BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Igor Pruenster (Bocconi University)) DTSTART:20211129T160000Z DTEND:20211129T164500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/1 DESCRIPTION:Title: Nonparametric priors for partially exchangeable data: dependenc e structure and borrowing of information\nby Igor Pruenster (Bocconi U niversity)) as part of CMO-Foundations of Objective Bayesian Methodology\n \nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Beatrice Franzolini (Bocconi University\, Italy) DTSTART:20211129T164500Z DTEND:20211129T173000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/2 DESCRIPTION:Title: Nonparametric priors with full-range borrowing of information\nby Beatrice Franzolini (Bocconi University\, Italy) as part of CMO-Fou ndations of Objective Bayesian Methodology\n\n\nAbstract\nWhen data are gr ouped into distinct samples\, they typically are homogeneous within and he terogeneous across groups. In this case\, the Bayesian paradigm requires a prior law over a collection of distributions. From a modelling point of v iew\, it is essential to study how this structure reflects on the observab les\, especially in nonparametric models. We introduce the notion of hyper -ties and show that they play the same role of actual ties in the exchange able setting\, driving the dependence between observations. Using hyper-ti es\, we can compute correlation between observables and show how its sign depends from the joint specification. Finally\, we propose a novel class o f dependent nonparametric priors\, which may induce either positive or neg ative correlation across samples.\n\n"\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Catalano (University of Warwick\, UK) DTSTART:20211129T180000Z DTEND:20211129T184500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/3 DESCRIPTION:Title: A Wasserstein index of dependence for Bayesian nonparametric mo deling\nby Marta Catalano (University of Warwick\, UK) as part of CMO- Foundations of Objective Bayesian Methodology\n\n\nAbstract\nOptimal trans port (OT) methods and Wasserstein distances are flourishing in many scient ific fields as an effective means for comparing and connecting different r andom structures. In this talk we describe the first use of an OT distance between Lévy measures with infinite mass to solve a statistical problem. Complex phenomena often yield data from different but related sources\, w hich are ideally suited to Bayesian modeling because of its inherent borro wing of information. In a nonparametric setting\, this is regulated by the dependence between random measures: we derive a general Wasserstein index for a principled quantification of the dependence gaining insight into th e models’ deep structure. It also allows for an informed prior elicitati on and provides a fair ground for model comparison. Our analysis unravels many key properties of the OT distance between Lévy measures\, whose inte rest goes beyond Bayesian statistics\, spanning to the theory of partial d ifferential equations and of Lévy processes.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Isadora Antoniano-Villalobos (Ca' Foscari University of Venice) DTSTART:20211129T184500Z DTEND:20211129T193000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/4 DESCRIPTION:Title: Bayesian mixture models for the prediction of extreme observati ons\nby Isadora Antoniano-Villalobos (Ca' Foscari University of Venice ) as part of CMO-Foundations of Objective Bayesian Methodology\n\n\nAbstra ct\nIn many applications with interest in large or extreme observations\, usual inferential methods may fail to reproduce the tail behaviour of the variables involved. Recent literature has proposed the use of multivariate extreme value theory to predict an unobserved component of a random vecto r given large observed values of the rest. This is achieved through the es timation of the angular measure controlling the dependence structure in th e tail of the distribution. The idea can be extended and used for predicti on of multiple components at adequately large levels\, provided the model used for the angular measure is sufficiently flexible enough to capture co mplex dependence structures. The use of Bernstein polynomials ensures such flexibility and their interpretation as mixture models allows the use of current trans-dimensional MCMC posterior simulation methods for inference. \n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Julyan Arbel (Inria Grenoble\, France) DTSTART:20211129T220000Z DTEND:20211129T224500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/5 DESCRIPTION:Title: Improving MCMC convergence diagnostic with a local version of R -hat\nby Julyan Arbel (Inria Grenoble\, France) as part of CMO-Foundat ions of Objective Bayesian Methodology\n\n\nAbstract\nDiagnosing convergen ce of Markov chain Monte Carlo (MCMC) is crucial in Bayesian analysis. Amo ng the most popular methods\, the potential scale reduction factor (common ly named R-hat) is an indicator that monitors the convergence of all chain s to the stationary distribution\, based on a comparison of the between- a nd within-variance of the chains. Several improvements have been suggested since its introduction by Gelman & Rubin (1992). Here\, we analyse some p roperties of the theoretical value R associated to R-hat in the case of a localized version that focuses on quantiles of the distribution. This lead s to proposing a new indicator\, which is shown to allow both for localizi ng the MCMC convergence in different quantiles of the distribution\, and a t the same time for handling some convergence issues not detected by other R-hat versions.