Related papers: A Fast Divide-and-Conquer Sparse Cox Regression
Stochastic scientific models and machine learning optimization estimators have a large number of variables; hence computing large sparse Jacobians and Hessians is important. Algorithmic differentiation (AD) greatly reduces the programming…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
We propose a general approach for encouraging fairness in survival analysis models based on minimizing a worst-case error across all subpopulations that occur with at least a user-specified probability. This approach can be used to convert…
We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND -- sparsified Nested Dissection. It is based on nested dissection, sparsification and low-rank compression. After…
Cox proportional hazard regression model is a popular tool to analyze the relationship between a censored lifetime variable with other relevant factors. The semi-parametric Cox model is widely used to study different types of data arising…
We present a probabilistic divide-and-conquer (PDC) method for \emph{exact} sampling of conditional distributions of the form $\mathcal{L}( {\bf X}\, |\, {\bf X} \in E)$, where ${\bf X}$ is a random variable on $\mathcal{X}$, a complete,…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network…
This paper presents a dynamic predictive sampling (DPS) based analog-to-digital converter (ADC) that provides a non-uniform sampling of input analog continuous-time signals. The processing unit generates a dynamic prediction of the input…
There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…
High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of…
We consider variable selection in high-dimensional linear models where the number of covariates greatly exceeds the sample size. We introduce the new concept of partial faithfulness and use it to infer associations between the covariates…
We develop the theory and practical implementation of p-adic sparse coding of data. Rather than the standard, sparsifying criterion that uses the $L_0$ pseudo-norm, we use the p-adic norm. We require that the hierarchy or tree be…
In survival analysis, longitudinal information on the health status of a patient can be used to dynamically update the predicted probability that a patient will experience an event of interest. Traditional approaches to dynamic prediction…
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…
We study how the divide and conquer principle --- partition the available data into subsamples, compute an estimate from each subsample and combine these appropriately to form the final estimator --- works in non-standard problems where…
$\ell_1$ penalized quantile regression is used in many fields as an alternative to penalized least squares regressions for high-dimensional data analysis. Existing algorithms for penalized quantile regression either use linear programming,…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
We present a graph-based technique for estimating sparse covariance matrices and their inverses from high-dimensional data. The method is based on learning a directed acyclic graph (DAG) and estimating parameters of a multivariate Gaussian…
Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…