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University of Cambridge > Talks.cam > Statistics > Optimal prediction of Markov chains without mixing conditions

## Optimal prediction of Markov chains without mixing conditionsAdd to your list(s) Download to your calendar using vCal - Yihong Wu (Yale University)
- Friday 13 May 2022, 15:00-16:00
- https://maths-cam-ac-uk.zoom.us/j/93998865836?pwd=VzVzN1VFQ0xjS3VDdlY0enBVckY5dz09.
If you have a question about this talk, please contact Qingyuan Zhao. Motivated by practical applications such as autocomplete and text generation, we study the following statistical problem with dependent data: Observing a trajectory of length $n$ from a stationary first-order Markov chain with $k$ states, how to predict (the distribution of) the next state? In contrast to the better-studied parameter estimation problem which relies on assumptions on the mixing time or the minimal probability of the stationary distribution, the prediction problem requires neither. This allows for an assumption-free framework but also results in new technical challenges due to the lack of concentration for sample path statistics. For $3 \leq k \leq O(\sqrt{n})$, using information-theoretic techniques including, in particular, those rooted in universal compression, we show that the optimal rate of Kullback-Leibler prediction risk is $\frac{k This is based on joint work with Yanjun Han and Soham Jana: https://arxiv.org/abs/2106.13947 This talk is part of the Statistics series. ## This talk is included in these lists:- All CMS events
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