Inverse covariance estimation from data with missing values using the Concave-Convex Procedure

Thai, Jérôme; Hunter, Timothy; Akametalu, Anayo K.; Tomlin, Claire J.; Bayen, Alexandre M.

doi:10.1109/cdc.2014.7040287

Cited by 14 publications

(6 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, ( 15) can be rewritten in the standard DCP form DCPs like (17) arise in many applications, such as riskaverse MDPs [28] and inverse covariance estimation in statistics [29]. In order to solve DCPs, we use a variant of the convex-concave procedure [30], wherein the concave terms are replaced by a convex upper bound and solved.…”

Section: Cvar-safe Controller Synthesismentioning

confidence: 99%

Risk-Averse Control via CVaR Barrier Functions: Application to Bipedal Robot Locomotion

Ahmadi

Xiong

Ames

2022

IEEE Control Syst. Lett.

View full text Add to dashboard Cite

Enforcing safety in the presence of stochastic uncertainty is a challenging problem. Traditionally, researchers have proposed safety in the statistical mean as a safety measure for systems subject to stochastic uncertainty. However, ensuring safety in the statistical mean is only reasonable if system's safe behavior in the large number of runs is of interest, which precludes the use of mean safety in practical scenarios. In this paper, we propose a risk sensitive notion of safety called conditional-value-atrisk (CVaR) safety. We introduce CVaR barrier functions as a tool to enforce CVaR-safety and propose conditions for their Boolean compositions. Given a legacy controller, we show that we can design a minimally interfering CVaR-safe controller via solving difference convex programs (DCPs). We elucidate the proposed method by applying it to a bipedal robot locomotion case study.

show abstract

Section: Cvar-safe Controller Synthesismentioning

confidence: 99%

Risk-Averse Control via CVaR Barrier Functions: Application to Bipedal Robot Locomotion

Ahmadi

Xiong

Ames

2022

IEEE Control Syst. Lett.

View full text Add to dashboard Cite

show abstract

“…In fact, optimization problem ( 15) is a standard DCP (Horst and Thoai 1999). DCPs arise in many applications, such as feature selection in machine learning (Le Thi et al 2008) and inverse covariance estimation in statistics (Thai et al 2014). Although DCPs can be solved globally (Horst and Thoai 1999), e.g.…”

Section: Dcps For Constrained Risk-averse Mdpsmentioning

confidence: 99%

Constrained Risk-Averse Markov Decision Processes

Ahmadi

Rosolia

Ingham

et al. 2021

AAAI

View full text Add to dashboard Cite

We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.

show abstract

“…This plug-in method is called the mGlasso algorithm. Thai et al (2014) proposed a new Concave-Convex procedure which is however not computationally faster than the existing EM algorithm in their numerical experiments.…”

Section: Model Selection For Gaussian Graphical Modelmentioning

confidence: 99%

A generalized EMS algorithm for model selection with incomplete data

Xu,

Shang,

Tang

et al. 2021

Preprint

View full text Add to dashboard Cite

Recently, a so-called E-MS algorithm was developed for model selection in the presence of missing data. Specifically, it performs the Expectation step (E step) and Model Selection step (MS step) alternately to find the minimum point of the observed generalized information criteria (GIC). In practice, it could be numerically infeasible to perform the MS-step for high dimensional settings. In this paper, we propose a more simple and feasible generalized EMS (GEMS) algorithm which simply requires a decrease in the observed GIC in the MS-step and includes the original EMS algorithm as a special case. We obtain several numerical convergence results of the GEMS algorithm under mild conditions. We apply the proposed GEMS algorithm to Gaussian graphical model selection and variable selection in generalized linear models and compare it with existing competitors via numerical experiments. We illustrate its application with three real data sets.

show abstract

Inverse covariance estimation from data with missing values using the Concave-Convex Procedure

Cited by 14 publications

References 32 publications

Risk-Averse Control via CVaR Barrier Functions: Application to Bipedal Robot Locomotion

Risk-Averse Control via CVaR Barrier Functions: Application to Bipedal Robot Locomotion

Constrained Risk-Averse Markov Decision Processes

A generalized EMS algorithm for model selection with incomplete data

Contact Info

Product

Resources

About