{0,1\}^n$ with Hamming weight $n/2$. We show that if $f(x)+f(y)=f(x+y)$ holds with probability $\frac{1+\delta}{2}$ over a uniform pair $(x,y)$…
In this paper, we explore a distributed setting, where a user seeks to compute a linearly-separable Boolean function of degree $M$ from $N$ servers, each with a cache size $M$. Exploiting the fundamental concepts of sensitivity and…
We describe a simple deterministic $O( \varepsilon^{-1} \log \Delta)$ round distributed algorithm for $(2\alpha+1)(1 + \varepsilon)$ approximation of minimum weighted dominating set on graphs with arboricity at most $\alpha$. Here $\Delta$…
The sensitivity of a Boolean function f is the maximum over all inputs x, of the number of sensitive coordinates of x. The well-known sensitivity conjecture of Nisan (see also Nisan and Szegedy) states that every sensitivity-s Boolean…
The {\em Total Influence} ({\em Average Sensitivity) of a discrete function is one of its fundamental measures. We study the problem of approximating the total influence of a monotone Boolean function \ifnum\plusminus=1 $f: \{\pm1\}^n…
A central problem in computational statistics is to convert a procedure for sampling combinatorial from an objects into a procedure for counting those objects, and vice versa. Weconsider sampling problems coming from *Gibbs distributions*,…
The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…