Related papers: On extracting common random bits from correlated s…

Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…

Sampling from combinatorial families can be difficult. However, complicated families can often be embedded within larger, simpler ones, for which easy sampling algorithms are known. We take advantage of such a relationship to describe a…

We develop an approach for unsupervised learning of associations between co-occurring perceptual events using a large graph. We applied this approach to successfully solve the image captcha of China's railroad system. The approach is based…

The decision problem of perfect matchings in uniform hypergraphs is famously an NP-complete problem. It has been shown by Keevash--Knox--Mycroft [STOC, 2013] that for every $\varepsilon>0$, such decision problem restricted to $k$-uniform…

Consider the following probability puzzle: A fair coin is flipped n times. For each HT in the resulting sequence, Bob gets a point, and for each HH Alice gets a point. Who is more likely to win? We provide a proof that Bob wins more often…

Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…

In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that,…

The problem of predicting a sequence $x_1,x_2,...$ generated by a discrete source with unknown statistics is considered. Each letter $x_{t+1}$ is predicted using information on the word $x_1x_2... x_t$ only. In fact, this problem is a…

Estimating a large alphabet probability distribution from a limited number of samples is a fundamental problem in machine learning and statistics. A variety of estimation schemes have been proposed over the years, mostly inspired by the…

We consider the problem of learning co-occurrence information between two word categories, or more in general between two discrete random variables taking values in a hierarchically classified domain. In particular, we consider the problem…

We consider the problem of private computation of approximate Heavy Hitters. Alice and Bob each hold a vector and, in the vector sum, they want to find the B largest values along with their indices. While the exact problem requires linear…

In communication complexity the input of a function $f:X\times Y\rightarrow Z$ is distributed between two players Alice and Bob. If Alice knows only $x\in X$ and Bob only $y\in Y$, how much information must Alice and Bob share to be able to…

A random k-out mapping (digraph) on [n] is generated by choosing k random images of each vertex one at a time, subject to a "preferential attachment" rule: the current vertex selects an image i with probability proportional to a given…

Quantum cryptography shows that one can guarantee the secrecy of correlation on the sole basis of the laws of physics, that is without limiting the computational power of the eavesdropper. The usual security proofs suppose that the…

We propose several sampling architectures for the efficient acquisition of an ensemble of correlated signals. We show that without prior knowledge of the correlation structure, each of our architectures (under different sets of assumptions)…

We address the problem of constructing a fast lossless code in the case when the source alphabet is large. The main idea of the new scheme may be described as follows. We group letters with small probabilities in subsets (acting as super…

This paper addresses the uniform random generation of words from a context-free language (over an alphabet of size $k$), while constraining every letter to a targeted frequency of occurrence. Our approach consists in a multidimensional…

In this paper we obtain some bounds on communication complexity of Gap Hamming Distance problem ($\mathsf{GHD}^n_{L, U}$): Alice and Bob are given binary string of length $n$ and they are guaranteed that Hamming distance between their…

Bilateral agreement based random undirected graphs were introduced and analyzed by La and Kabkab in 2015. The construction of the graph with $n$ vertices in this model uses a (random) preference order on other $n-1$ vertices and each vertex…

We consider an abstraction of computational security in password protected systems where a user draws a secret string of given length with i.i.d. characters from a finite alphabet, and an adversary would like to identify the secret string…