Empirical bounds for functions with weak interactions
We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U- and V-statistics, Lipschitz L-statistics and various error functionals of L2-regularized algorithms and Gibbs algorithms.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A maximal inequality for local empirical processes under weak dependence
We introduce a maximal inequality for a local empirical process under strongly mixing data. Local empirical processes are defined as the (local) averages $\frac{1}{nh}\sum_{i=1}^n \mathbf{1}\{x - h \leq X_i \leq x+h\}f(Z…
Density EstimationUniform Deviation Bounds for Unbounded Loss Functions like k-Means
Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk m…
ClusteringOnline Active Learning with Surrogate Loss Functions
We derive a novel active learning algorithm in the streaming setting for binary classification tasks. The algorithm leverages weak labels to minimize the number of label requests, and trains a model to optimize a surroga…
Active LearningBinary ClassificationUniform Deviation Bounds for k-Means Clustering
Uniform deviation bounds limit the difference between a model’s expected loss and its loss on an empirical sample uniformly for all models in a learning problem. In this paper, we provide a novel framework to obtain…
ClusteringWeak Identification with Bounds in a Class of Minimum Distance Models
When parameters are weakly identified, bounds on the parameters may provide a valuable source of information. Existing weak identification estimation and inference results are unable to combine weak identification with b…