Related papers: Randomized Dimension Reduction with Statistical Gu…
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…
Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…
The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to…
Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw…
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…
Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…
Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…
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…
High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the…
We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i.e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…
It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace. Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. Even…
In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…