Related papers: Principal component analysis balancing prediction …
The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…
In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…
The root-cause diagnostics of product quality defects in multistage manufacturing processes often requires a joint identification of crucial stages and process variables. To meet this requirement, this paper proposes a novel penalized…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
When working with large biological data sets, exploratory analysis is an important first step for understanding the latent structure and for generating hypotheses to be tested in subsequent analyses. However, when the number of variables is…
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…
This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…
Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the…
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…
Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…
We study private matrix analysis in the sliding window model where only the last $W$ updates to matrices are considered useful for analysis. We give first efficient $o(W)$ space differentially private algorithms for spectral approximation,…
Large-scale numerical simulations often produce high-dimensional gridded data that is challenging to process for downstream applications. A prime example is numerical weather prediction, where atmospheric processes are modeled using…
We consider change-point estimation in a sequence of high-dimensional signals given noisy observations. Classical approaches to this problem such as the filtered derivative method are useful for sequences of scalar-valued signals, but they…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
Most biological data are multidimensional, posing a major challenge to human comprehension and computational analysis. Principal component analysis is the most popular approach to rendering two- or three-dimensional representations of the…
In our "big data" age, the size and complexity of data is steadily increasing. Methods for dimension reduction are ever more popular and useful. Two distinct types of dimension reduction are "data-oblivious" methods such as random…