Related papers: Probabilistic methods for approximate archetypal a…

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely…

We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…

Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…

Archetypal analysis is a data decomposition method that describes each observation in a dataset as a convex combination of "pure types" or archetypes. These archetypes represent extrema of a data space in which there is a trade-off between…

We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…

The increasing digitalization in industry and society leads to a growing abundance of data available to be processed and exploited. However, the high volume of data requires considerable computational resources for applying machine learning…

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…

Approximate Bayesian Computation (ABC) methods are applicable to statistical models specified by generative processes with analytically intractable likelihoods. These methods try to approximate the posterior density of a model parameter by…

Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…

Hierarchical learning algorithms that gradually approximate a solution to a data-driven optimization problem are essential to decision-making systems, especially under limitations on time and computational resources. In this study, we…

Archetypal analysis and non-negative matrix factorization (NMF) are staples in a statisticians toolbox for dimension reduction and exploratory data analysis. We describe a geometric approach to both NMF and archetypal analysis by…

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…

In this thesis I develop a variety of techniques to train, evaluate, and sample from intractable and high dimensional probabilistic models. Abstract exceeds arXiv space limitations -- see PDF.

In this work, we provide the first practical evaluation of the structural rounding framework for approximation algorithms. Structural rounding works by first editing to a well-structured class, efficiently solving the edited instance, and…

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…

Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…

Many new database application domains such as experimental sciences and medicine are characterized by large sequences as their main form of data. Using approximate representation can significantly reduce the required storage and search…