Stark: Fast and Scalable Strassen’s Matrix Multiplication Using Apache Spark

Scalable SDE Filtering and Inference with Apache Spark

In this paper, we consider the problem of Bayesian filtering and inference for time series data modeled as noisy, discrete-time observations of a stochastic differential equation (SDE) with undetermined parameters. We develop a Metropolis algorithm to sample from the high-dimensional joint posterior density of all SDE parameters and state time series. Our approach relies on an innovative densit...

Fast matrix multiplication using coherent configurations

We introduce a relaxation of the notion of tensor rank, called s-rank, and show that upper bounds on the s-rank of the matrix multiplication tensor imply upper bounds on the ordinary rank. In particular, if the “s-rank exponent of matrix multiplication” equals 2, then ω = 2. This connection between the s-rank exponent and the ordinary exponent enables us to significantly generalize the group-th...

Real-time News Recommendations using Apache Spark

Recommending news articles is a challenging task due to the continuous changes in the set of available news articles and the contextdependent preferences of users. Traditional recommender approaches are optimized for analyzing static data sets. In news recommendation scenarios, characterized by continuous changes, high volume of messages, and tight time constraints, alternative approaches are n...

Fast Matrix Multiplication

We give an overview of the history of fast algorithms for matrix multiplication. Along the way, we look at some other fundamental problems in algebraic complexity like polynomial evaluation. This exposition is self-contained. To make it accessible to a broad audience, we only assume a minimal mathematical background: basic linear algebra, familiarity with polynomials in several variables over r...

Fast matrix multiplication