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Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…
We propose a novel resampling-based method to construct an asymptotically exact test for any subset of hypotheses on coefficients in high-dimensional linear regression. It can be embedded into any multiple testing procedure to make…
The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Subsampling is one of the popular methods to balance statistical efficiency and computational efficiency in the big data era. Most approaches aim at selecting informative or representative sample points to achieve good overall information…
Subsampling from a large data set is useful in many supervised learning contexts to provide a global view of the data based on only a fraction of the observations. Diverse (or space-filling) subsampling is an appealing subsampling approach…
The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…
Variance estimation is a fundamental problem in statistical modeling. In ultrahigh dimensional linear regressions where the dimensionality is much larger than sample size, traditional variance estimation techniques are not applicable.…
Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…
The problem of dimension reduction is of increasing importance in modern data analysis. In this paper, we consider modeling the collection of points in a high dimensional space as a union of low dimensional subspaces. In particular we…
Supervised learning under measurement constraints is a common challenge in statistical and machine learning. In many applications, despite extensive design points, acquiring responses for all points is often impractical due to resource…
Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…
Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
Background: Embedded feature selection in high-dimensional data with very small sample sizes requires optimized hyperparameters for the model building process. For this hyperparameter optimization, nested cross-validation must be applied to…
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…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
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…