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Campbell Trevor (University of British Columbia\, Canada) DTSTART:20211129T224500Z DTEND:20211129T230000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/6 DESCRIPTION:Title: Parallel Tempering on Optimized Paths\nby Campbell Trevor ( University of British Columbia\, Canada) as part of CMO-Foundations of Obj ective Bayesian Methodology\n\n\nAbstract\nParallel tempering (PT) is a cl ass of Markov chain Monte Carlo algorithms that constructs a path of distr ibutions annealing between a tractable reference and an intractable target \, and then interchanges states along the path to improve mixing in the ta rget. The performance of PT depends on how quickly a sample from the refer ence distribution makes its way to the target\, which in turn depends on t he particular path of annealing distributions. However\, past work on PT h as used only simple paths constructed from convex combinations of the refe rence and target log-densities. In this talk I'll show that this path perf orms poorly in the common setting where the reference and target are nearl y mutually singular. To address this issue\, I'll present an extension of the PT framework to general families of paths\, formulate the choice of pa th as an optimization problem that admits tractable gradient estimates\, a nd present a flexible new family of spline interpolation paths for use in practice. Theoretical and empirical results will demonstrate that the prop osed methodology breaks previously-established upper performance limits fo r traditional paths.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/6/ END:VEVENT BEGIN:VEVENT SUMMARY:María Fernanda Gil Leyva Villa (Bocconi University) DTSTART:20211130T000000Z DTEND:20211130T004500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/7 DESCRIPTION:Title: Gibbs sampling for mixtures in order of appearance: the ordered allocation sampler\nby María Fernanda Gil Leyva Villa (Bocconi Unive rsity) as part of CMO-Foundations of Objective Bayesian Methodology\n\n\nA bstract\nGibbs sampling methods for mixture models are based on data augme ntation schemes that account for the unobserved partition in the data. The y have been broadly classified into two categories: marginal and condition al samplers. Marginal samplers are termed this way because they integrate out part of the mixing distribution and model directly the partition struc ture. They can be used to implement mixture models with a tractable exchan geable partition probability function (EPPF) associated to the mixing dist ribution. However\, if the EPPF is not available in closed form\, marginal samplers are hard to adapt. In contrast\, conditional samplers rely on al location variables that identify each observation with a mixture component . While conditional samplers are more broadly applicable and allow direct inference on the mixing distribution\, they are known to suffer from slow mixing. Moreover\, for mixtures models with infinitely many components so me form of truncation\, either deterministic or random\, is required. As f or mixtures with a random number of components\, the exploration of parame ter spaces of different dimensions can also be challenging. We tackle thes e issues by expressing the mixture components in the random order of appea rance in an exchangeable sequence directed by the mixing distribution. We derive a sampler\, called the ordered allocation sampler\, that is straigh tforward to implement for mixing distributions with tractable size-biased ordered weights. In infinite mixtures\, no form of truncation is necessary . As for finite mixtures with random dimension\, a simple updating of the number of components is obtained by a blocking argument\, thus easing chal lenges found in trans-dimensional moves via Metropolis-Hasting steps. Alth ough the ordered allocation sampler is a conditional sampler\, sampling oc curs in the space of ordered partitions with blocks labelled in the least element order. This improves mixing and promotes a consistent labelling of mixture components throughout iterations.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Anirban Bhattarcharya (Texas A&M University) DTSTART:20211130T004500Z DTEND:20211130T013000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/8 DESCRIPTION:Title: Coupling-based convergence assessment of some Gibbs samplers fo r high-dimensional Bayesian regression with shrinkage priors\nby Anirb an Bhattarcharya (Texas A&M University) as part of CMO-Foundations of Obje ctive Bayesian Methodology\n\n\nAbstract\nWe consider Markov chain Monte C arlo (MCMC) algorithms for Bayesian high-dimensional regression with conti nuous shrinkage priors. A common challenge with these algorithms is the ch oice of the number of iterations to perform. This is critical when each it eration is expensive\, as is the case when dealing with modern data sets\, such as genome-wide association studies with thousands of rows and up to hundreds