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BEGIN:VEVENT
SUMMARY:Igor Pruenster (Bocconi University))
DTSTART:20211129T160000Z
DTEND:20211129T164500Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/1
DESCRIPTION:Title: Nonparametric priors for partially exchangeable data: dependence struc
ture and borrowing of information\nby Igor Pruenster (Bocconi Universi
ty)) as part of CMO-Foundations of Objective Bayesian Methodology\n\nAbstr
act: TBA\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beatrice Franzolini (Bocconi University\, Italy)
DTSTART:20211129T164500Z
DTEND:20211129T173000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/2
DESCRIPTION:Title: Nonparametric priors with full-range borrowing of information\nby
Beatrice Franzolini (Bocconi University\, Italy) as part of CMO-Foundation
s of Objective Bayesian Methodology\n\n\nAbstract\nWhen data are grouped i
nto distinct samples\, they typically are homogeneous within and heterogen
eous across groups. In this case\, the Bayesian paradigm requires a prior
law over a collection of distributions. From a modelling point of view\, i
t is essential to study how this structure reflects on the observables\, e
specially in nonparametric models. We introduce the notion of hyper-ties a
nd show that they play the same role of actual ties in the exchangeable se
tting\, driving the dependence between observations. Using hyper-ties\, we
can compute correlation between observables and show how its sign depends
from the joint specification. Finally\, we propose a novel class of depen
dent nonparametric priors\, which may induce either positive or negative c
orrelation across samples.\n\n"\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Catalano (University of Warwick\, UK)
DTSTART:20211129T180000Z
DTEND:20211129T184500Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/3
DESCRIPTION:Title: A Wasserstein index of dependence for Bayesian nonparametric modeling<
/a>\nby Marta Catalano (University of Warwick\, UK) as part of CMO-Foundat
ions of Objective Bayesian Methodology\n\n\nAbstract\nOptimal transport (O
T) methods and Wasserstein distances are flourishing in many scientific fi
elds as an effective means for comparing and connecting different random s
tructures. In this talk we describe the first use of an OT distance betwee
n Lévy measures with infinite mass to solve a statistical problem. Comple
x phenomena often yield data from different but related sources\, which ar
e ideally suited to Bayesian modeling because of its inherent borrowing of
information. In a nonparametric setting\, this is regulated by the depend
ence between random measures: we derive a general Wasserstein index for a
principled quantification of the dependence gaining insight into the model
s’ deep structure. It also allows for an informed prior elicitation and
provides a fair ground for model comparison. Our analysis unravels many ke
y properties of the OT distance between Lévy measures\, whose interest go
es beyond Bayesian statistics\, spanning to the theory of partial differen
tial equations and of Lévy processes.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isadora Antoniano-Villalobos (Ca' Foscari University of Venice)
DTSTART:20211129T184500Z
DTEND:20211129T193000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/4
DESCRIPTION:Title: Bayesian mixture models for the prediction of extreme observations
\nby Isadora Antoniano-Villalobos (Ca' Foscari University of Venice) as pa
rt of CMO-Foundations of Objective Bayesian Methodology\n\n\nAbstract\nIn
many applications with interest in large or extreme observations\, usual i
nferential methods may fail to reproduce the tail behaviour of the variabl
es involved. Recent literature has proposed the use of multivariate extrem
e value theory to predict an unobserved component of a random vector given
large observed values of the rest. This is achieved through the estimatio
n of the angular measure controlling the dependence structure in the tail
of the distribution. The idea can be extended and used for prediction of m
ultiple components at adequately large levels\, provided the model used fo
r the angular measure is sufficiently flexible enough to capture complex d
ependence structures. The use of Bernstein polynomials ensures such flexib
ility and their interpretation as mixture models allows the use of current
trans-dimensional MCMC posterior simulation methods for inference.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julyan Arbel (Inria Grenoble\, France)
DTSTART:20211129T220000Z
DTEND:20211129T224500Z
DTSTAMP:20260422T185331Z
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-Foundations of
Objective Bayesian Methodology\n\n\nAbstract\nDiagnosing convergence of M
arkov chain Monte Carlo (MCMC) is crucial in Bayesian analysis. Among the
most popular methods\, the potential scale reduction factor (commonly name
d R-hat) is an indicator that monitors the convergence of all chains to th
e stationary distribution\, based on a comparison of the between- and with
in-variance of the chains. Several improvements have been suggested since
its introduction by Gelman & Rubin (1992). Here\, we analyse some properti
es of the theoretical value R associated to R-hat in the case of a localiz
ed version that focuses on quantiles of the distribution. This leads to pr
oposing a new indicator\, which is shown to allow both for localizing the
