Related papers: Randomized algorithms for matrices and data

In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…

Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…

The growing interest for high dimensional and functional data analysis led in the last decade to an important research developing a consequent amount of techniques. Parallelized algorithms, which consist in distributing and treat the data…

In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…

This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…

Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…

We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…

Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…

There is an increasing body of work exploring the integration of random projection into algorithms for numerical linear algebra. The primary motivation is to reduce the overall computational cost of processing large datasets. A suitably…

Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…

Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…

Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…

We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…

This thesis explores the benefits machine learning algorithms can bring to online planning and scheduling for autonomous vehicles in off-road situations. Mainly, we focus on typical problems of interest which include computing itineraries…

The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…

Randomized algorithms have proven to perform well on a large class of numerical linear algebra problems. Their theoretical analysis is critical to provide guarantees on their behaviour, and in this sense, the stochastic analysis of the…