of thousands of columns. We develop coupling techniques tailored to the setting of high-dimensional regression with shrinkage priors\, whic h enable practical\, non-asymptotic diagnostics of convergence without rel ying on traceplots or long-run asymptotics. By establishing geometric drif t and minorization conditions for the algorithm under consideration\, we p rove that the proposed couplings have finite expected meeting time. Focusi ng on a class of shrinkage priors which includes the 'Horseshoe'\, we empi rically demonstrate the scalability of the proposed couplings. A highlight of our findings is that less than 1000 iterations can be enough for a Gib bs sampler to reach stationarity in a regression on 100\,000 covariates. T he numerical results also illustrate the impact of the prior on the comput ational efficiency of the coupling\, and suggest the use of priors where t he local precisions are Half-t distributed with degree of freedom larger t han one. (Joint work with Niloy Biswas\, Pierre Jacob\, and James Johndrow )\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Helen Ogden (University of Southampton\, UK09:45 - 10:30) DTSTART:20211130T160000Z DTEND:20211130T164500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/9 DESCRIPTION:Title: Approximate cross validation for mixture models\nby Helen O gden (University of Southampton\, UK09:45 - 10:30) as part of CMO-Foundati ons of Objective Bayesian Methodology\n\n\nAbstract\nChoosing appropriate priors and hyperparameters to control the number of components used by a m ixture model is often challenging: it is typically hard to interpret such parameters directly\, which makes it difficult to use subjective prior kno wledge. I will focus instead on how to choose these quantities to give a m odel with good frequentist properties. In principle\, models could be asse ssed by cross validation\, but in practice direct calculation of a cross v alidation criterion is computationally expensive and numerically unstable. I will discuss methods for approximating cross validation criteria for mi xture models\, which aim to address both of these issues.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Ly (University of Amsterdam/CWI Amsterdam) DTSTART:20211130T164500Z DTEND:20211130T173000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/10 DESCRIPTION:Title: Default Bayes Factors for Testing the (In)equality of Several Population Variances\nby Alexander Ly (University of Amsterdam/CWI Ams terdam) as part of CMO-Foundations of Objective Bayesian Methodology\n\n\n Abstract\nThe goal of this presentation is to elaborate on the notion of o bjectivity Bayesian tests. Concretely\, I’ll discuss Harold Jeffreys’s desiderata for objective Bayes factors that were formalised by Bayarri\, Berger\, Forte and García-Donato (2012) within the context of testing the (in)equality of several population variances. I’ll also put forth the d esideratum of across-sample consistency for K-sample problems\, and show t hat for this problem\, such an objective Bayes factor adhering to all thes e desiderata (1) exists\, (2) is easily calculable\, and (3) has good freq uentist properties. If time allows\, I’ll also discuss the sequential pr operties of the resulting Bayes factor.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis E. Nieto-Barajas (ITAM Mexico) DTSTART:20211130T180000Z DTEND:20211130T184500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/11 DESCRIPTION:Title: Characterizing variation of nonparametric random probability m easures using the Kullback–Leibler divergence\nby Luis E. Nieto-Bara jas (ITAM Mexico) as part of CMO-Foundations of Objective Bayesian Methodo logy\n\n\nAbstract\nThis work characterizes the dispersion of some popular random probability measures\, including the bootstrap\, the Bayesian boot strap\, and the Pólya tree prior. This dispersion is measured in terms of the variation of the Kullback–Leibler divergence of a random draw from the process to that of its baseline centring measure. By providing a quant itative expression of this dispersion around the baseline distribution\, o ur work provides insight for comparing different parameterizations of the models and for the setting of prior parameters in applied Bayesian setting s. This highlights some limitations of the existing canonical choice of pa rameter settings in the Pólya tree process.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Holmes (Oxford University) DTSTART:20211130T184500Z DTEND:20211130T193000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/12 DESCRIPTION:Title: Predictive Inference: a view towards objectivity\nby Chris Holmes (Oxford University) as part of CMO-Foundations of Objective Bayesi an Methodology\n\n\nAbstract\nWe revisit the predictive approach to Bayesi an statistics\, advocated by Geisser and others\, as a framework to facili tate objective inference. We explore the predictive viewpoint of Bayesian nonparametric learning as a means to improve robustness in M-open and we p oint to future research directions.