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Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations such as Bayesian and Markov networks…
Stochastic approximation algorithms are iterative procedures which are used to approximate a target value in an environment where the target is unknown and direct observations are corrupted by noise. These algorithms are useful, for…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…
To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is…
The process of data mining produces various patterns from a given data source. The most recognized data mining tasks are the process of discovering frequent itemsets, frequent sequential patterns, frequent sequential rules and frequent…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…
In this paper, we derive nearly tight probabilistic norm bounds for a class of random matrices we call graph matrices. While the classical case of symmetric matrices with independent random entries (Wigner's matrices) is a special case, in…
This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
We study algorithms for approximating the permanent of a random matrix when the entries are slightly biased away from zero. This question is motivated by the goal of understanding the classical complexity of linear optics and \emph{boson…
We study dynamic algorithms for maintaining fundamental algebraic properties of matrices, specifically, rank, basis, and full-rank submatrices, with applications to maximum matching on dynamic graphs. Prior dynamic algorithms for rank…
We propose a proximal point algorithm to solve LAROS problem, that is the problem of finding a "large approximately rank-one submatrix". This LAROS problem is used to sequentially extract features in data. We also develop a new stopping…
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
Baswana, Gupta and Sen [FOCS'11] showed that fully dynamic maximal matching can be maintained in general graphs with logarithmic amortized update time. More specifically, starting from an empty graph on $n$ fixed vertices, they devised a…
A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…
The preferential attachment (PA) model is a popular way of modeling dynamic social networks, such as collaboration networks. Assuming that the PA function takes a parametric form, we propose and study the maximum likelihood estimator of the…
We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of $n$ objects from data through interactions of comparison or collaboration. Under a general framework of…
We show an algorithm for computing the permanent of a random matrix with vanishing mean in quasi-polynomial time. Among special cases are the Gaussian, and biased-Bernoulli random matrices with mean 1/lnln(n)^{1/8}. In addition, we can…
Randomized trace estimation is a popular and well studied technique that approximates the trace of a large-scale matrix $B$ by computing the average of $x^T Bx$ for many samples of a random vector $X$. Often, $B$ is symmetric positive…