arXiv research

Develops inequalities for high-dimensional linear processes with dependent innovations.

Proposes GPLFR for predicting high-dimensional outputs with few data.

Simple linear models outperform complex BO methods in high dimensions.

Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates better understanding of the underlying processes, and enables their optimization. I…

Paper analyzes adaptive Lasso for high-dimensional diffusion processes, improving support recovery and bias.

Proposes a new method for causal inference in high-dimensional complex data.

We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical difficulties. We further introduce a novel technique for approximately marginalizing GP hype…

PROD method improves high-dimensional regression by handling strong correlations.

SA-REMBO adapts to nonstationary high-dimensional optimization.

Additive Gaussian process framework handles monotonicity constraints in high dimensions.

TRNN combines tensor geometry with neural network nonlinearity for HD data.

Two methods monitor high-dimensional processes via manifold fitting or learning.

Deep Jump Gaussian Processes model high-dimensional piecewise functions.

We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a bridge to connect the estimation error of the mean difference and the misclassificat…

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some {known} graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity for short, that goes beyond product graphs. Joint stationarity helps by reducin…

A neural network model tackles high-dimensional data with latent structures.

Paper develops a method for estimating PFLM with minimized rates in high dimensions.

Study improves ERM for heavy-tailed data with dependent inputs.

Overview of high-dimensional dynamical systems and their applications to machine learning.

A new method scales Gaussian process variational autoencoders to handle high-dimensional time series.

A scalable model for high-dimensional longitudinal data.

In this paper, we propose a non-parametric conditional factor regression (NCFR)model for domains with high-dimensional input and response. NCFR enhances linear regression in two ways: a) introducing low-dimensional latent factors leading to dimensionality reduction and b) integrating an Indian Buffet Process as a prior…

Two-layer networks learn hard GLMs with SGD in high dimensions.

This paper finds a linear relationship between t-SNE perplexity and data set size.

The nullspace and regularization impact high-dimensional linear regression interpretability.

Develops an efficient method for real-time data analysis and visualization.

Mean-field approximations simplify insurance liability calculations.

Unified derivation of high-dimensional linear models using stochastic gradient descent.

High-dimensional unimodal distributions can cause MCMC methods to fail.

Learning predictive models from small high-dimensional data sets is a key problem in high-dimensional statistics. Expert knowledge elicitation can help, and a strong line of work focuses on directly eliciting informative prior distributions for parameters. This either requires considerable statistical expertise or is l…

The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to …

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcom…

Review of privacy-preserving linear models for high-dimensional data.

Given the observation of a high-dimensional Ornstein-Uhlenbeck (OU) process in continuous time, we proceed to the inference of the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of the process, penalized by an $\ell^1$-penalization (Lasso and Adaptive Lasso). …

Study shows high-dimensional sparse RL hardness and Lasso Q-iteration's nearly dimension-free regret.

Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking (Fan and Lv, 2008) or feature selection using a two-sample t-test in high-dimension…

Enhances Gaussian process regression with multi-fidelity models and active subspaces for high-dimensional problems.

The paper introduces a method for interpretable principal component analysis of high-dimensional time series.

Tensor analysis tackles complex multidimensional data across fields.

Unified framework for inference in complex nonlinear processes.

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in all likelihoods as latent functions. Our multi-output Gaussian process uses a c…

We simplify complex regression coefficients using linearization and feature comparison.

Hypothesis tests in models whose dimension far exceeds the sample size can be formulated much like the classical studentized tests only after the initial bias of estimation is removed successfully. The theory of debiased estimators can be developed in the context of quantile regression models for a fixed quantile value…

Nested model averaging improves high-dimensional linear regression performance.

KPCA-BO improves BO for high-dimensional optimization problems by learning a non-linear sub-manifold.

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and …

Artificial Intelligence (AI) systems sometimes make errors and will make errors in the future, from time to time. These errors are usually unexpected, and can lead to dramatic consequences. Intensive development of AI and its practical applications makes the problem of errors more important. Total re-engineering of the…

New method speeds up diffusion models inference to sub-linear time.