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Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
For massive data stored at multiple machines, we propose a distributed subsampling procedure for the composite quantile regression. By establishing the consistency and asymptotic normality of the composite quantile regression estimator from…
Independence screening is a variable selection method that uses a ranking criterion to select significant variables, particularly for statistical models with nonpolynomial dimensionality or "large p, small n" paradigms when p can be as…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
For distributed graph processing on massive graphs, a graph is partitioned into multiple equally-sized parts which are distributed among machines in a compute cluster. In the last decade, many partitioning algorithms have been developed…
Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…
This PhD thesis presents a distributional view of optimization in place of a worst-case perspective. We motivate this view with an investigation of the failure point of classical optimization. Subsequently we consider the optimization of a…
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…
In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…
In this paper, we consider a Bayesian bi-level variable selection problem in high-dimensional regressions. In many practical situations, it is natural to assign group membership to each predictor. Examples include that genetic variants can…
We present a novel segmentation algorithm based on a hierarchical representation of images. The main contribution of this work is to explore the capabilities of the A Contrario reasoning when applied to the segmentation problem, and to…
This paper develops a unified framework, based on iterated random operator theory, to analyze the convergence of constant stepsize recursive stochastic algorithms (RSAs). RSAs use randomization to efficiently compute expectations, and so…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…
Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…
Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…
We propose a divide-and-conquer approach to filtering which decomposes the state variable into low-dimensional components to which standard particle filtering tools can be successfully applied and recursively merges them to recover the full…
Clustering has become an increasingly important task in analysing huge amounts of data. Traditional applications require that all data has to be located at the site where it is scrutinized. Nowadays, large amounts of heterogeneous, complex…
Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck.…