MCMC convergence in different quantiles of the distribution\, and at the s
ame time for handling some convergence issues not detected by other R-hat
versions.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Campbell Trevor (University of British Columbia\, Canada)
DTSTART:20211129T224500Z
DTEND:20211129T230000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/6
DESCRIPTION:Title: Parallel Tempering on Optimized Paths\nby Campbell Trevor (Univers
ity of British Columbia\, Canada) as part of CMO-Foundations of Objective
Bayesian Methodology\n\n\nAbstract\nParallel tempering (PT) is a class of
Markov chain Monte Carlo algorithms that constructs a path of distribution
s annealing between a tractable reference and an intractable target\, and
then interchanges states along the path to improve mixing in the target. T
he performance of PT depends on how quickly a sample from the reference di
stribution makes its way to the target\, which in turn depends on the part
icular path of annealing distributions. However\, past work on PT has used
only simple paths constructed from convex combinations of the reference a
nd target log-densities. In this talk I'll show that this path performs po
orly in the common setting where the reference and target are nearly mutua
lly singular. To address this issue\, I'll present an extension of the PT
framework to general families of paths\, formulate the choice of path as a
n optimization problem that admits tractable gradient estimates\, and pres
ent a flexible new family of spline interpolation paths for use in practic
e. Theoretical and empirical results will demonstrate that the proposed me
thodology breaks previously-established upper performance limits for tradi
tional paths.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Fernanda Gil Leyva Villa (Bocconi University)
DTSTART:20211130T000000Z
DTEND:20211130T004500Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/7
DESCRIPTION:Title: Gibbs sampling for mixtures in order of appearance: the ordered alloca
tion sampler\nby María Fernanda Gil Leyva Villa (Bocconi University)
as part of CMO-Foundations of Objective Bayesian Methodology\n\n\nAbstract
\nGibbs sampling methods for mixture models are based on data augmentation
schemes that account for the unobserved partition in the data. They have
been broadly classified into two categories: marginal and conditional samp
lers. Marginal samplers are termed this way because they integrate out par
t of the mixing distribution and model directly the partition structure. T
hey can be used to implement mixture models with a tractable exchangeable
partition probability function (EPPF) associated to the mixing distributio
n. However\, if the EPPF is not available in closed form\, marginal sample
rs are hard to adapt. In contrast\, conditional samplers rely on allocatio
n variables that identify each observation with a mixture component. Whil
e conditional samplers are more broadly applicable and allow direct infere
nce on the mixing distribution\, they are known to suffer from slow mixing
. Moreover\, for mixtures models with infinitely many components some form
of truncation\, either deterministic or random\, is required. As for mixt
ures with a random number of components\, the exploration of parameter spa
ces of different dimensions can also be challenging. We tackle these issue
s by expressing the mixture components in the random order of appearance i
n an exchangeable sequence directed by the mixing distribution. We derive
a sampler\, called the ordered allocation sampler\, that is straightforwar
d to implement for mixing distributions with tractable size-biased ordered
weights. In infinite mixtures\, no form of truncation is necessary. As fo
r finite mixtures with random dimension\, a simple updating of the number
of components is obtained by a blocking argument\, thus easing challenges
found in trans-dimensional moves via Metropolis-Hasting steps. Although th
e ordered allocation sampler is a conditional sampler\, sampling occurs in
the space of ordered partitions with blocks labelled in the least element
order. This improves mixing and promotes a consistent labelling of mixtur
e components throughout iterations.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anirban Bhattarcharya (Texas A&M University)
DTSTART:20211130T004500Z
DTEND:20211130T013000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/8
DESCRIPTION:Title: Coupling-based convergence assessment of some Gibbs samplers for high-
dimensional Bayesian regression with shrinkage priors\nby Anirban Bhat
tarcharya (Texas A&M University) as part of CMO-Foundations of Objective B
ayesian Methodology\n\n\nAbstract\nWe consider Markov chain Monte Carlo (M
CMC) algorithms for Bayesian high-dimensional regression with continuous s
hrinkage priors. A common challenge with these algorithms is the choice of
the number of iterations to perform. This is critical when each iteration
is expensive\, as is the case when dealing with modern data sets\, such a
s genome-wide association studies with thousands of rows and up to hundred
s of thousands of columns. We develop coupling techniques tailored to the
setting of high-dimensional regression with shrinkage priors\, which enabl
e practical\, non-asymptotic diagnostics of convergence without relying on
traceplots or long-run asymptotics. By establishing geometric drift and m
