Related papers: Tight Bounds for Hashing Block Sources
Given two discrete random variables $X$ and $Y,$ with probability distributions ${\bf p}=(p_1, \ldots , p_n)$ and ${\bf q}=(q_1, \ldots , q_m)$, respectively, denote by ${\cal C}({\bf p}, {\bf q})$ the set of all couplings of ${\bf p}$ and…
We develop some theoretical results for a robust similarity measure named "generalized min-max" (GMM). This similarity has direct applications in machine learning as a positive definite kernel and can be efficiently computed via…
Hashing has recently sparked a great revolution in cross-modal retrieval because of its low storage cost and high query speed. Recent cross-modal hashing methods often learn unified or equal-length hash codes to represent the multi-modal…
Precise quantum key distribution (QKD) secure bound analysis is essential for practical QKD systems. The effect of uniformity of random number seed for privacy amplification is not considered in existing secure bound analysis. In this…
Randomness extraction is an essential post-processing step in practical quantum cryptography systems. When statistical fluctuations are taken into consideration, the requirement of large input data size could heavily penalise the speed and…
Given complex numbers $a, b, c$ and a non-negative continuous function $\varphi$ defined on $[0, +\infty)$, consider the $2 \times 2$ matrix $$ M_t = \begin{pmatrix} a & t \\ ct & b\varphi(t) \end{pmatrix}, \quad t \in [0, +\infty). $$ We…
Characterising the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterising all information inequalities. The majority of…
The Leftover Hash Lemma states that the output of a two-universal hash function applied to an input with sufficiently high entropy is almost uniformly random. In its standard formulation, the lemma refers to a notion of randomness that is…
Given two jointly distributed random variables $(X,Y)$, a functional representation of $X$ is a random variable $Z$ independent of $Y$, and a deterministic function $g(\cdot, \cdot)$ such that $X=g(Y,Z)$. The problem of finding a minimum…
We show that the conditional min-entropy Hmin(A|B) of a bipartite state rho_AB is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the B-part of rho_AB are allowed. In the special…
Quantum key distribution (QKD) achieves information-theoretic security, without relying on computational assumptions, by distributing quantum states. To establish secret bits, two honest parties exploit key distillation protocols over…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
In this paper we analyze a hash function for $k$-partitioning a set into bins, obtaining strong concentration bounds for standard algorithms combining statistics from each bin. This generic method was originally introduced by Flajolet and…
Clustering is a fundamental task in machine learning and data analysis, but it frequently fails to provide fair representation for various marginalized communities defined by multiple protected attributes -- a shortcoming often caused by…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
We study the communication complexity of multiplying $k\times t$ elements from the group $H=\text{SL}(2,q)$ in the number-on-forehead model with $k$ parties. We prove a lower bound of $(t\log H)/c^{k}$. This is an exponential improvement…
Inspired by mobile satellite communication systems and the important and prevalent applications of computational tasks, we consider a distributed source coding model for compressing vector-linear functions, which consists of multiple…
We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The algorithm uses a weighted average of the Shannon Entropies of the string and all but the last binary…
We introduce simple, efficient algorithms for computing a MinHash of a probability distribution, suitable for both sparse and dense data, with equivalent running times to the state of the art for both cases. The collision probability of…
Learning to hash is an efficient paradigm for exact and approximate nearest neighbor search from massive databases. Binary hash codes are typically extracted from an image by rounding output features from a CNN, which is trained on a…