BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sergei Zuyev (Chalmers) DTSTART:20240417T111500Z DTEND:20240417T120000Z DTSTAMP:20260422T155020Z UID:gbgstats/49 DESCRIPTION:Title: Training Bayesian neural networks with measure optimisation algorithms\nby Sergei Zuyev (Chalmers) as part of Gothenburg statistics seminar\n\ nLecture held in MVL14.\n\nAbstract\nOn a high abstraction level\, a Bayes ian neural network (BNN) can be seen as a function\nof input data and thei r prior probability distribution which yields\,\namong other outputs\, the ir estimated posterior probability\ndistribution. This distribution is a r esult of optimisation of a\nchosen score function aiming to favour these p robability distributions\nwhich describe best the observed data and take i nto account the prior\ndistribution.\n\nInstead of constraint optimisation over the simplex of probability distributions\, it is typical to\nmap thi s simplex into Euclidean space\, for example with Softmax function or its variants\, and then do optimisation in the whole\nspace without constrain ts. It is\, however\, widely acknowledged that such mapping often suffers from undesirable properties for optimisation and\nstability of the algorit hms. To counterfeit this\, a few regularisation procedures have been propo sed in the literature.\n\nInstead of trying to modify the mapping approac h\, we suggest\nturning back to optimisation on the original simplex using recently\ndeveloped algorithms for constrained optimisation of functional s of measures. \nWe demonstrate that our algorithms run tens times faster\ nthan the standard algorithms involving softmax mapping and lead to exact solutions rather than to their approximations.\n LOCATION:https://researchseminars.org/talk/gbgstats/49/ END:VEVENT END:VCALENDAR