Learning Mixtures of Continuous-Time Markov Chains

Fabian Christian Spaeh, Charalampos Tsourakakis

Keywords: Stochastic Processes, Mixture Models, Continuous-Time Markov Chains

TL;DR: We recover continuous-time Markov chains from discrete observations

Abstract:

Sequential data naturally arises from user engagement on digital platforms like social media, music streaming services, and web navigation, encapsulating evolving user preferences and behaviors through continuous information streams. A notable unresolved query in stochastic processes is learning mixtures of continuous-time Markov chains (CTMCs). While there is progress in learning mixtures of discrete-time Markov chains with recovery guarantees [GKV16, ST23 , KTT22], the continuous scenario entails unique unexplored challenges. The intrigue in CTMC mixtures stems from their potential to model intricate continuous-time stochastic processes prevalent in various fields including social media, finance, and biology.

In this study, we introduce a novel framework for studying CTMCs, emphasizing the influence of trail length and mixture parameters to different problem regimes, which demand specific algorithms. Through thorough experimentation, we examine the impact of discretizing continuous-time trails on the learnability
of the continuous-time mixture, given that these processes are often observed via discrete, resource-demanding observations. Our comparative analysis with leading methods explores sample complexity and the trade-off between the number of trails and their lengths, offering crucial insights for method selection in different problem instances. We further demonstrate a unique application of our methodology on an NBA dataset to decipher specific attack strategies of various teams, underscoring the pragmatic utility and versatility of our proposed framework.

Track: COI (submissions co-authored by SAC)

Submission Guidelines Scope: Yes

Submission Guidelines Blind: Yes

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Student Author: Yes

Submission Number: 1098