inorization conditions for the algorithm under consideration\, we prove th
at the proposed couplings have finite expected meeting time. Focusing on a
class of shrinkage priors which includes the 'Horseshoe'\, we empirically
demonstrate the scalability of the proposed couplings. A highlight of our
findings is that less than 1000 iterations can be enough for a Gibbs samp
ler to reach stationarity in a regression on 100\,000 covariates. The nume
rical results also illustrate the impact of the prior on the computational
efficiency of the coupling\, and suggest the use of priors where the loca
l precisions are Half-t distributed with degree of freedom larger than one
. (Joint work with Niloy Biswas\, Pierre Jacob\, and James Johndrow)\n
LOCATION:https://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:20260422T185331Z
UID:CMO-21w5107/9
DESCRIPTION:Title: Approximate cross validation for mixture models\nby Helen Ogden (U
niversity of Southampton\, UK09:45 - 10:30) as part of CMO-Foundations of
Objective Bayesian Methodology\n\n\nAbstract\nChoosing appropriate priors
and hyperparameters to control the number of components used by a mixture
model is often challenging: it is typically hard to interpret such paramet
ers directly\, which makes it difficult to use subjective prior knowledge.
I will focus instead on how to choose these quantities to give a model wi
th good frequentist properties. In principle\, models could be assessed by
cross validation\, but in practice direct calculation of a cross validati
on criterion is computationally expensive and numerically unstable. I will
discuss methods for approximating cross validation criteria for mixture m
odels\, which aim to address both of these issues.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Ly (University of Amsterdam/CWI Amsterdam)
DTSTART:20211130T164500Z
DTEND:20211130T173000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/10
DESCRIPTION:Title: Default Bayes Factors for Testing the (In)equality of Several Populat
ion Variances\nby Alexander Ly (University of Amsterdam/CWI Amsterdam)
as part of CMO-Foundations of Objective Bayesian Methodology\n\n\nAbstrac
t\nThe goal of this presentation is to elaborate on the notion of objectiv
ity Bayesian tests. Concretely\, I’ll discuss Harold Jeffreys’s deside
rata for objective Bayes factors that were formalised by Bayarri\, Berger\
, Forte and García-Donato (2012) within the context of testing the (in)eq
uality of several population variances. I’ll also put forth the desidera
tum of across-sample consistency for K-sample problems\, and show that for
this problem\, such an objective Bayes factor adhering to all these desid
erata (1) exists\, (2) is easily calculable\, and (3) has good frequentist
properties. If time allows\, I’ll also discuss the sequential propertie
s of the resulting Bayes factor.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis E. Nieto-Barajas (ITAM Mexico)
DTSTART:20211130T180000Z
DTEND:20211130T184500Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/11
DESCRIPTION:Title: Characterizing variation of nonparametric random probability measures
using the Kullback–Leibler divergence\nby Luis E. Nieto-Barajas (IT
AM Mexico) as part of CMO-Foundations of Objective Bayesian Methodology\n\
n\nAbstract\nThis work characterizes the dispersion of some popular random
probability measures\, including the bootstrap\, the Bayesian bootstrap\,
and the Pólya tree prior. This dispersion is measured in terms of the va
riation of the Kullback–Leibler divergence of a random draw from the pro
cess to that of its baseline centring measure. By providing a quantitative
expression of this dispersion around the baseline distribution\, our work
provides insight for comparing different parameterizations of the models
and for the setting of prior parameters in applied Bayesian settings. This
highlights some limitations of the existing canonical choice of parameter
settings in the Pólya tree process.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Holmes (Oxford University)
DTSTART:20211130T184500Z
DTEND:20211130T193000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/12
DESCRIPTION:Title: Predictive Inference: a view towards objectivity\nby Chris Holmes
(Oxford University) as part of CMO-Foundations of Objective Bayesian Meth
odology\n\n\nAbstract\nWe revisit the predictive approach to Bayesian stat
istics\, advocated by Geisser and others\, as a framework to facilitate ob
jective inference. We explore the predictive viewpoint of Bayesian nonpara
metric learning as a means to improve robustness in M-open and we point to
future research directions.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Judith Rousseau (University of Oxford)
DTSTART:20211130T220000Z
DTEND:20211130T224500Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/13
DESCRIPTION:Title: Using cut posterior in semi parametric inference with applications to
semiparametric and nonparametric Bayesian inference in hidden Markov mode
ls\nby Judith Rousseau (University of Oxford) as part of CMO-Foundatio
ns of Objective Bayesian Methodology\n\n\nAbstract\nIf the theory of Bayes
ian approaches in standard nonparametric or high dimensional models is beg
inning to be well developed\, not so much is known in the context of semi-
parametric models outside very specific priors and models. We propose in t
his talk a pseudo Bayesian approach\, based on the cut posterior which all
