Information-theoretic determination of minimax rates of convergence

1999

Citations in the corpus

• Additive models with trend filtering (2017, positive): “Now, following the strategy in Yang and Barron [1999], we use these bounds on the packing and covering numbers, along with Fano’s inequality, to establish the desired result.”
• Estimating Divergence Functionals and the Likelihood Ratio by Convex Risk Minimization (2008, neutral): “Therefore, an easy-to-use minimax lower bound such as that of [36] is not immediately applicable.”
• Minimax Optimal Procedures for Locally Private Estimation (2016, positive): “…a density function f ∈ F β [ C ] and that quality is measured in terms of the squared error (squared L 2 [0 , 1]-norm): The well-known (Yu 1997; Yang and Barron 1999; Tsybakov 2009) (nonprivate) minimax mean squared error scales as The goal of this section is to understand how this minimax…”
• Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation (2013, neutral): “It is well known [26, 25, 22] that the minimax risk for nonprivate estimation of densities in the class Fβ scales as”
• Information-Theoretic Limits on Sparsity Recovery in the High-Dimensional and Noisy Setting (2007, unknown): “We note the Fano method is a standard approach for obtaining minimax lower bounds in nonparametric statistical problems [18], [20], [35], [34].”
• Information-Theoretic Lower Bounds on the Oracle Complexity of Stochastic Convex Optimization (2010, unknown): “, [9], [10], [11], [12]) an d Le Cam’s bound (e.”
• Some inequalities for information divergence and related measures of discrimination (2000, unknown): “This is of importance for (parts of) research as that of LeCam [25], Birge [5], Birge and Massart [6], and Yang and Barron [ 42 ], where the lack of metric properties for information divergence is compensated for by researching relations to true distances (typically, the Hellinger distance is the pr”
• Regularized Policy Iteration with Nonparametric Function Spaces (2016, unknown): “…generally, the rate of O(n −1/(1+α ) is optimal too: For a regression function belonging to a function space F with a packing entropy in the same form as in the upper bound of Assumption A4, the rate Ω(n −1/(1+α) ) is its minimax lower bound (Yang and Barron, 1999), making the upper bound optimal.”
• Information-theoretic lower bounds on the oracle complexity of convex optimization (2009, unknown): “As we will see, the proof techniques are also similar to those employed in statistics, particularly in the areas of non-parametric regression [8, 9] as well as in learning theory [10, 11, 12].”
• Minimax Rates of Estimation for High-Dimensional Linear Regression Over q -Balls (2009, unknown): “(3) Finally, following a technique introduced by Yang and Ba rron [34], we derive an upper bound on the mutual information between Y andΘ by constructing anǫn-covering set forBq(Rq) with respect to thel2-prediction semi-norm.”
• Local Privacy and Statistical Minimax Rates (2013, unknown): “We first establish the minimax framework we use throughout this paper; see [27, 28, 23] for further background.”
• Regularization in reinforcement learning (2011, unknown): “samples under the assumption that m ∈ F and F has a packing entropy in the same form as in the upper bound of Assumption A2 [Yang and Barron, 1999].”
• Handbook of Big Data (2016, unknown): “In fact, Yang and Barron [73] showed that for many smooth nonparametric classes the metric entropy number characterizes the sample complexity of learning.”