Related papers: Optimal Indexes for Sparse Bit Vectors

We consider the problem of preprocessing $N$ points in 2D, each endowed with a priority, to answer the following queries: given a axis-parallel rectangle, determine the point with the largest priority in the rectangle. Using the ideas of…

This paper develops theoretical results regarding noisy 1-bit compressed sensing and sparse binomial regression. We show that a single convex program gives an accurate estimate of the signal, or coefficient vector, for both of these models.…

Semi-structured N:M sparsity and low-bit quantization (e.g., 1.58-bit BitNet) are two promising approaches for improving the efficiency of large language models (LLMs), yet they have largely been studied in isolation. In this work, we…

The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…

The increasing importance of multicore processors calls for a reevaluation of established numerical algorithms in view of their ability to profit from this new hardware concept. In order to optimize the existent algorithms, a detailed…

We propose a routing algorithm that takes a sequence of vectors and computes a new sequence with specified length and vector size. Each output vector maximizes "bang per bit," the difference between a net benefit to use and net cost to…

In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…

Expand-and-sparsify representations are a class of theoretical models that capture sparse representation phenomena observed in the sensory systems of many animals. At a high level, these representations map an input $x \in \mathbb{R}^d$ to…

Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…

In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…

One of the most challenging problems in kernel online learning is to bound the model size and to promote the model sparsity. Sparse models not only improve computation and memory usage, but also enhance the generalization capacity, a…

Analysis of high-dimensional data has led to increased interest in both single index models (SIMs) and the best-subset selection. SIMs provide an interpretable and flexible modeling framework for high-dimensional data, while the best-subset…

Similarity search approaches based on graph walks have recently attained outstanding speed-accuracy trade-offs, taking aside the memory requirements. In this paper, we revisit these approaches by considering, additionally, the memory…

The fully-functional succinct tree representation of Navarro and Sadakane (ACM Transactions on Algorithms, 2014) supports a large number of operations in constant time using $2n+o(n)$ bits. However, the full idea is hard to implement. Only…

Rank and select are fundamental operations in succinct data structures, that is, data structures whose space consumption approaches the information-theoretic optimal. The performance of these primitives is central to the overall performance…

Coreset selection is powerful in reducing computational costs and accelerating data processing for deep learning algorithms. It strives to identify a small subset from large-scale data, so that training only on the subset practically…

We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead…

One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary…

Large spatial datasets often represent a number of spatial point processes generated by distinct entities or classes of events. When crossed with covariates, such as discrete time buckets, this can quickly result in a data set with millions…

The choice dictionary is introduced as a data structure that can be initialized with a parameter $n\in\mathbb{N}=\{1,2,\ldots\}$ and subsequently maintains an initially empty subset $S$ of $\{1,\ldots,n\}$ under insertion, deletion,…