ows for the construction of a distribution on the whole parameter and is c
onstructed such that the marginal posterior on the parameter of interest h
as optimal properties. We apply this approach to the setup of nonparametri
c hidden Markov models with finite state space and nonparametric emission
distributions. Since the seminal paper of Gassiat et al. (2016)\, it is kn
own that in such models the transition matrix $Q$ and the emission distrib
utions $F_1\, · · · \, F_K$ are identifiable\, up to label switching. W
e a cut posterior to simultaneously estimate $Q$ at the rate $\\sqrt{n}$ a
nd the emission distributions at the usual nonparametric rates. To do so\,
we first consider a prior $\\pi_1$ on $Q$ and $F_1\, · · · \, F_K$ whi
ch leads to a posterior marginal distribution on $Q$ which verifies the Be
rnstein von mises property and thus to an estimator of $Q$ which is effici
ent. We then combine the marginal posterior on $Q$ with an other posterior
distribution on the emission distributions\, following the cut-posterior
approach\, to obtain a posterior which also concentrates around the emissi
on distributions at the minimax rates. In addition an important intermedia
te result of our work is an inversion inequality which allows to upper bou
nd the $L_1$ norms between the emission densities by the $L_1$ norms betwe
en marginal densities of 3 consecutive observations.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinead Williamson (University of Texas at Austin)
DTSTART:20211130T224500Z
DTEND:20211130T230000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/14
DESCRIPTION:Title: Posterior normalizing flows\nby Sinead Williamson (University of
Texas at Austin) as part of CMO-Foundations of Objective Bayesian Methodol
ogy\n\n\nAbstract\nNormalizing flows allow us to construct complex probabi
lity distributions $\\mathbb{P}(X)$ by transforming simpler distributions
$\\mathbb{Q}(Z)$\, via a change of variables $X=f_\\theta(Z)$. If we model
the change-of-variables transformation $f_\\theta$ using an invertible ne
ural network with an analytically tractable Jacobian\, we can evaluate lik
elihoods under the resulting distribution $\\mathbb{P}(X)$\, allowing us t
o perform maximum likelihood density estimation. Such maximum likelihood d
ensity estimation is likely to overfit\, particularly if the number of obs
ervations is small. Rather than creating a mapping between a pair of distr
ibutions\, we use normalizing flows to describe the relationship between t
wo families of distributions. This allows us to use nonparametric learning
techniques to learn posterior distributions in a lightweight manner. (Jo
int work with Evan Ott)\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Guindani (University of California\, USA)
DTSTART:20211201T000000Z
DTEND:20211201T004500Z
DTSTAMP:20260422T185331Z
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\nThe use
of large datasets for targeted therapeutic interventions requires new ways
to characterize the heterogeneity observed across subgroups of a specific
population. In particular\, models for partially exchangeable data are ne
eded for inference on nested datasets\, where the observations are assumed
to be organized in different units and some sharing of information is req
uired to learn distinctive features of the units. In this talk\, we propos
e a nested Common Atoms Model (CAM) that is particularly suited for the an
alysis of nested datasets where the distributions of the units are expecte
d to differ only over a small fraction of the observations sampled from ea
ch unit. The proposed CAM allows a two-layered clustering at the distribut
ional and observational level and is amenable to scalable posterior infere
nce through the use of a computationally efficient nested slice sampler al
gorithm. We further discuss how to extend the proposed modeling framework
to handle discrete measurements\, and we conduct posterior inference on a
real microbiome dataset from a diet swap study to investigate how the alte
rations in intestinal microbiota composition are associated with different
eating habits. If time allows\, we will also discuss an application to th
e analysis of time series calcium imaging experiments in awake behaving an
imals. We further investigate the performance of our model in capturing tr
ue distributional structures in the population by means of simulation stud
ies.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Rebaudo (University of Texas at Austin)
DTSTART:20211201T004500Z
DTEND:20211201T013000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/16
DESCRIPTION:Title: Graph-Aligned Random Partition Model\nby Giovanni Rebaudo (Univer
sity of Texas at Austin) as part of CMO-Foundations of Objective Bayesian
Methodology\n\n\nAbstract\nBayesian nonparametric mixtures and random part
ition models are effective tools to perform probabilistic clustering. How
ever\, standard independent mixture models can be restrictive in some appl
ications such as inference on cell-lineage due to the biological relations
of the clusters. The increasing availability of large genomics data and s
tudies require new statistical tolls to perform model-based clustering and
infer the relationship between the homogeneous subgroups of units. Motiva
ted by single-cell RNA applications we develop a novel dependent mixture m
odel to jointly perform cluster analysis and align the cluster on a graph.
