Related papers: Dimension Reduction for Data with Heterogeneous Mi…
When pre-processing observational data via matching, we seek to approximate each unit with maximally similar peers that had an alternative treatment status--essentially replicating a randomized block design. However, as one considers a…
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…
Class prediction is an important application of microarray gene expression data analysis. The high-dimensionality of microarray data, where number of genes (variables) is very large compared to the number of samples (obser- vations), makes…
Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…
Large high-dimensional datasets are becoming more and more popular in an increasing number of research areas. Processing the high dimensional data incurs a high computational cost and is inherently inefficient since many of the values that…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
Attribute reduction is a basic issue in knowledge representation and data mining. Rough sets provide a theoretical foundation for the issue. Matroids generalized from matrices have been widely used in many fields, particularly greedy…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…
We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics. One strategy of dimension reduction is to derive a low-dimensional dynamical system…
This paper studies the dimension effect of the linear discriminant analysis (LDA) and the regularized linear discriminant analysis (RLDA) classifiers for large dimensional data where the observation dimension $p$ is of the same order as the…
There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite…
As network data has become ubiquitous in the sciences, there has been growing interest in network models whose structure is driven by latent node-level variables in a (typically low-dimensional) latent geometric space. These "latent…
A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…
Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…
The multivariate adaptive regression spline (MARS) is one of the popular estimation methods for nonparametric multivariate regressions. However, as MARS is based on marginal splines, to incorporate interactions of covariates, products of…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…