
Fast Rates of ERM and Stochastic Approximation: Adaptive to Error Bound Conditions
Error bound conditions (EBC) are properties that characterize the growth...
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Convergence rates of Kernel Conjugate Gradient for random design regression
We prove statistical rates of convergence for kernelbased least squares...
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Regularized Contextual Bandits
We consider the stochastic contextual bandit problem with additional reg...
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Exponential convergence of testing error for stochastic gradient methods
We consider binary classification problems with positive definite kernel...
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Asymptotics of Ridge(less) Regression under General Source Condition
We analyze the prediction performance of ridge and ridgeless regression ...
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Learning to Predict Combinatorial Structures
The major challenge in designing a discriminative learning algorithm for...
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Fast classification rates without standard margin assumptions
We consider the classical problem of learning rates for classes with fin...
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Fast rates in structured prediction
Discrete supervised learning problems such as classification are often tackled by introducing a continuous surrogate problem akin to regression. Bounding the original error, between estimate and solution, by the surrogate error endows discrete problems with convergence rates already shown for continuous instances. Yet, current approaches do not leverage the fact that discrete problems are essentially predicting a discrete output when continuous problems are predicting a continuous value. In this paper, we tackle this issue for general structured prediction problems, opening the way to "super fast" rates, that is, convergence rates for the excess risk faster than n^1, where n is the number of observations, with even exponential rates with the strongest assumptions. We first illustrate it for predictors based on nearest neighbors, generalizing rates known for binary classification to any discrete problem within the framework of structured prediction. We then consider kernel ridge regression where we improve known rates in n^1/4 to arbitrarily fast rates, depending on a parameter characterizing the hardness of the problem, thus allowing, under smoothness assumptions, to bypass the curse of dimensionality.
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