Our flexible graph-aligned random partition model (gRPM) cleverly exploit
s Gibbs -type priors as building blocks allowing us to derive analytical r
esults on the probability mass function of the random partition. From the
pmf of the random partition\, we derive a generalization of the well-known
Chinese restaurant process and a related efficient MCMC algorithm to perf
orm Bayesian inference. We perform posterior inference on real single-cell
RNA data from mice stem cells. We further investigate the performance of
our model in capturing underlying clustering structure as well as the unde
rlying graph by means of a simulation study.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Rossell (Universitat Pompeu Fabra\, Spain)
DTSTART:20211201T160000Z
DTEND:20211201T164500Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/17
DESCRIPTION:Title: Confounder importance learning for treatment effect inference\nby
David Rossell (Universitat Pompeu Fabra\, Spain) as part of CMO-Foundatio
ns of Objective Bayesian Methodology\n\n\nAbstract\nAn important basic pro
blem is to estimate the association of a set of covariates of interest (tr
eatments) while accounting for many potential confounders. It has been sho
wn that standard high-dimensional Bayesian and penalized likelihood method
s perform poorly in practice. The sparsity embedded in such methods leads
to low power when there are strong correlations between treatments and con
founders\, or between confoundres\, which causes an under-selection (or om
itted variable) bias. Current solutions encourage the inclusion of confoun
ders to increase power\, but as we show this can lead to serious over-sele
ction problems. To address these issues\, we propose an empirical Bayes fr
amework to learn what confounders should be encouraged (or disencouraged)
to feature in the regression. We develop exact computations and a faster e
xpectation-propagation strategy for the family of exponential regression m
odels. We illustrate the applied impact of these issues to study the assoc
iation between salary and potentially discriminatory factors such as gende
r\, race and place of birth.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Jewson (Universitat Pompeu Fabra\, Spain)
DTSTART:20211201T164500Z
DTEND:20211201T173000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/18
DESCRIPTION:Title: General Bayesian Loss Function Selection and the use of Improper Mode
ls\nby Jack Jewson (Universitat Pompeu Fabra\, Spain) as part of CMO-F
oundations of Objective Bayesian Methodology\n\n\nAbstract\nStatisticians
often face the choice between using probability models or a paradigm defin
ed by minimising a loss function. Both approaches are useful and\, if the
loss can be re-cast into a proper probability model\, there are many tool
s to decide which model or loss is more appropriate for the observed data
\, in the sense of explaining \nthe data’s nature. However\, when the lo
ss leads to an improper model\, there are no principled ways to guide thi
s choice. We address this task by combining the Hyvarinen score\, which na
turally targets infinitesimal relative probabilities\, and general Bayesia
n updating\, which provides a unifying framework for inference on losses a
nd models. Specifically we propose the H-score\, a general Bayesian select
ion criterion and prove that it consistently selects the (possibly imprope
r) model closest to \nthe data-generating truth in Fisher’s divergence.
