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Bounds for the Sum of Dependent Risks and Worst Value-at-Risk with Monotone Marginal Densities
Complete mixability Monotone density Sum of dependent risks Value-at- Risk
2016/1/25
In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependenc...
Bounds for the Sum of Dependent Risks and Worst Value-at-Risk with Monotone Marginal Densities
Complete mixability Monotone density Sum of dependent risks Value-at- Risk
2016/1/20
In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependenc...
On l2 Error Bounds of the Elastic Net when p>>n
Lasso naive Elastic Net Elastic Net model selection consistency estimation consistency
2016/1/20
We study the estimation property of the Elastic Net in high-dimensional settings where the number of parameters p is comparable to or larger than the sample size n. In such a situation one often assum...
Computing Bounds for the Structured Singular Value via an Interior Point Algorithm
Computing Bounds Structured Singular Value Interior Point Algorithm
2015/7/13
We describe an interior point algorithm for computing the upper bound for the structured singular value described in the paper by Fan, Tits and Doyle, IEEE Trans AC, Jan. 1991. We demonstrate the perf...
Likelihood Bounds for Constrained Estimation with Uncertainty
Likelihood Bounds Constrained Estimation Uncertainty
2015/7/10
This paper addresses the problem of finding bounds on the optimal maximum a posteriori (or maximum likelihood) estimate in a linear model under the presence of model uncertainty. We introduce the nove...
Generalized Chebyshev Bounds via Semidefinite Programming
semidefi nite programming convex optimization duality theory Chebyshev inequalities
2015/7/10
A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed using convex optimization. This result g...
Performance Bounds and Suboptimal Policies for Linear Stochastic Control via LMIs
dynamic programming stochastic control convex optimization
2015/7/9
In a recent paper, the authors showed how to compute performance bounds for infinite horizon stochastic control problems with linear system dynamics and arbitrary constraints, objective, and noise dis...
Fluid Heuristics, Lyapunov Bounds, and Efficient Importance Sampling for a Heavy-tailed G/G/1 Queue
State-dependent importance sampling Rare-event simulation Heavy-tails
2015/7/6
We develop a strongly efficient rare-event simulation algorithm for computing the tail of the steady-state waiting time in a single server queue with regularly varying service times. Our algorithm is ...
Simulation-Based Confidence Bounds for Two-Stage Stochastic Programs
Stochastic programming Linear programming Probability theory
2015/7/6
This paper provides a rigorous asymptotic analysis and justification of upper and lower confidence bounds proposed by Dantzig and Infanger (1995) for an iterative sampling-based decomposition algorith...
Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation
Local Privacy Minimax Bounds Sharp Rates Probability Estimation
2013/6/14
We provide a detailed study of the estimation of probability distributions---discrete and continuous---in a stringent setting in which data is kept private even from the statistician. We give sharp mi...
Parametric Stein operators and variance bounds
Chernoff inequality Cramer-Rao inequality parameter of interest Stein charac-terization Stein’s method
2013/6/17
Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (conti...
Learning subgaussian classes : Upper and minimax bounds
Learning subgaussian classes Upper and minimax bounds
2013/6/14
We obtain sharp oracle inequalities for the empirical risk minimization procedure in the regression model under the assumption that the target $Y$ and the model $\cF$ are subgaussian. The bound we obt...
Global risk bounds and adaptation in univariate convex regression
Global risk bounds adaptation univariate convex regression
2013/6/13
We consider the problem of nonparametric estimation of a convex regression function $\phi_0$. We study global risk bounds and adaptation properties of the least squares estimator (LSE) of $\phi_0$. Un...
Regret Bounds for Reinforcement Learning with Policy Advice
Regret Bounds Reinforcement LearningPolicy Advice
2013/6/13
In some reinforcement learning problems an agent may be provided with a set of input policies, perhaps learned from prior experience or provided by advisors. We present a reinforcement learning with p...
Independent Vector Analysis: Identification Conditions and Performance Bounds
Independent Vector Analysis Identification Conditions Performance Bounds
2013/5/2
Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has a...