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Judith Rousseau (University of Oxford) DTSTART:20211130T220000Z DTEND:20211130T224500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/13 DESCRIPTION:Title: Using cut posterior in semi parametric inference with applicat ions to semiparametric and nonparametric Bayesian inference in hidden Mark ov models\nby Judith Rousseau (University of Oxford) as part of CMO-Fo undations of Objective Bayesian Methodology\n\n\nAbstract\nIf the theory o f Bayesian approaches in standard nonparametric or high dimensional models is beginning to be well developed\, not so much is known in the context o f semi-parametric models outside very specific priors and models. We propo se in this talk a pseudo Bayesian approach\, based on the cut posterior wh ich allows for the construction of a distribution on the whole parameter a nd is constructed such that the marginal posterior on the parameter of int erest has optimal properties. We apply this approach to the setup of nonpa rametric hidden Markov models with finite state space and nonparametric em ission distributions. Since the seminal paper of Gassiat et al. (2016)\, i t is known that in such models the transition matrix $Q$ and the emission distributions $F_1\, · · · \, F_K$ are identifiable\, up to label switc hing. We a cut posterior to simultaneously estimate $Q$ at the rate $\\sqr t{n}$ and the emission distributions at the usual nonparametric rates. To do so\, we first consider a prior $\\pi_1$ on $Q$ and $F_1\, · · · \, F _K$ which leads to a posterior marginal distribution on $Q$ which verifies the Bernstein von mises property and thus to an estimator of $Q$ which is efficient. We then combine the marginal posterior on $Q$ with an other po sterior distribution on the emission distributions\, following the cut-pos terior approach\, to obtain a posterior which also concentrates around the emission distributions at the minimax rates. In addition an important int ermediate result of our work is an inversion inequality which allows to up per bound the $L_1$ norms between the emission densities by the $L_1$ norm s between marginal densities of 3 consecutive observations.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Sinead Williamson (University of Texas at Austin) DTSTART:20211130T224500Z DTEND:20211130T230000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/14 DESCRIPTION:Title: Posterior normalizing flows\nby Sinead Williamson (Univers ity of Texas at Austin) as part of CMO-Foundations of Objective Bayesian M ethodology\n\n\nAbstract\nNormalizing flows allow us to construct complex probability distributions $\\mathbb{P}(X)$ by transforming simpler distrib utions $\\mathbb{Q}(Z)$\, via a change of variables $X=f_\\theta(Z)$. If w e model the change-of-variables transformation $f_\\theta$ using an invert ible neural network with an analytically tractable Jacobian\, we can evalu ate likelihoods under the resulting distribution $\\mathbb{P}(X)$\, allowi ng us to perform maximum likelihood density estimation. Such maximum likel ihood density estimation is likely to overfit\, particularly if the number of observations is small. Rather than creating a mapping between a pair o f distributions\, we use normalizing flows to describe the relationship be tween two families of distributions. This allows us to use nonparametric l earning techniques to learn posterior distributions in a lightweight manne r. (Joint work with Evan Ott)\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Guindani (University of California\, USA) DTSTART:20211201T000000Z DTEND:20211201T004500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/15 DESCRIPTION:Title: A Common Atom Model for the Bayesian Nonparametric Analysis of Nested Data\nby Michele Guindani (University of California\, USA) as part of CMO-Foundations of Objective Bayesian Methodology\n\n\nAbstract\nT he use of large datasets for targeted therapeutic interventions requires n ew ways to characterize the heterogeneity observed across subgroups of a s pecific population. In particular\, models for partially exchangeable data are needed for inference on nested datasets\, where the observations are assumed to be organized in different units and some sharing of information is required to learn distinctive features of the units. In this talk\, we propose a nested Common Atoms Model (CAM) that is particularly suited for the analysis of nested datasets where the distributions of the units are expected to differ only over a small fraction of the observations sampled from each unit. The proposed CAM allows a two-layered clustering at the di stributional and observational level and is amenable to scalable posterior inference through the use of a computationally efficient nested slice sam pler algorithm. We further discuss how to extend the proposed modeling fra mework to handle discrete measurements\, and we conduct posterior inferenc e on a real microbiome dataset from a diet swap study to investigate how t he alterations in intestinal microbiota composition are associated with di fferent eating habits. If time allows\, we will also discuss an applicatio n to the analysis of time series calcium imaging experiments in awake beha ving animals. We further investigate the performance of our model in captu ring true distributional structures in the population by means of simulati on studies.