相关论文: Cleaning the correlation matrix with a denoising a…

We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…

The asymptotic behavior of estimates and information criteria in linear models are studied in the context of hierarchically correlated sampling units. The work is motivated by biological data collected on species where autocorrelation is…

Although data may be abundant, complete data is less so, due to missing columns or rows. This missingness undermines the performance of downstream data products that either omit incomplete cases or create derived completed data for…

Optimization in the latent space of variational autoencoders is a promising approach to generate high-dimensional discrete objects that maximize an expensive black-box property (e.g., drug-likeness in molecular generation, function…

Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…

Self-taught learning is a technique that uses a large number of unlabeled data as source samples to improve the task performance on target samples. Compared with other transfer learning techniques, self-taught learning can be applied to a…

In this paper, we show that the diagonal of a high-dimensional sample covariance matrix stemming from $n$ independent observations of a $p$-dimensional time series with finite fourth moments can be approximated in spectral norm by the…

Eigenvalue-based detectors are considered as an important method of spectrum sensing since they do not require the information about the primary user (PU) signal. In this paper we propose a method to improve the performance of the…

In this paper, we apply a mini-batch based negative sampling method to efficiently train a latent factor autoencoder model on large scale and sparse data for implicit feedback collaborative filtering. We compare our work against a…

Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and…

With the inexorable digitalisation of the modern world, every subset in the field of technology goes through major advancements constantly. One such subset is digital images which are ever so popular. Images can not always be as visually…

We study the problem of approximating an unknown function $f:\mathbb{R}\to\mathbb{R}$ by a degree-$d$ polynomial using as few function evaluations as possible, where error is measured with respect to a probability distribution $\mu$.…

Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…

Dimensional reduction of high dimensional data can be achieved by keeping only the relevant eigenmodes after principal component analysis. However, differentiating relevant eigenmodes from the random noise eigenmodes is problematic. A new…

We consider the problem of estimating a low-dimensional parameter in high-dimensional linear regression. Constructing an approximately unbiased estimate of the parameter of interest is a crucial step towards performing statistical…

We propose an adaptive random quantum algorithm to obtain an optimized eigensolver. Specifically, we introduce a general method to parametrize and optimize the probability density function of a random number generator, which is the core of…

We show that the variance of the Monte Carlo estimator that is importance sampled from an exponential family is a convex function of the natural parameter of the distribution. With this insight, we propose an adaptive importance sampling…

A rapidly growing area of research is the use of machine learning approaches such as autoencoders for dimensionality reduction of data and models in scientific applications. We show that the canonical formulation of autoencoders suffers…

The application of convolutional autoencoder deep learning to imaging data for planetary science and astrobiological use is briefly reviewed and explored with a focus on the need to understand algorithmic rationale, process, and results…

This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based…