Related papers: The Optimal Quantile Estimator for Compressed Coun…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
A data sketch algorithm scans a big data set, collecting a small amount of data -- the sketch, which can be used to statistically infer properties of the big data set. Some data sketch algorithms take a fixed-size random sample of a big…
Quantized Indexing is a fast and space-efficient form of enumerative (combinatorial) coding, the strongest among asymptotically optimal universal entropy coding algorithms. The present advance in enumerative coding is similar to that made…
The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
The distortion-rate performance of certain randomly-designed scalar quantizers is determined. The central results are the mean-squared error distortion and output entropy for quantizing a uniform random variable with thresholds drawn…
The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…
Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped…
As a competitive alternative to least squares regression, quantile regression is popular in analyzing heterogenous data. For quantile regression model specified for one single quantile level $\tau$, major difficulties of semiparametric…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
Statistical modeling often involves identifying an optimal estimate to some underlying probability distribution known to satisfy some given constraints. I show here that choosing as estimate the centroid, or center of mass, of the set…
In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum…
Based on the maximum likelihood estimation principle, we derive a collaborative estimation framework that fuses several different estimators and yields a better estimate. Applying it to compressive sensing (CS), we propose a collaborative…
We describe a general framework -- compressive statistical learning -- for resource-efficient large-scale learning: the training collection is compressed in one pass into a low-dimensional sketch (a vector of random empirical generalized…
Efficient estimation of wideband spectrum is of great importance for applications such as cognitive radio. Recently, sub-Nyquist sampling schemes based on compressed sensing have been proposed to greatly reduce the sampling rate. However,…
Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
We present a general problem formulation for optimal parameter estimation based on quantized observations, with application to antenna array communication and processing (channel estimation, time-of-arrival (TOA) and direction-of-arrival…
The recent framework of compressive statistical learning aims at designing tractable learning algorithms that use only a heavily compressed representation-or sketch-of massive datasets. Compressive K-Means (CKM) is such a method: it…
The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We begin by establishing…
A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits.…