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Rebaudo (University of Texas at Austin) DTSTART:20211201T004500Z DTEND:20211201T013000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/16 DESCRIPTION:Title: Graph-Aligned Random Partition Model\nby Giovanni Rebaudo (University of Texas at Austin) as part of CMO-Foundations of Objective Ba yesian Methodology\n\n\nAbstract\nBayesian nonparametric mixtures and rand om partition models are effective tools to perform probabilistic clusteri ng. However\, standard independent mixture models can be restrictive in so me applications such as inference on cell-lineage due to the biological re lations of the clusters. The increasing availability of large genomics dat a and studies require new statistical tolls to perform model-based cluster ing and infer the relationship between the homogeneous subgroups of units. Motivated by single-cell RNA applications we develop a novel dependent mi xture model to jointly perform cluster analysis and align the cluster on a graph. Our flexible graph-aligned random partition model (gRPM) cleverly exploits Gibbs -type priors as building blocks allowing us to derive analy tical results on the probability mass function of the random partition. Fr om the pmf of the random partition\, we derive a generalization of the wel l-known Chinese restaurant process and a related efficient MCMC algorithm to perform Bayesian inference. We perform posterior inference on real sing le-cell RNA data from mice stem cells. We further investigate the performa nce of our model in capturing underlying clustering structure as well as t he underlying graph by means of a simulation study.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/16/ END:VEVENT BEGIN:VEVENT SUMMARY:David Rossell (Universitat Pompeu Fabra\, Spain) DTSTART:20211201T160000Z DTEND:20211201T164500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/17 DESCRIPTION:Title: Confounder importance learning for treatment effect inference< /a>\nby David Rossell (Universitat Pompeu Fabra\, Spain) as part of CMO-Fo undations of Objective Bayesian Methodology\n\n\nAbstract\nAn important ba sic problem is to estimate the association of a set of covariates of inter est (treatments) while accounting for many potential confounders. It has b een shown that standard high-dimensional Bayesian and penalized likelihood methods perform poorly in practice. The sparsity embedded in such methods leads to low power when there are strong correlations between treatments and confounders\, or between confoundres\, which causes an under-selection (or omitted variable) bias. Current solutions encourage the inclusion of confounders to increase power\, but as we show this can lead to serious ov er-selection problems. To address these issues\, we propose an empirical B ayes framework to learn what confounders should be encouraged (or disencou raged) to feature in the regression. We develop exact computations and a f aster expectation-propagation strategy for the family of exponential regre ssion models. We illustrate the applied impact of these issues to study th e association between salary and potentially discriminatory factors such a s gender\, race and place of birth.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Jack Jewson (Universitat Pompeu Fabra\, Spain) DTSTART:20211201T164500Z DTEND:20211201T173000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/18 DESCRIPTION:Title: General Bayesian Loss Function Selection and the use of Improp er Models\nby Jack Jewson (Universitat Pompeu Fabra\, Spain) as part o f CMO-Foundations of Objective Bayesian Methodology\n\n\nAbstract\nStatist icians often face the choice between using probability models or a paradig m defined by minimising a loss function. Both approaches are useful and\, if the loss can be re-cast into a proper probability model\, there are ma ny tools to decide which model or loss is more appropriate for the observ ed data\, in the sense of explaining \nthe data’s nature. However\, when the loss leads to an improper model\, there are no principled ways to gu ide this choice. We address this task by combining the Hyvarinen score\, w hich naturally targets infinitesimal relative probabilities\, and general Bayesian updating\, which provides a unifying framework for inference on l osses and models. Specifically we propose the H-score\, a general Bayesian selection criterion and prove that it consistently selects the (possibly improper) model closest to \nthe data-generating truth in Fisher’s diver gence. We also prove that an associated H-posterior consistently learns op timal hyper-parameters featuring in loss functions\, including a challengi ng tempering parameter in generalised Bayesian inference. As salient examp les\, we consider robust regression and non-parametric density estimation where popular loss functions define improper models for the data and hence cannot be dealt with using standard model selection tools. These examples illustrate advantages in robustness-efficiency tradeoffs and provide a Ba yesian implementation for kernel density estimation\, opening a new avenue for Bayesian non-parametrics.