Related papers: Fast inference of ill-posed problems within a conv…
Quite generally, constraint-based metabolic flux analysis describes the space of viable flux configurations for a metabolic network as a high-dimensional polytope defined by the linear constraints that enforce the balancing of production…
In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
The last decade has witnessed an explosion in the development of models, theory and computational algorithms for "big data" analysis. In particular, distributed computing has served as a natural and dominating paradigm for statistical…
In this work we propose a novel algorithmic strategy that allows for an efficient characterization of the whole set of stable fluxes compatible with the metabolic constraints. The algorithm, based on the well-known Bethe approximation,…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…
Analysis of high-dimensional data is currently a popular field of research, thanks to many applications e.g. in genetics (DNA data in genomewide association studies), spectrometry or web analysis. At the same time, the type of problems that…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
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…
In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…
In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
The presence of missing values within high-dimensional data is an ubiquitous problem for many applied sciences. A serious limitation of many available data mining and machine learning methods is their inability to handle partially missing…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a…
In large-scale, data-driven applications, parameters are often only known approximately due to noise and limited data samples. In this paper, we focus on high-dimensional optimization problems with linear constraints under uncertain…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…