Related papers: Homogeneity in Regression
High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…
This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…
The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…
Machine learning often needs to model density from a multidimensional data sample, including correlations between coordinates. Additionally, we often have missing data case: that data points can miss values for some of coordinates. This…
In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…
$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
Low-rank tensors are an established framework for high-dimensional least-squares problems. We propose to extend this framework by including the concept of block-sparsity. In the context of polynomial regression each sparsity pattern…
In modern randomized experiments, large-scale data collection increasingly yields rich baseline covariates and auxiliary information from multiple sources. Such information offers opportunities for more precise treatment effect estimation,…
We study the fundamental tradeoffs between statistical accuracy and computational tractability in the analysis of high dimensional heterogeneous data. As examples, we study sparse Gaussian mixture model, mixture of sparse linear…
In the field of population health research, understanding the similarities between geographical areas and quantifying their shared effects on health outcomes is crucial. In this paper, we synthesise a number of existing methods to create a…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Silhouette coefficient is an established internal clustering evaluation measure that produces a score per data point, assessing the quality of its clustering assignment. To assess the quality of the clustering of the whole dataset, the…
In many applications, data can be heterogeneous in the sense of spanning latent groups with different underlying distributions. When predictive models are applied to such data the heterogeneity can affect both predictive performance and…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
Current modularity-based community detection algorithms attempt to find cluster memberships that maximize modularity within a fixed graph topology. Diverging from this conventional approach, our work introduces a novel strategy that employs…
This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much…
Multivariate association analysis is of primary interest in many applications. Despite the prevalence of high-dimensional and non-Gaussian data (such as count-valued or binary), most existing methods only apply to low-dimensional data with…
In medical image analysis, multi-organ semi-supervised segmentation faces challenges such as insufficient labels and low contrast in soft tissues. To address these issues, existing studies typically employ semi-supervised segmentation…
Regression trees are becoming increasingly popular as omnibus predicting tools and as the basis of numerous modern statistical learning ensembles. Part of their popularity is their ability to create a regression prediction without ever…