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Veronika Rockova (University of Chicago) DTSTART:20211201T180000Z DTEND:20211201T184500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/19 DESCRIPTION:Title: Metropolis-Hastings via Classification\nby Veronika Rockov a (University of Chicago) as part of CMO-Foundations of Objective Bayesian Methodology\n\n\nAbstract\nThis paper develops a Bayesian computational p latform at the interface between posterior sampling and optimization in mo dels whose marginal likelihoods are difficult to evaluate. Inspired by con trastive learning and Generative Adversarial Networks (GAN)\, we reframe t he likelihood function estimation problem as a classification problem. Pit ting a Generator\, who simulates fake data\, against a Classifier\, who tr ies to distinguish them from the real data\, one obtains likelihood (ratio ) estimators which can be plugged into the Metropolis-Hastings algorithm. The resulting Markov chains generate\, at a steady state\, samples from an approximate posterior whose asymptotic properties we characterize. Drawin g upon connections with empirical Bayes and Bayesian mis-specification\, w e quantify the convergence rate in terms of the contraction speed of the a ctual posterior and the convergence rate of the Classifier. Asymptotic no rmality results are also provided which justify the inferential potential of our approach. We illustrate the usefulness of our approach on examples which have challenged for existing Bayesian likelihood-free approaches.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Rajesh Ranganath (Courant Institute NYU\, USA) DTSTART:20211201T184500Z DTEND:20211201T193000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/20 DESCRIPTION:Title: Where did my Bayes Go?\nby Rajesh Ranganath (Courant Insti tute NYU\, USA) as part of CMO-Foundations of Objective Bayesian Methodolo gy\n\n\nAbstract\nI've spent time working on Bayesian methods\, especially scalable computation. However\, my recent work has developed algorithms t ailored to problems in healthcare that do not easily translate to standard Bayesian computation. In this talk\, I will highlight two such methods\, one for survival analysis based on multiplayer games and another for build ing predictive models in the presence of spurious correlations. At the end \, I'll highlight thoughts on how Bayesian analysis might play a role in t hese problems.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Noirrit Chandra (The University of exas at Austin\, USA) DTSTART:20211202T160000Z DTEND:20211202T164500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/21 DESCRIPTION:Title: Bayesian Scalable Precision Factor Analysis for Massive Sparse Gaussian Graphical Models\nby Noirrit Chandra (The University of exas at Austin\, USA) as part of CMO-Foundations of Objective Bayesian Methodo logy\n\n\nAbstract\n"We propose a novel approach to estimating the precisi on matrix of multivariate Gaussian data that relies on decomposing them in to a low-rank and a diagonal component. Such decompositions are very popul ar for modeling large covariance matrices as they admit a latent factor ba sed representation that allows easy inference. The same is however not tru e for precision matrices due to the lack of computationally convenient rep resentations which restricts inference to low-to-moderate dimensional prob lems. We address this remarkable gap in the literature by building on a la tent variable representation for such decomposition for precision matrices . The construction leads to an efficient Gibbs sampler that scales very we ll to high-dimensional problems far beyond the limits of the current state -of-the-art. The ability to efficiently explore the full posterior space a lso allows the model uncertainty to be easily assessed. The decomposition crucially additionally allows us to adapt sparsity inducing priors to shr ink the insignificant entries of the precision matrix toward zero\, making the approach adaptable to high-dimensional small-sample-size sparse setti ngs. Exact zeros in the matrix encoding the underlying conditional indepen dence graph are then determined via a novel posterior false discovery rate control procedure. A near minimax optimal posterior concentration rate fo r estimating precision matrices is attained by our method under mild regul arity assumptions.\nWe evaluate the method's empirical performance through synthetic experiments and illustrate its practical utility in data sets f rom two different application domains.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Durante (Bocconi University\, Italy) DTSTART:20211202T164500Z DTEND:20211202T173000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/22 DESCRIPTION:Title: Advances in Bayesian inference for regression models with bina ry\, categorical and partially-discretized data\nby Daniele Durante (B occoni University\, Italy) as part of CMO-Foundations of Objective Bayesia n Methodology\n\n\nAbstract\nA broad class of models that routinely appear in several fields of application can be expressed as partially or fully d iscretized Gaussian linear regressions. Besides including the classical Ga ussian response setting\, this class crucially encompasses probit\, multin omial probit and tobit models\, among others\, and further includes key ex tensions to dynamic\, skewed and multivariate contexts. The relevance of s uch representations has motivated decades of research in the Bayesian fie ld. The main reason for this active interest is that\, unlike for the Gaus sian response setting\, the posterior distribution induced by these models does not apparently belong to a known and tractable class\, under