Related papers: Independence of Tabulation-Based Hash Classes
Learning-based hashing algorithms are ``hot topics" because they can greatly increase the scale at which existing methods operate. In this paper, we propose a new learning-based hashing method called ``fast supervised discrete hashing"…
We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to the space of ordered barcodes, from which derivatives can be…
We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an…
Tagging items with descriptive annotations or keywords is a very natural way to compress and highlight information about the properties of the given entity. Over the years several methods have been proposed for extracting a hierarchy…
Hashing method maps similar data to binary hashcodes with smaller hamming distance, and it has received a broad attention due to its low storage cost and fast retrieval speed. However, the existing limitations make the present algorithms…
Consider an experiment involving a potentially small number of subjects. Some random variables are observed on each subject: a high-dimensional one called the "observed" random variable, and a one-dimensional one called the "outcome" random…
We continue the investigation of tabular algebras with trace (a certain class of associative ${\Bbb Z}[v, v^{-1}]$-algebras equipped with distinguished bases) by determining the extent to which the tabular structure may be recovered from a…
Recent theoretical and empirical work in statistical machine learning has demonstrated the importance of learning algorithms for deep architectures, i.e., function classes obtained by composing multiple non-linear transformations.…
Card-based cryptography uses physical playing cards to construct protocols for secure multi-party computation. Existing card-based protocols employ various types of shuffles, some of which are easy to implement in practice while others are…
Although cuckoo hashing has significant applications in both theoretical and practical settings, a relevant downside is that it requires lookups to multiple locations. In many settings, where lookups are expensive, cuckoo hashing becomes a…
Given a suitable collection of partitions of sets, there exists a connection to easy quantum groups via intertwiner maps. A sufficient condition for this correspondence to be one-to-one are particular linear independences on the level of…
Differential privacy is a strong notion for protecting individual privacy in privacy preserving data analysis or publishing. In this paper, we study the problem of differentially private histogram release for random workloads. We study two…
Dictionary learning is a cornerstone of image classification. We set out to address a longstanding challenge in using dictionary learning for classification; that is to simultaneously maximise the discriminability and…
The information theoretic approach to security entails harnessing the correlated randomness available in nature to establish security. It uses tools from information theory and coding and yields provable security, even against an adversary…
Discovery of (strong) association rules, or implications, is an important task in data management, and it finds application in artificial intelligence, data mining and the semantic web. We introduce a novel approach for the discovery of a…
An independent set in a graph is a set of pairwise non-adjacent vertices. Let $\alpha(G)$ denote the cardinality of a maximum independent set in the graph $G = (V, E)$. Gutman and Harary defined the independence polynomial of $G$ \[ I(G;x)…
This paper uses typed linear algebra (LA) to represent data and perform analytical querying in a single, unified framework. The typed approach offers strong type checking (as in modern programming languages) and a diagrammatic way of…
Let $m$ be a positive integer and $D_m(\mathcal {A})$ be the $m$-periodic derived category of a finitary hereditary abelian category $\mathcal {A}$. Applying the derived Hall numbers of the bounded derived category $D^b(\mathcal {A})$, we…
We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…
Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction…