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        "datetime_modified":"20260119T092447",
        "datetime_start":"20260121T160000",
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        "date_start":"2026-01-21",
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        "time_start":"16:00:00",
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        "time_zone":"America\/Detroit",
        "event_title":"Student AIM Seminar: Sampling with Langevin Dynamics: Theory, Algorithms, and Limitations",
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        "combined_title":"Student AIM Seminar: Sampling with Langevin Dynamics: Theory, Algorithms, and Limitations: Ian Augsburger",
        "event_subtitle":"Ian Augsburger",
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        "event_type_id":"21",
        "description":"This talk introduces the overdamped Langevin stochastic differential equation as a method for sampling from complex probability distributions, with brief historical context from statistical physics. We begin by deriving the infinitesimal generator of the Langevin diffusion and the associated Fokker\u2013Planck equation, which governs the evolution of probability densities. This correspondence allows us to characterize invariant (stationary) distributions and to analyze qualitative dynamical behavior, including probability flow and transition times between modes of the distributions.\r\n\r\nExploiting the special Gibbs form of the stationary distribution, we show how overdamped Langevin dynamics can be used as a practical sampling mechanism for high-dimensional target distributions. We then compare classical Metropolis\u2013Hastings algorithms with Langevin-based methods, highlighting their respective strengths, such as improved scalability with data through gradient information, as well as their limitations, including discretization bias and sensitivity to step size. We conclude with remarks on challenges that arise when applying Langevin-based samplers to latent-variable models, such as latent Dirichlet allocation and tree-structured latent variable models, where other methods such as Variational Inference perform much quicker with great results.",
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        "tags":["Applied Mathematics"],
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    {
        "datetime_modified":"20251126T124446",
        "datetime_start":"20260121T160000",
        "datetime_end":"20260121T170000",
        "has_end_time":1,
        "date_start":"2026-01-21",
        "date_end":"2026-01-21",
        "time_start":"16:00:00",
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        "time_zone":"America\/Detroit",
        "event_title":"Thompson Sampling Algorithm for Stochastic Differential Games",
        "occurrence_title":"",
        "combined_title":"Thompson Sampling Algorithm for Stochastic Differential Games: Ruolan He, UM",
        "event_subtitle":"Ruolan He, UM",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"We study a stochastic differential game with $N$ competitive players in a linear-quadratic framework with ergodic cost, where $d$-dimensional diffusion processes govern the state dynamics with an unknown common drift (matrix). Assuming a Gaussian prior on the drift, we use filtering techniques to update its posterior estimates. Based on these estimates, we propose a Thompson-sampling-based algorithm with dynamic episode lengths to approximate strategies. We show that the Bayesian regret for each player has an error bound of order $O(\\sqrt{T\\log(T)})$, where $T$ is the time-horizon, independent of the number of players. This implies that average regret per unit time goes to zero. Finally, we prove that the algorithm results in a Nash equilibrium.",
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        "tags":["Mathematics"],
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                "group_name":"Financial\/Actuarial Mathematics Seminar - Department of Mathematics",
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