the com monly-assumed Gaussian priors. This has motivated the development of sever al alternative solutions for posterior inference relying either on samplin g-based strategies or on deterministic approximations\, which\, however\, still experience scalability\, mixing and accuracy issues\, especially in high dimension. The scope of this talk is to review\, unify and extend rec ent advances in Bayesian inference and computation for such a class of mod els. To address this goal\, I will prove that the likelihoods induced by a ll these formulations crucially share a common analytical structure which implies conjugacy with a broad class of distributions\, namely the unified skew-normals (SUN)\, that generalize multivariate Gaussians to skewed con texts\, and include these variables as a special case. This result unifies and extends recent conjugacy properties for specific models within the cl ass analyzed\, and opens new avenues for improved posterior inference\, un der a broader class of core formulations and prior distributions\, via nov el closed-form expressions\, tractable Monte Carlo methods based on indepe ndent and identically distributed samples from the exact SUN posteriors\, and more accurate and scalable approximations from variational Bayes and e xpectation-propagation. These advantages are illustrated in extensive simu lation studies and applications\, and are expected to boost the routine-us e of these such core Bayesian models\, while providing a novel framework f or studying general theoretical properties and developing future extension s.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Filippo Ascolani (Bocconi University\, Italy) DTSTART:20211202T180000Z DTEND:20211202T184500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/23 DESCRIPTION:Title: Trees of random probability measures and Bayesian nonparametri c modelling\nby Filippo Ascolani (Bocconi University\, Italy) as part of CMO-Foundations of Objective Bayesian Methodology\n\n\nAbstract\nWe int roduce a way to generate trees of random probability measures\, where the link between two nodes is given by a hierarchical procedure: starting from a common root\, each node of the tree is endowed with a random probabilit y measure\, whose baseline distribution is again random and given by the a ssociated node in the previous layer. The data can be observed at any nod e of the tree and different branches may have different length: the split mechanism can be also considered random or based on covariates of interest . When the branches have the same length and the observations are linked o nly to the leaves\, we recover the well known family of discrete hierarchi cal processes We prove that\, if the distribution at each node is given by the normalization of a completely random measure (NRMI)\, the model is an alytically tractable: conditional on a suitable latent structure\, the pos terior is still given by a deep NRMI. Furthermore\, the asymptotic behavio ur of the number of clusters is derived\, when either the sample size at a particular layer diverges or the number of levels grows. Finally\, the ex tension to kernel mixtures is discussed.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Yang Ni (Texas A&M University\, USA) DTSTART:20211202T184500Z DTEND:20211202T193000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/24 DESCRIPTION:Title: Individualized Causal Discovery with Latent Trajectory Embedde d Bayesian Networks\nby Yang Ni (Texas A&M University\, USA) as part o f CMO-Foundations of Objective Bayesian Methodology\n\n\nAbstract\nBayesia n networks have been widely used for generating causal hypotheses from mul tivariate data. Despite their popularity\, the vast majority of existing c ausal discovery approaches make the strong assumption of a (partially) hom ogeneous sampling scheme. However\, such assumption can be seriously viola ted causing significant biases when the underlying population is inherentl y heterogeneous. To explicitly account for the heterogeneity\, we propose a novel Bayesian network model\, termed BN-LTE\, that embeds the heterogen eous data onto a low-dimensional manifold and builds Bayesian networks con ditional on the embedding. This new framework allows for more precise netw ork inference by improving the estimation resolution from population level to observation level (individualized causal models). Moreover\, while Bay esian networks are in general not identifiable with purely observational\, cross-sectional data due to Markov equivalence\, with the blessing of het erogeneity\, we prove that the proposed BN-LTE is uniquely identifiable un der common causal assumptions. Through extensive experiments\, we demonstr ate the superior performance of BN-LTE in discovering causal relationships as well as inferring observation-specific gene regulatory networks from o bservational data.