BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Adrien Corenflos (University of Warwick) DTSTART:20240529T111500Z DTEND:20240529T120000Z DTSTAMP:20260422T155153Z UID:gbgstats/57 DESCRIPTION:Title: Particle-MALA and Particle-mGrad: Gradient-based MCMC methods for high-d imensional state-space models\nby Adrien Corenflos (University of Warw ick) as part of Gothenburg statistics seminar\n\nLecture held in MVL14.\n\ nAbstract\nState-of-the-art methods for Bayesian inference in state-space models are (a) conditional sequential Monte Carlo (CSMC) algorithms\; (b) sophisticated 'classical' MCMC algorithms like MALA\, or mGRAD from Titsia s and Papaspiliopoulos (2018). The former propose N particles at each time step to exploit the model's 'decorrelation-over-time' property and thus s cale favourably with the time horizon\, T\, but break down if the dimensio n of the latent states\, D\, is large. The latter leverage gradient/prior- informed local proposals to scale favourably with D but exhibit sub-optima l scalability with T due to a lack of model-structure exploitation. We int roduce methods which combine the strengths of both approaches. The first\, Particle-MALA\, spreads N particles locally around the current state usin g gradient information\, thus extending MALA to T>1 time steps and N>1 pro posals. The second\, Particle-mGRAD\, additionally incorporates (condition ally) Gaussian prior dynamics into the proposal\, thus extending the mGRAD algorithm. We prove that Particle-mGRAD interpolates between CSMC and Par ticle-MALA\, resolving the 'tuning problem' of choosing between CSMC (supe rior for highly informative prior dynamics) and Particle-MALA (superior fo r weakly informative prior dynamics). We similarly extend other 'classical ' MCMC approaches like auxiliary MALA\, aGRAD\, and preconditioned Crank-N icolson-Langevin (PCNL). In experiments\, our methods substantially improv e upon both CSMC and sophisticated `classical' MCMC approaches for both hi ghly and weakly informative prior dynamics.\n\nTL\;DR: We aim to solve the curse of dimensionality in state-space model inferences by combining the nice property (in time) of conditional particle filtering methods\, with t he nice property (in space) of MALA and other gradient-based algorithms.\n LOCATION:https://researchseminars.org/talk/gbgstats/57/ END:VEVENT END:VCALENDAR