We also prove that an associated H-posterior consistently learns optimal h
yper-parameters featuring in loss functions\, including a challenging temp
ering parameter in generalised Bayesian inference. As salient examples\, w
e consider robust regression and non-parametric density estimation where p
opular loss functions define improper models for the data and hence cannot
be dealt with using standard model selection tools. These examples illust
rate advantages in robustness-efficiency tradeoffs and provide a Bayesian
implementation for kernel density estimation\, opening a new avenue for Ba
yesian non-parametrics.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veronika Rockova (University of Chicago)
DTSTART:20211201T180000Z
DTEND:20211201T184500Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/19
DESCRIPTION:Title: Metropolis-Hastings via Classification\nby Veronika Rockova (Univ
ersity of Chicago) as part of CMO-Foundations of Objective Bayesian Method
ology\n\n\nAbstract\nThis paper develops a Bayesian computational platform
at the interface between posterior sampling and optimization in models wh
ose marginal likelihoods are difficult to evaluate. Inspired by contrastiv
e learning and Generative Adversarial Networks (GAN)\, we reframe the like
lihood function estimation problem as a classification problem. Pitting a
Generator\, who simulates fake data\, against a Classifier\, who tries to
distinguish them from the real data\, one obtains likelihood (ratio) estim
ators which can be plugged into the Metropolis-Hastings algorithm. The res
ulting Markov chains generate\, at a steady state\, samples from an approx
imate posterior whose asymptotic properties we characterize. Drawing upon
connections with empirical Bayes and Bayesian mis-specification\, we quant
ify the convergence rate in terms of the contraction speed of the actual p
osterior and the convergence rate of the Classifier. Asymptotic normality
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://researchseminars.org/talk/CMO-21w5107/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajesh Ranganath (Courant Institute NYU\, USA)
DTSTART:20211201T184500Z
DTEND:20211201T193000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/20
DESCRIPTION:Title: Where did my Bayes Go?\nby Rajesh Ranganath (Courant Institute NY
U\, USA) as part of CMO-Foundations of Objective Bayesian Methodology\n\n\
nAbstract\nI've spent time working on Bayesian methods\, especially scalab
le computation. However\, my recent work has developed algorithms tailored
to problems in healthcare that do not easily translate to standard Bayesi
an computation. In this talk\, I will highlight two such methods\, one for
survival analysis based on multiplayer games and another for building pre
dictive models in the presence of spurious correlations. At the end\, I'll
highlight thoughts on how Bayesian analysis might play a role in these pr
oblems.\n
LOCATION:https://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:20260422T185331Z
UID:CMO-21w5107/21
DESCRIPTION:Title: Bayesian Scalable Precision Factor Analysis for Massive Sparse Gaussi
an Graphical Models\nby Noirrit Chandra (The University of exas at Aus
tin\, USA) as part of CMO-Foundations of Objective Bayesian Methodology\n\
n\nAbstract\n"We propose a novel approach to estimating the precision matr
ix of multivariate Gaussian data that relies on decomposing them into a lo
w-rank and a diagonal component. Such decompositions are very popular for
modeling large covariance matrices as they admit a latent factor based rep
resentation that allows easy inference. The same is however not true for p
recision matrices due to the lack of computationally convenient representa
tions which restricts inference to low-to-moderate dimensional problems. W
e address this remarkable gap in the literature by building on a latent va
riable representation for such decomposition for precision matrices. The c
onstruction leads to an efficient Gibbs sampler that scales very well to h
igh-dimensional problems far beyond the limits of the current state-of-the
-art. The ability to efficiently explore the full posterior space also all
ows the model uncertainty to be easily assessed. The decomposition crucial
ly additionally allows us to adapt sparsity inducing priors to shrink the
insignificant entries of the precision matrix toward zero\, making the ap
proach adaptable to high-dimensional small-sample-size sparse settings. Ex
act zeros in the matrix encoding the underlying conditional independence g
raph are then determined via a novel posterior false discovery rate contro
l procedure. A near minimax optimal posterior concentration rate for estim
ating precision matrices is attained by our method under mild regularity a
ssumptions.\nWe evaluate the method's empirical performance through synthe
tic experiments and illustrate its practical utility in data sets from two
different application domains.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Durante (Bocconi University\, Italy)
DTSTART:20211202T164500Z
DTEND:20211202T173000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/22
DESCRIPTION:Title: Advances in Bayesian inference for regression models with binary\, ca
tegorical and partially-discretized data\nby Daniele Durante (Bocconi
University\, Italy) as part of CMO-Foundations of Objective Bayesian Metho
dology\n\n\nAbstract\nA broad class of models that routinely appear in sev
eral fields of application can be expressed as partially or fully discreti
zed Gaussian linear regressions. Besides including the classical Gaussian
