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In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…
Graph sketching is a powerful paradigm for analyzing graph structure via linear measurements introduced by Ahn, Guha, and McGregor (SODA'12) that has since found numerous applications in streaming, distributed computing, and massively…
Compressed Counting (CC), based on maximally skewed stable random projections, was recently proposed for estimating the p-th frequency moments of data streams. The case p->1 is extremely useful for estimating Shannon entropy of data…
We study the problem of residual error estimation for matrix and vector norms using a linear sketch. Such estimates can be used, for example, to quickly assess how useful a more expensive low-rank approximation computation will be. The…
We determine the minimal experimental resources that ensure a unique solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is…
We adapt a well known streaming algorithm for approximating item frequencies to the matrix sketching setting. The algorithm receives the rows of a large matrix $A \in \R^{n \times m}$ one after the other in a streaming fashion. It maintains…
Maximal clique enumeration (MCE) is a fundamental problem in graph theory and is used in many applications, such as social network analysis, bioinformatics, intelligent agent systems, cyber security, etc. Most existing MCE algorithms focus…
This paper develops a theory and methodology for estimation of Gini index such that both cost of sampling and estimation error are minimum. Methods in which sample size is fixed in advance, cannot minimize estimation error and sampling cost…
Sketching is a dimensionality reduction technique where one compresses a matrix by linear combinations that are chosen at random. A line of work has shown how to sketch the Hessian to speed up each iteration in a second order method, but…
To investigate a dilemma of statistical and computational efficiency faced by long-run variance estimators, we propose a decomposition of kernel weights in a quadratic form and some online inference principles. These proposals allow us to…
We present a formulation of the problem of finding the smallest T -Count circuit that implements a given unitary as a binary search over a sequence of continuous minimization problems, and demonstrate that these problems are numerically…
Kernel methods are learning algorithms that enjoy solid theoretical foundations while suffering from important computational limitations. Sketching, which consists in looking for solutions among a subspace of reduced dimension, is a well…
Statistical inference is often simplified by sample-splitting. This simplification comes at the cost of the introduction of randomness not native to the data. We propose a simple procedure for sequentially aggregating statistics constructed…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
Counting is among the most fundamental operations in computing. For example, counting the pth frequency moment has been a very active area of research, in theoretical computer science, databases, and data mining. When p=1, the task (i.e.,…
Statistical model checking avoids the exponential growth of states associated with probabilistic model checking by estimating properties from multiple executions of a system and by giving results within confidence bounds. Rare properties…
As sketch research has collectively matured over time, its adaptation for at-mass commercialisation emerges on the immediate horizon. Despite an already mature research endeavour for photos, there is no research on the efficient inference…
Computing space-efficient summary, or \textit{a.k.a. sketches}, of large data, is a central problem in the streaming algorithm. Such sketches are used to answer \textit{post-hoc} queries in several data analytics tasks. The algorithm for…
We study the problem of constructing a linear sketch of minimum dimension that allows approximation of a given real-valued function $f \colon \mathbb{F}_2^n \rightarrow \mathbb R$ with small expected squared error. We develop a general…