Related papers: An Iterative Scheme for Leverage-based Approximate…

The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…

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…

Statistical inference is often simplified by sample-splitting. This simplification comes at the cost of the introduction of randomness not native to the data. We propose a simple procedure for sequentially aggregating statistics constructed…

In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…

In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately…

This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

This article introduces subbagging (subsample aggregating) estimation approaches for big data analysis with memory constraints of computers. Specifically, for the whole dataset with size $N$, $m_N$ subsamples are randomly drawn, and each…

The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an…

This paper studies statistical aggregation procedures in the regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types…

We consider the challenges that arise when fitting complex ecological models to 'large' data sets. In particular, we focus on random effect models which are commonly used to describe individual heterogeneity, often present in ecological…

The use of big data in official statistics and the applied sciences is accelerating, but statistics computed using only big data often suffer from substantial selection bias. This leads to inaccurate estimation and invalid statistical…

Biological screens are plagued by false positive hits resulting from aggregation. Thus, methods to triage small colloidally aggregating molecules (SCAMs) are in high demand. Herein, we disclose a bespoke machine-learning tool to confidently…

We propose a novel randomized framework for the estimation problem of large-scale linear statistical models, namely Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), which integrates Sketch-and-Solve and…

This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…

We present a subset selection algorithm designed to work with arbitrary model families in a practical batch setting. In such a setting, an algorithm can sample examples one at a time but, in order to limit overhead costs, is only able to…

We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…

Modern statistical analysis often encounters high-dimensional problems but with a limited sample size. It poses great challenges to traditional statistical estimation methods. In this work, we adopt auxiliary learning to solve the…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

We consider the problem of solving a large-scale system of linear equations in a distributed or federated manner by a taskmaster and a set of machines, each possessing a subset of the equations. We provide a comprehensive comparison of two…