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/24/ END:VEVENT BEGIN:VEVENT SUMMARY:José Antonio Perusquía (University of Kent\, UK) DTSTART:20211202T220000Z DTEND:20211202T224500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/25 DESCRIPTION:Title: A Bayesian Approach to Anomaly Detection in Computer Systems: A Review\nby José Antonio Perusquía (University of Kent\, UK) as par t of CMO-Foundations of Objective Bayesian Methodology\n\n\nAbstract\nComp uter systems are vast\, complex and dynamic objects that have become cruci al in modern life. To ensure their correct performance\, there is a need t o efficiently detect vulnerabilities and anomalies that could shut them do wn with potentially catastrophic consequences. Nowadays\, there exist a wi de number of classical and machine learning models used for such an import ant task. However\, these approaches lack the flexibility and the inherent probabilistic characterisation of uncertainty that Bayesian statistics of fer. That is why\, in recent years Bayesian anomaly detection models appli ed specifically to computer systems have gained considerable attention\, i n particular in the field of cyber security. That is why in this talk we c entre our attention on how these models have been used\, the specific chal lenges and interesting areas of opportunity.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Katherine Heller (Google Research) DTSTART:20211202T224500Z DTEND:20211202T233000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/26 DESCRIPTION:Title: Towards Trustworthy Machine Learning in Medicine and the Role of Uncertainty\nby Katherine Heller (Google Research) as part of CMO-F oundations of Objective Bayesian Methodology\n\n\nAbstract\nAs ML is incre asingly used in society\, we need methods that we have confidence that we can rely on\, particularly in the medical domain. In this talk I discuss 3 pieces of work\, the role uncertainty plays in understanding and combatin g issues with generalization and bias\, and particular mitigations that we can take into consideration.\n\n1) Sepsis Watch - I present a Gaussian Pr ocess (GP) + Recurrent Neural Network (RNN) model for predicting sepsis in fections in Emergency Department patients. I will discuss the benefit of u ncertainty given by the GP. I will then discuss the social context in intr oducing such a system into a hospital setting.\n\n2) Uncertainty and Elect ronic Health Records (EHR) - I will discuss Bayesian RNN models developed for mortality prediction\, and the distinction between population level pr edictive performance and individual level predictive performance\, and its implications for bias.\n\n3) Underspecification and the credibility impli cations of hyperparameter choices in ML models -- I will discuss medical i maging applications and how using the uncertainty of model performance con ditioned on choice of hyperparameters can help identify situations in whic h methods may not generalize well outside the training domain.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Mengyang Gu (University of California Santa Barbara\, USA) DTSTART:20211203T000000Z DTEND:20211203T004500Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/27 DESCRIPTION:Title: Marginalization of latent variables for correlated data\nb y Mengyang Gu (University of California Santa Barbara\, USA) as part of CM O-Foundations of Objective Bayesian Methodology\n\n\nAbstract\nWe will dis cuss marginalization of latent variables for correlated outcomes\, such as multiple time series\, spatio-temporal processes\, and computer simulatio ns. We first review the Kalman filter and its connection to Gaussian proce sses with Matern covariance. Then we discuss vector regressive models\, li near models of coregionalization\, and their connections to Gaussian proce sses with product covariance. We show marginalizing correlated latent vari ables leads to efficient estimation of model parameters and predictions. A s an example\, we will introduce generalized probabilistic principal compo nent analysis (GPPCA) to study the latent factor model for multiple correl ated outcomes. Our method generalizes the previous probabilistic formulati on of principal component analysis (PPCA) by providing the closed-form max imum marginal likelihood estimator of the factor loadings and other parame ters\, where each factor is modeled by a Gaussian process. Lastly we will introduce efficient representation of Gaussian processes with product Mate rn covariance and its applications on emulating massive computer simulatio ns. We will present numerical studies of simulated and real data that conf irms good predictive accuracy and computational efficiency of proposed app roaches.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Alan Riva-Palacio (IIMAS-UNAM\, Mexico) DTSTART:20211203T004500Z DTEND:20211203T013000Z DTSTAMP:20260404T060945Z UID:CMO-21w5107/28 DESCRIPTION:Title: Bayesian analysis of vectors of subordinators\nby Alan Riv a-Palacio (IIMAS-UNAM\, Mexico) as part of CMO-Foundations of Objective Ba yesian Methodology\n\n\nAbstract\nNon-decreasing additive processes\, also called subordinators\, have many applications throughout mathematical mo deling\; for instance\, they have been quite used in risk and finance. Wel l known examples of subordinators are the stable\, gamma and compound Pois son processes with positive jumps. Extension to a multivariate setting fo r studying heterogeneous data by considering vectors of subordinators can be performed and has been studied in a frequentist setting. In this talk w e will discuss the challenges for the Bayesian analysis of models based on such vectors of subordinators.\n LOCATION:https://stable.researchseminars.org/talk/CMO-21w5107/28/ END:VEVENT END:VCALENDAR