response setting\, this class crucially encompasses probit\, multinomial p
robit and tobit models\, among others\, and further includes key extension
s to dynamic\, skewed and multivariate contexts. The relevance of such rep
resentations has motivated decades of research in the Bayesian field. The
main reason for this active interest is that\, unlike for the Gaussian re
sponse setting\, the posterior distribution induced by these models does n
ot apparently belong to a known and tractable class\, under the commonly-a
ssumed Gaussian priors. This has motivated the development of several alte
rnative solutions for posterior inference relying either on sampling-based
strategies or on deterministic approximations\, which\, however\, still e
xperience scalability\, mixing and accuracy issues\, especially in high di
mension. The scope of this talk is to review\, unify and extend recent adv
ances in Bayesian inference and computation for such a class of models. To
address this goal\, I will prove that the likelihoods induced by all thes
e formulations crucially share a common analytical structure which implies
conjugacy with a broad class of distributions\, namely the unified skew-n
ormals (SUN)\, that generalize multivariate Gaussians to skewed contexts\,
and include these variables as a special case. This result unifies and ex
tends recent conjugacy properties for specific models within the class ana
lyzed\, and opens new avenues for improved posterior inference\, under a b
roader class of core formulations and prior distributions\, via novel clos
ed-form expressions\, tractable Monte Carlo methods based on independent a
nd identically distributed samples from the exact SUN posteriors\, and mor
e accurate and scalable approximations from variational Bayes and expectat
ion-propagation. These advantages are illustrated in extensive simulation
studies and applications\, and are expected to boost the routine-use of th
ese such core Bayesian models\, while providing a novel framework for stud
ying general theoretical properties and developing future extensions.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filippo Ascolani (Bocconi University\, Italy)
DTSTART:20211202T180000Z
DTEND:20211202T184500Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/23
DESCRIPTION:Title: Trees of random probability measures and Bayesian nonparametric model
ling\nby Filippo Ascolani (Bocconi University\, Italy) as part of CMO-
Foundations of Objective Bayesian Methodology\n\n\nAbstract\nWe introduce
a way to generate trees of random probability measures\, where the link be
tween two nodes is given by a hierarchical procedure: starting from a comm
on root\, each node of the tree is endowed with a random probability measu
re\, whose baseline distribution is again random and given by the associat
ed node in the previous layer. The data can be observed at any node of th
e tree and different branches may have different length: the split mechani
sm can be also considered random or based on covariates of interest. When
the branches have the same length and the observations are linked only to
the leaves\, we recover the well known family of discrete hierarchical pro
cesses We prove that\, if the distribution at each node is given by the no
rmalization of a completely random measure (NRMI)\, the model is analytica
lly tractable: conditional on a suitable latent structure\, the posterior
is still given by a deep NRMI. Furthermore\, the asymptotic behaviour of t
he number of clusters is derived\, when either the sample size at a partic
ular layer diverges or the number of levels grows. Finally\, the extension
to kernel mixtures is discussed.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Ni (Texas A&M University\, USA)
DTSTART:20211202T184500Z
DTEND:20211202T193000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/24
DESCRIPTION:Title: Individualized Causal Discovery with Latent Trajectory Embedded Bayes
ian Networks\nby Yang Ni (Texas A&M University\, USA) as part of CMO-F
oundations of Objective Bayesian Methodology\n\n\nAbstract\nBayesian netwo
rks have been widely used for generating causal hypotheses from multivaria
te data. Despite their popularity\, the vast majority of existing causal d
iscovery approaches make the strong assumption of a (partially) homogeneou
s sampling scheme. However\, such assumption can be seriously violated cau
sing significant biases when the underlying population is inherently heter
ogeneous. To explicitly account for the heterogeneity\, we propose a novel
Bayesian network model\, termed BN-LTE\, that embeds the heterogeneous da
ta onto a low-dimensional manifold and builds Bayesian networks conditiona
l on the embedding. This new framework allows for more precise network inf
erence by improving the estimation resolution from population level to obs
ervation level (individualized causal models). Moreover\, while Bayesian n
etworks are in general not identifiable with purely observational\, cross-
sectional data due to Markov equivalence\, with the blessing of heterogene
ity\, we prove that the proposed BN-LTE is uniquely identifiable under com
mon causal assumptions. Through extensive experiments\, we demonstrate the
superior performance of BN-LTE in discovering causal relationships as wel
l as inferring observation-specific gene regulatory networks from observat
ional data.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Antonio Perusquía (University of Kent\, UK)
DTSTART:20211202T220000Z
