Related papers: Compression for Quadratic Similarity Queries
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
In practical data integration systems, it is common for the data sources being integrated to provide conflicting information about the same entity. Consequently, a major challenge for data integration is to derive the most complete and…
We introduce a new distance-preserving compact representation of multi-dimensional point-sets. Given $n$ points in a $d$-dimensional space where each coordinate is represented using $B$ bits (i.e., $dB$ bits per point), it produces a…
We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved…
In various data settings, it is necessary to compare observations from disparate data sources. We assume the data is in the dissimilarity representation and investigate a joint embedding method that results in a commensurate representation…
Random Number Generators play a critical role in a number of important applications. In practice, statistical testing is employed to gather evidence that a generator indeed produces numbers that appear to be random. In this paper, we…
Today's exponentially increasing data volumes and the high cost of storage make compression essential for the Big Data industry. Although research has concentrated on efficient compression, fast decompression is critical for analytics…
Data deduplication saves storage space by identifying and removing repeats in the data stream. Compared with traditional compression methods, data deduplication schemes are more time efficient and are thus widely used in large scale storage…
The information spectrum approach gives general formulae for optimal rates of various information theoretic protocols, under minimal assumptions on the nature of the sources, channels and entanglement resources involved. This paper…
In Sequential Massive Random Access (SMRA), a set of correlated sources is jointly encoded and stored on a server, and clients want to access to only a subset of the sources. Since the number of simultaneous clients can be huge, the server…
We provide a framework for one-shot quantum rate distortion coding, in which the goal is to determine the minimum number of qubits required to compress quantum information as a function of the probability that the distortion incurred upon…
The distortion-rate function of output-constrained lossy source coding with limited common randomness is analyzed for the special case of squared error distortion measure. An explicit expression is obtained when both source and…
Data compression algorithms typically rely on identifying repeated sequences of symbols from the original data to provide a compact representation of the same information, while maintaining the ability to recover the original data from the…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
Understanding the impact of data structure on the computational tractability of learning is a key challenge for the theory of neural networks. Many theoretical works do not explicitly model training data, or assume that inputs are drawn…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
Computable Information Density (CID), the ratio of the length of a losslessly compressed data file to that of the uncompressed file, is a measure of order and correlation in both equilibrium and nonequilibrium systems. Here we show that…
Approximating the solution of the nonlinear filtering problem with Gaussian mixtures has been a very popular method since the 1970s. However, the vast majority of such approximations are introduced in an ad-hoc manner without theoretical…
In recent years, as data and problem sizes have increased, distributed learning has become an essential tool for training high-performance models. However, the communication bottleneck, especially for high-dimensional data, is a challenge.…
This paper studies the minimum achievable source coding rate as a function of blocklength $n$ and probability $\epsilon$ that the distortion exceeds a given level $d$. Tight general achievability and converse bounds are derived that hold at…