Related papers: Fast Covariance Estimation for High-dimensional Fu…
In the realm of high-dimensional data analysis, the estimation of covariance matrices is a fundamental task, and this holds true for interval-valued data as well. However, there is no unified definition for the covariance matrix of…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
We propose a two-stage procedure for estimating the location $\bolds{\mu}$ and size M of the maximum of a smooth d-variate regression function f. In the first stage, a preliminary estimator of $\bolds{\mu}$ obtained from a standard…
Two popular variable screening methods under the ultra-high dimensional setting with the desirable sure screening property are the sure independence screening (SIS) and the forward regression (FR). Both are classical variable screening…
We seek to extract a small number of representative scenarios from large panel data that are consistent with sample moments. Among two novel algorithms, the first identifies scenarios that have not been observed before, and comes with a…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
In recent year, tremendous strides have been made in face detection thanks to deep learning. However, most published face detectors deteriorate dramatically as the faces become smaller. In this paper, we present the Small Faces Attention…
Large health surveys increasingly collect high-dimensional functional data from wearable devices, and function on scalar regression (FoSR) is often used to quantify the relationship between these functional outcomes and scalar covariates…
We propose a scalable, efficient and statistically motivated computational framework for Graphical Lasso (Friedman et al., 2007b) - a covariance regularization framework that has received significant attention in the statistics community…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
The crossed random effects model is widely used, finding applications in various fields such as longitudinal studies, e-commerce, and recommender systems, among others. However, these models encounter scalability challenges, as the…
The major sources of abundant data are constantly expanding with the available data collection methodologies in various applications - medical, insurance, scientific, bio-informatics and business. These data sets may be distributed…
We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…
In this paper, covariance matrices are exploited to encode the deep convolutional neural networks (DCNN) features for facial expression recognition. The space geometry of the covariance matrices is that of Symmetric Positive Definite (SPD)…
In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting…
Let $\mathbf{x}_j = \mathbf{\theta} + \mathbf{\epsilon}_j$, $j=1,\dots,n$ be i.i.d. copies of a Gaussian random vector $\mathbf{x}\sim\mathcal{N}(\mathbf{\theta},\mathbf{\Sigma})$ with unknown mean $\mathbf{\theta} \in \mathbb{R}^d$ and…
Estimating graphical model structure from high-dimensional and undersampled data is a fundamental problem in many scientific fields. Existing approaches, such as GLASSO, latent variable GLASSO, and latent tree models, suffer from high…
High-dimensional functional data are becoming increasingly common in fields such as environmental monitoring and neuroimaging. This paper studies high-dimensional functional linear regression models that relate a scalar response to…