DTEND:20211202T224500Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/25
DESCRIPTION:Title: A Bayesian Approach to Anomaly Detection in Computer Systems: A Revie
w\nby José Antonio Perusquía (University of Kent\, UK) as part of CM
O-Foundations of Objective Bayesian Methodology\n\n\nAbstract\nComputer sy
stems are vast\, complex and dynamic objects that have become crucial in m
odern life. To ensure their correct performance\, there is a need to effic
iently detect vulnerabilities and anomalies that could shut them down with
potentially catastrophic consequences. Nowadays\, there exist a wide numb
er of classical and machine learning models used for such an important tas
k. However\, these approaches lack the flexibility and the inherent probab
ilistic characterisation of uncertainty that Bayesian statistics offer. Th
at is why\, in recent years Bayesian anomaly detection models applied spec
ifically to computer systems have gained considerable attention\, in parti
cular in the field of cyber security. That is why in this talk we centre o
ur attention on how these models have been used\, the specific challenges
and interesting areas of opportunity.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katherine Heller (Google Research)
DTSTART:20211202T224500Z
DTEND:20211202T233000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/26
DESCRIPTION:Title: Towards Trustworthy Machine Learning in Medicine and the Role of Unce
rtainty\nby Katherine Heller (Google Research) as part of CMO-Foundati
ons of Objective Bayesian Methodology\n\n\nAbstract\nAs ML is increasingly
used in society\, we need methods that we have confidence that we can rel
y on\, particularly in the medical domain. In this talk I discuss 3 pieces
of work\, the role uncertainty plays in understanding and combating issue
s with generalization and bias\, and particular mitigations that we can ta
ke into consideration.\n\n1) Sepsis Watch - I present a Gaussian Process (
GP) + Recurrent Neural Network (RNN) model for predicting sepsis infection
s in Emergency Department patients. I will discuss the benefit of uncertai
nty given by the GP. I will then discuss the social context in introducing
such a system into a hospital setting.\n\n2) Uncertainty and Electronic H
ealth Records (EHR) - I will discuss Bayesian RNN models developed for mor
tality prediction\, and the distinction between population level predictiv
e performance and individual level predictive performance\, and its implic
ations for bias.\n\n3) Underspecification and the credibility implications
of hyperparameter choices in ML models -- I will discuss medical imaging
applications and how using the uncertainty of model performance conditione
d on choice of hyperparameters can help identify situations in which metho
ds may not generalize well outside the training domain.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mengyang Gu (University of California Santa Barbara\, USA)
DTSTART:20211203T000000Z
DTEND:20211203T004500Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/27
DESCRIPTION:Title: Marginalization of latent variables for correlated data\nby Mengy
ang Gu (University of California Santa Barbara\, USA) as part of CMO-Found
ations of Objective Bayesian Methodology\n\n\nAbstract\nWe will discuss ma
rginalization of latent variables for correlated outcomes\, such as multip
le time series\, spatio-temporal processes\, and computer simulations. We
first review the Kalman filter and its connection to Gaussian processes wi
th Matern covariance. Then we discuss vector regressive models\, linear mo
dels of coregionalization\, and their connections to Gaussian processes wi
th product covariance. We show marginalizing correlated latent variables l
eads to efficient estimation of model parameters and predictions. As an ex
ample\, we will introduce generalized probabilistic principal component an
alysis (GPPCA) to study the latent factor model for multiple correlated ou
tcomes. Our method generalizes the previous probabilistic formulation of p
rincipal component analysis (PPCA) by providing the closed-form maximum ma
rginal likelihood estimator of the factor loadings and other parameters\,
where each factor is modeled by a Gaussian process. Lastly we will introdu
ce efficient representation of Gaussian processes with product Matern cova
riance and its applications on emulating massive computer simulations. We
will present numerical studies of simulated and real data that confirms go
od predictive accuracy and computational efficiency of proposed approaches
.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Riva-Palacio (IIMAS-UNAM\, Mexico)
DTSTART:20211203T004500Z
DTEND:20211203T013000Z
DTSTAMP:20260422T185331Z
UID:CMO-21w5107/28
DESCRIPTION:Title: Bayesian analysis of vectors of subordinators\nby Alan Riva-Palac
io (IIMAS-UNAM\, Mexico) as part of CMO-Foundations of Objective Bayesian
Methodology\n\n\nAbstract\nNon-decreasing additive processes\, also called
subordinators\, have many applications throughout mathematical modeling\
; for instance\, they have been quite used in risk and finance. Well known
examples of subordinators are the stable\, gamma and compound Poisson pro
cesses with positive jumps. Extension to a multivariate setting for study
ing heterogeneous data by considering vectors of subordinators can be perf
ormed and has been studied in a frequentist setting. In this talk we will
discuss the challenges for the Bayesian analysis of models based on such v
ectors of subordinators.\n
LOCATION:https://researchseminars.org/talk/CMO-21w5107/28/
END:VEVENT
END:VCALENDAR