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Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…
Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…
In many randomized trials, outcomes such as essays or open-ended responses must be manually scored as a preliminary step to impact analysis, a process that is costly and limiting. Model-assisted estimation offers a way to combine surrogate…
In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…
Shape-constrained inference has wide applicability in bioassay, medicine, economics, risk assessment, and many other fields. Although there has been a large amount of work on monotone-constrained univariate curve estimation, multivariate…
We herein propose a new robust estimation method based on random projections that is adaptive and, automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted…
To fast approximate maximum likelihood estimators with massive data, this paper studies the Optimal Subsampling Method under the A-optimality Criterion (OSMAC) for generalized linear models. The consistency and asymptotic normality of the…
When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…
Approximate Bayesian Computation (ABC) is a powerful method for carrying out Bayesian inference when the likelihood is computationally intractable. However, a drawback of ABC is that it is an approximate method that induces a systematic…
We consider the Ensemble Kalman Inversion which has been recently introduced as an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting. In the case of large data sets, the Ensemble Kalman…
Sharpness-aware Minimization (SAM) has been proposed recently to improve model generalization ability. However, SAM calculates the gradient twice in each optimization step, thereby doubling the computation costs compared to stochastic…
Data reduction is a fundamental challenge of modern technology, where classical statistical methods are not applicable because of computational limitations. We consider multiple linear regression for an extraordinarily large number of…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
Model performance evaluation is a critical and expensive task in machine learning and computer vision. Without clear guidelines, practitioners often estimate model accuracy using a one-time completely random selection of the data. However,…
This work aims to improve the sample efficiency of parallel large-scale ranking and selection (R&S) problems by leveraging correlation information. We modify the commonly used "divide and conquer" framework in parallel computing by adding a…
The method of stable random projections is a tool for efficiently computing the $l_\alpha$ distances using low memory, where $0<\alpha \leq 2$ is a tuning parameter. The method boils down to a statistical estimation task and various…
The problem of automatically clustering data is an age old problem. People have created numerous algorithms to tackle this problem. The execution time of any of this algorithm grows with the number of input points and the number of cluster…