The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs
- Han Liu, J. Lafferty, L. Wasserman
- Mathematics, Computer ScienceJournal of machine learning research
- 3 March 2009
A method is derived for estimating the nonparanormal, the method's theoretical properties are studied, and it is shown that it works well in many examples.
High Dimensional Semiparametric Gaussian Copula Graphical Models
- Han Liu, Fang Han, M. Yuan, J. Lafferty, L. Wasserman
- Computer Science, MathematicsInternational Conference on Machine Learning
- 10 February 2012
It is proved that the nonparanormal skeptic achieves the optimal parametric rates of convergence for both graph recovery and parameter estimation, and this result suggests that the NonParanormal graphical models can be used as a safe replacement of the popular Gaussian graphical models, even when the data are truly Gaussian.
Stochastic compositional gradient descent: algorithms for minimizing compositions of expected-value functions
- Mengdi Wang, Ethan X. Fang, Han Liu
- Computer Science, MathematicsMathematical programming
- 14 November 2014
It is proved that the SCGD converge almost surely to an optimal solution for convex optimization problems, as long as such a solution exists and any limit point generated by SCGD is a stationary point, for which the convergence rate analysis is provided.
Challenges of Big Data Analysis.
Big Data bring new opportunities to modern society and challenges to data scientists. On one hand, Big Data hold great promises for discovering subtle population patterns and heterogeneities that are…
Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models
The method has a clear interpretation: the authors use the least amount of regularization that simultaneously makes a graph sparse and replicable under random sampling, which requires essentially no conditions.
A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models
The decorrelated score function can be used to construct point and confidence region estimators that are semiparametrically efficient and extended to handle high dimensional null hypothesis, where the number of parameters of interest can increase exponentially fast with the sample size.
SpAM: Sparse Additive Models
A statistical analysis of the properties of SpAM and empirical results on synthetic and real data show that SpAM can be effective in fitting sparse nonparametric models in high dimensional data.
A Strictly Contractive Peaceman-Rachford Splitting Method for Convex Programming
This paper focuses on the application of the Peaceman-Rachford splitting method to a convex minimization model with linear constraints and a separable objective function, and suggests attaching an underdetermined relaxation factor with PRSM to guarantee the strict contraction of its iterative sequence and proposes a strictly contractive PRSM.
The huge Package for High-dimensional Undirected Graph Estimation in R
- T. Zhao, Han Liu, K. Roeder, J. Lafferty, L. Wasserman
- Computer ScienceJournal of machine learning research
- 1 March 2012
An R package named huge which provides easy-to-use functions for estimating high dimensional undirected graphs from data and allows the user to apply both lossless and lossy screening rules to scale up large-scale problems, making a tradeoff between computational and statistical efficiency.
OPTIMAL COMPUTATIONAL AND STATISTICAL RATES OF CONVERGENCE FOR SPARSE NONCONVEX LEARNING PROBLEMS.
These results show that the final estimator attains an oracle statistical property due to the usage of nonconvex penalty, and improves upon existing results by providing a more refined sample complexity bound as well as an exact support recovery result for the final estimation.