Workshopon Statistical mixtures and latent-structure
modelling 28–30 March Scientific Organising Committee:
Christian Robert (Paris) Michael Titterington (Glasgow)
Supported by: The Engineering and Physical Sciences Research
Council The Royal Statistical Society
The motivation for the
Workshop was the awareness that the topic of mixture modelling and the wider
versions that constitute latent structure analysis are currently of major
interest to an increasingly wide range of scientific disciplines. A number of
aspects underpinned the eventual format of the Workshop and the choice of
invitees:
- the fact that mixture models and their generalisations are not
amenable to standard theory in some likelihood-ratio testing contexts, with
work ongoing to deal with this non-regularity;
- the ubiquity of the EM algorithm for obtaining maximum
likelihood or maximum a posteriori estimates of parameters in incomplete-data
contexts;
- the recent exploitation of Markov chain Monte Carlo simulation
methods for facilitating practical inference in both Bayesian and likelihood
approaches to latent-structure models;
- the surge of interest during the last few years among the
neural computing community in models involving latent structure, especially in
the context of very large scale practical problems
The formal programme began with an overview lecture by Professor
Robert and was wound up by a ‘summing-up’ session led by Professor
Titterington. In between there were 18 invited lectures and there was time for
a poster session at which 14 items were on display. In advance of the poster
session the presenters were allowed two-minute spotlight opportunities at which
they could give very brief trailers of the posters and thereby attract interest
to the displayed posters. All presentations were based on research that was
either very recent or still under development.
The speakers (of whom 11
were based overseas) and titles for the invited talks were the following.
M Aitkin: |
A general mixture ML analysis for
random effect models |
C Andrieu: |
SAME, SA^{2}ME, FAME and
RDA |
C M Bishop: |
Variational methods and latent
variables |
G Celeux: |
Assessing the number of mixture
components: a survey |
P Dellaportas: |
Latent variables for modelling
volatility processes |
B Garel: |
Likelihood ratio test for
univariate Gaussian mixture |
E Gassiat: |
The number of populations in a
mixture with Markov regime |
P J Green: |
Mixtures in time and space |
B G Lindsay: |
On determining an adequate number
of mixture components |
N L Hjort: |
On attempts at generalising the
Dirichlet process |
D J C MacKay: |
The state of the art in error
correcting codes |
G J McLachlan: |
On the incremental EM algorithm
for speeding up the fitting of finite mixture models |
R M Neal: |
Hierarchical mixtures using
diffusion tree priors |
G O Roberts: |
Bayesian inference for discretely
observed diffusion processes |
T Rydén: |
Continuous-time jump MCMC and model
selection for HMMs |
C Skinner: |
Estimation of distributions in the
presence of measurement error |
M Stephens: |
Inferring latent population
structure from genetic data |
C K I Williams: |
Image modelling with dynamic
trees |
Attendance at the Workshop had been strictly limited, partly
because of the constraints imposed by the venue at the ICMS, but also by the
desire to create an intimate ambience. Seven places were allocated to PhD
students who were selected, from those who responded to a call for expressions
of interest, on the basis of the perceived relevance of the Workshop to their
research project.
The dominant aspects of the Workshop were the
following
- Even the simple mixture models continue to attract much
attention, in terms of classical frequentist theory (Garel), in the development
of modifications to the now-standard EM algorithm (McLachlan), in the study of
distance-based estimators (Besbeas) and in computational and other aspects of
the Bayesian approach (Andrieu, Nobile, Mengersen).
- In both simple mixtures and more complicated latent structure
models, there is still considerable activity concerning the thorny problem of
assessing the cardinality of the latent state space, e.g. ‘the number of
components in a mixture’ (Gassiat, Lindsay, Celeux, Stephens). The
approaches varied and included the search for valid frequentist asymptotic
theory, the use of model-selection criteria and Bayesian analysis of
variable-dimension parameter spaces.
- The general nature of latent structure modelling was much in
evidence, as in the variations corresponding to random effects models and
measurement error models (Aitkin, Skinner, Richardson), situations involving
spatio-temporal effects (Green), diffusion process (Roberts), Dirichlet
processes (Hjort, Rasmussen), hierarchical structures (Neal), hidden Markov
models (Gassiat, Rydén), graphical models (Salgueiro) and mixtures of
factor analysers (Seeger).
- The pervasiveness of the models in application areas was
remarkable, including genetics (Stephens), finance (Dellaportas), solar
radiation (Glasbey), social statistics (Salgueiro), epidemiology (Mooney),
error-correcting codes (MacKay), forensic science (Aitken), ornithology
(Darnell) and many others referred to in passing throughout the Workshop. (v)
Although the majority of the participants were from the statistical
- community, a sizeable and prominent minority were at least
partially based in computer science environments, even though their research
interests matched those of the Workshop very well. This led to a very positive
atmosphere of mutual enlightenment and interest. Although there was some
agreement to differ in some areas, the overall impression was given that
everyone gleaned useful knowledge; for instance, for many statisticians this
was their first exposure to so-called variational approximations (Bishop,
Beal).
Informal feedback from the participants has been universally and
gratifyingly positive, principally concerning the quality of the scientific
material and its presentation, but significantly concerning the pleasant,
relaxed atmosphere provided by the ICMS premises in James Clerk Maxwell’s
place of birth.
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List
Participants:
Aitken, Colin – University of
Edinburgh Aitkin, Murray – Education Statistics Services Centre
Andrieu, Christophe – University of Bristol Beal, Matt –
University College London Besbeas, Panagiotis – University of Kent
Bishop, Christopher – Microsoft Research Celeux, Gilles –
INRIA Chauveau, Didier – Université Marne-la-Vallee Croft,
Jonathan – University of Warwick Darnell, Ross – University of
Newcastle-upon-Tyne Dellaportas, Petros – Athens Univ. of Economics
& Business Ecob, Russell – Ecob Consulting Fokoué,
Ernest – University of Glasgow Garel, Bernard – National
Polytechnic Institute, Toulouse Gassiat, Elisabeth – Université
Paris-Sud Glasbey, Chris – Biomathematics & Statistics Scotland
Green, Peter – University of Bristol Hjort, Nils – University
of Oslo Hurn, Merrilee – University of Bristol Kauermann,
Göran – University of Glasgow Lindsay, Bruce – Pennsylvania
State University MacKay, David – University of Cambridge McLachan,
Geoff – University of Queensland Mengersen, Kerrie – University
of Newcastle, Australia Mooney, Jenny – University of Aberdeen
Murphy, Brendan – Trinity College Dublin Murray-Smith, Roderick
– University of Glasgow Neal, Radford – University of Toronto
Nobile, Agostino – University of Glasgow Rasmussen, Carl –
University College, London Richardson, Sylvia – Imperial School of
Medicine Robert, Christian – Université Paris IX Dauphine
Roberts, Gareth – University of Lancaster Rydén, Tobias
– University of Lund Salgueiro, Maria – University of Southampton
Seeger, Matthias – University of Edinburgh Shi, Jian Qing –
University of Glasgow Skinner, Chris – University of Southampton
Stephens, Matthew – University of Washington Storkey, Amos –
University of Edinburgh Titterington, Mike – University of Glasgow
Wild, Pascal – INRS Williams, Chris – University of Edinburgh
Worton, Bruce – University of Edinburgh
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