
High Probability Frequency Moment Sketches
We consider the problem of sketching the pth frequency moment of a vect...
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Tight Regret Bounds for Noisy Optimization of a Brownian Motion
We consider the problem of Bayesian optimization of a onedimensional Br...
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Generalised Mixability, Constant Regret, and Bayesian Updating
Mixability of a loss is known to characterise when constant regret bound...
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On Learning Markov Chains
The problem of estimating an unknown discrete distribution from its samp...
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An InformationTheoretic Proof of the Streaming Switching Lemma for Symmetric Encryption
Motivated by a fundamental paradigm in cryptography, we consider a recen...
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Tight MMSE Bounds for the AGN Channel Under KL Divergence Constraints on the Input Distribution
Tight bounds on the minimum mean square error for the additive Gaussian ...
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New Error Bounds for Solomonoff Prediction
Solomonoff sequence prediction is a scheme to predict digits of binary s...
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Concentration and Confidence for Discrete Bayesian Sequence Predictors
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only limited results on the distribution of this error. We prove tight highprobability bounds on the cumulative error, which is measured in terms of the KullbackLeibler (KL) divergence. We also consider the problem of constructing upper confidence bounds on the KL and Hellinger errors similar to those constructed from Hoeffdinglike bounds in the i.i.d. case. The new results are applied to show that Bayesian sequence prediction can be used in the Knows What It Knows (KWIK) framework with bounds that match the stateoftheart.
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