Related papers: Randomized Dimension Reduction with Statistical Gu…
Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
Many machine learning algorithms minimize a regularized risk, and stochastic optimization is widely used for this task. When working with massive data, it is desirable to perform stochastic optimization in parallel. Unfortunately, many…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
Recent work has shown that data augmentation has the potential to significantly improve the generalization of deep learning models. Recently, automated augmentation strategies have led to state-of-the-art results in image classification and…
Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of ``components.'' Typically, these components are linear combinations of the rows and columns of the matrix, and are thus…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…
Modern biomedical datasets are increasingly high dimensional and exhibit complex correlation structures. Generalized Linear Mixed Models (GLMMs) have long been employed to account for such dependencies. However, proper specification of the…
The growing interest for high dimensional and functional data analysis led in the last decade to an important research developing a consequent amount of techniques. Parallelized algorithms, which consist in distributing and treat the data…
In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…
In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension…
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…
We present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $n \times n$ distance matrix as input, where $n$ is the number of individuals,…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the…
We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm.…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
The rapid growth of digital data has heightened the demand for efficient lossless compression methods. However, existing algorithms exhibit trade-offs: some achieve high compression ratios, others excel in encoding or decoding speed, and…