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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...
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...
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...
Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo
Information visualization Formal Concept Analysis Galois sub-hierarchy
2013/4/27
In [Chen, D., Owen, Ann. Stat., 39, 673--701, 2011] Markov chain Monte Carlo (MCMC) was studied under the assumption that the driver sequence is a deterministic sequence rather than independent U(0,1)...
Further Optimal Regret Bounds for Thompson Sampling
Further Optimal Regret Bounds Thompson Sampling
2012/11/23
Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several s...
We consider the restless Markov bandit problem, in which the state of each arm evolves according to a Markov process independently of the learner's actions. We suggest an algorithm that after $T$ step...
Cramer-Rao-Induced Bounds for CANDECOMP/PARAFAC tensor decomposition
CANDECOMP/PARAFAC Cramer-Rao-Induced tensor decomposition Bounds
2012/11/22
This paper presents a Cramer-Rao lower bound (CRLB) on the variance of unbiased estimates of factor matrices in Canonical Polyadic (CP) or CANDECOMP/PARAFAC (CP) decompositions of a tensor from noisy ...