Related papers: Massive data compression for parameter-dependent c…
Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
Accurate covariance matrices are required for a reliable estimation of cosmological parameters from pseudo-power spectrum estimators. In this work, we focus on the analytical calculation of covariance matrices. We consider the case of…
Using 1000 ray-tracing simulations for a {\Lambda}-dominated cold dark model in Sato et al. (2009), we study the covariance matrix of cosmic shear correlation functions, which is the standard statistics used in the previous measurements.…
Pruning and quantization techniques have been broadly successful in reducing the number of parameters needed for large neural networks, yet theoretical justification for their empirical success falls short. We consider a randomized greedy…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
Scientific practice typically involves repeatedly studying a system, each time trying to unravel a different perspective. In each study, the scientist may take measurements under different experimental conditions (interventions,…
Cosmological parameter estimation requires that the likelihood function of the data is accurately known. Assuming that cosmological large-scale structure power spectra data are multivariate Gaussian-distributed, we show the accuracy of…
Data management is becoming increasingly important in dealing with the large amounts of data produced by large-scale scientific simulations and instruments. Existing multilevel compression algorithms offer a promising way to manage…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
Recent studies have demonstrated improved skill in numerical weather prediction via the use of spatially correlated observation error covariance information in data assimilation systems. In this case, the observation weighting matrices…
Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples…
The excellent performance of deep neural networks is usually accompanied by a large number of parameters and computations, which have limited their usage on the resource-limited edge devices. To address this issue, abundant methods such as…
We consider the $\mathcal{H}^2$-formatted compression and computational estimation of covariance functions on a compact set in $\mathbb{R}^d$. The classical sample covariance or Monte Carlo estimator is prohibitively expensive for many…
We propose a computationally intensive method, the random lasso method, for variable selection in linear models. The method consists of two major steps. In step 1, the lasso method is applied to many bootstrap samples, each using a set of…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
With the advent of deep learning application on edge devices, researchers actively try to optimize their deployments on low-power and restricted memory devices. There are established compression method such as quantization, pruning, and…
Deep neural networks are often highly overparameterized, prohibiting their use in compute-limited systems. However, a line of recent works has shown that the size of deep networks can be considerably reduced by identifying a subset of…
We propose a data segmentation methodology for the high-dimensional linear regression problem where regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages: first, the data are…
One strategy for adversarially training a robust model is to maximize its certified radius -- the neighborhood around a given training sample for which the model's prediction remains unchanged. The scheme typically involves analyzing a…