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Bayesian Learning for Dynamic Inference
The traditional statistical inference is static, in the sense that the estimate of the quantity of interest does not affect the future evolution of the quantity.
Dynamic Inference
How the optimal estimation strategy works is illustrated through two examples, stock trend prediction and vehicle behavior prediction.
Continuity of Generalized Entropy and Statistical Learning
We study the continuity property of the generalized entropy as a function of the underlying probability distribution, defined with an action space and a loss function, and use this property to answer the basic questions in statistical learning theory: the excess risk analyses for various learning methods.
Minimum Excess Risk in Bayesian Learning
We analyze the best achievable performance of Bayesian learning under generative models by defining and upper-bounding the minimum excess risk (MER): the gap between the minimum expected loss attainable by learning from data and the minimum expected loss that could be achieved if the model realization were known.
Information-theoretic analysis of generalization capability of learning algorithms
We derive upper bounds on the generalization error of a learning algorithm in terms of the mutual information between its input and output.
