Gemeinsames Seminar mit Alexander Schliep vom MPI molekulare Genetik
Berlin/Rutgers, Raymond Hemmecke von der Otto-von-Guericke Universität
Magdeburg/TU Darmstadt sowie Nihat Ay und Thomas Kahle vom MPI Mathematik
in den Naturwissenschaften.
| Datum | Ort | Thema | VortragendeR |
| 16.9. |
ÚTIA, Prague, CZ |
Announcement with practical hints and registration information |
Organized by Milan Studený and František Matúš
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10:30 A survey of some issues that arise in statistical model selection |
Joe Whittaker, Lancaster University, UK |
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Statistical model selection has for many years been of interest to
the academic and scientific profession. Here we discuss some of the
current issues and, in particular, make a comparison to what was
available thirty years ago.
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11:30 coffee break |
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11:45 Polytopes of Bayesian network structures |
Raymond Hemmecke, TU Darmstadt & OvGU Magdeburg |
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In this talk we consider polytopes associated to Bayesian network
structures. The study of these polytopes is fundamental for improving
existing algorithms for learning such Bayesian network structures. By
restricting our attention to special Bayesian networks, e.g. those that have
an undirected tree or forest as the essential graph, we obtain very nice
structural results on these associated polytopes. In particular, they allow
us to give a mathematical proof that the GES algorithm (greedy
equivalence search) is guaranteed to find an optimal Bayesian network
structure of the pre-described special type. We give an example that this
need not be the case in the general case.
[This is joint work with Silvia Lindner, Milan Studeny and Jirka Vomlel.]
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12:45 lunch break |
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14:00 Maximizing the multi-information of stochastic processes |
Nihat Ay, MPI Leipzig |
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I will discuss various approaches to the geometry of the set of stochastic
matrices motivated by information geometry. Based on this, I introduce a
notion of multi-information for stochastic processes and study the
corresponding maximization problem. The main result sets bounds on the
entropy of a Markov process with maximal multi-information. Finally, I
comment on some open problems related to the Kolmogorov-Sinai entropy of
dynamical systems.
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15:00 coffee break |
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15:15 Limiting in closures of exponential families |
František Matúš, ASCR |
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The closures of exponential families of probability measures in
the variation distance and reversed information divergence have
been used to understand better the optimization of likelihood and
entropies. Existing results on the closures will be reviewed, including
a quantum setting if time permits. For the standard exponential families
on Euclidean spaces with finite supports limiting in the mean
parametrization
towards the boundary can be described in a considerable detail.
This provides a control of the behavior of information divergences and
variance functions around boundaries. Resulting expansions of variance
functions at boundary points are used to prove that an exponential
family has a finite support and quadratic variance function if and only
if it is the product of multinomial families up to an affine transformation.
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| 6.4. |
TU Darmstadt |
11:00 Model Selection for Coevolution in Virology, Drug Resistance Developement, and Biophyiscs |
Kay Hamacher (TU Darmstadt) |
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Evolution reveals itself on the level of single amino acid changes in viral and other proteins. Particular positions in a protein are under varying selective pressure and show
different dynamics. We are interested in models and measures for the correlated evolutionary dynamics, that is coevolution of amino acids and nucleotids in biomolecules.
Commanding of such models would then allow us to leverage our biophysical models and structural arguments to annotate selective advantages in the molecular phenotype.
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12.15 Moment matrices and real root finding |
Philipp Rostalski (ETH Zurich) |
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The problem of determining the existence of a measure, such that a given multi-sequence of real numbers agrees with its first moments is known as the truncated moment
problem. The main tool to analyze this question is the so called moment matrix, a positive semi-definite matrix with quasi-Hankel structure, whose entries consist of the
given moments. We will analyze the algebraic structure of this matrix and show, how it can be turned into an algorithm for computing all real roots, or even all roots in a
given semi-algebraic subset.
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14:30 Model Selection and Testing for Mixtures and Hidden Markov Models |
Hajo Holzmann (University of Marburg) |
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We investigate likelihood-based model selection and testing for mixtures and hidden Markov models (HMMs), in particular for choosing the number of components in the
mixture or the number of states in the HMM. We discuss in which situations hypothesis testing or model selection based on information criteria is more suitable. Concerning
model testing, we investigate testing for homogeneity in finite mixtures and testing for two states in an HMM. We also consider further non-standard testing situations such
as testing for bimodality in two-component mixtures. The procedures are illustrated by several examples from economics and biology.
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15:45 Selecting Dynamic Alternatives in Logical Signaling Networks |
Utz-Uwe Haus (University of Magdeburg) |
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Logical models of signaling events have proved to be a useful tool to model the signaling behavior of biological systems. We discuss how infeasibility of satisfiability problems
underlying these models can be analyzed to gain insight into the dynamics of the a priory static models. A surprising computational feature of these non-monotonic boolean
systems is discussed. We show how this problem can be embedded into much more general questions about combinatorial aspects of discretized dynamical systems.
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| Datum | Ort | Thema | VortragendeR |
| 30.10. |
ZIB Seminarraum |
10:30 Matroids and Conditional Independence |
Thomas Kahle, MPI Mathematik in den Naturwissenschaften, Leipzig |
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11:45 The implication problem for conditional indepence |
Milan Studeny, Academy of Sciences of the Czech
Republic, Prague |
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14:15 Model selection by empirical risk penalization: outlook and some
applications to machine learning |
Gilles Blanchard, Fraunhofer FIRST, Berlin |
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| 20.2. |
MPI Leipzig |
10:00 On the Optimization of binary
functions using probabilistic relaxation |
Luigi Malago, AIRLab, Politecnico di Milano |
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11:15 Markov Bases and Beyond |
Johannes Rauh, MPI Mathematik in den Naturwissenschaften, Leipzig |
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In many applications (hypothesis testing and disclosure limitation)
one wants to investigate the set of probability measures or
contingency tables satisfying a given set of linear constraints. The
main examples for such constraints are fixed expectation values or
marginal distributions and conditional distributions of
subsystems. Markov bases can be used to explore these sets. However,
the use of Markov bases may not always be applicable, for example when
the linear constraints are not given by integral equations. Some ideas
how to generalize the Markov bases technique are presented.
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14:00 Structure validation in clustering by stability analysis |
Joachim M. Buhmann, Department of Computer Science, ETH Zürich |
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Partitioning of data sets into groups defines
an important preprocessing step for compression, prototype
extraction or outlier removal. Various criteria of connectedness
or proximity have been proposed to group data according to
structural similarity but in general it is unclear which method
or model to use. In the spirit of information theory we propose a
decision process to determine the extractable information from
data conditioned on a hypothesis class of structures. Maximizing
the amount of information which can be reliably learned from data
in the presence of noise selects appropriate models. Empirical
evidence for this model selection concept is provided by cluster
validation in bioinformatics and in computer security, i.e., the
analysis of microarray data and multilabel clustering of Boolean
data for role based access control. |
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15:00 Mathematical models of cancer progression |
Niko Beerenwinkel, Department of Biosystems Science and Engineering, ETH Zürich |
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Cancer progression is an evolutionary process that is driven
by mutation and selection in a population of tumor cells. We discuss
mathematical models of cancer progression, starting from traditional
multistage theory. Each stage is associated with the occurrence of
genetic alterations and their fixation in the population. We describe
the accumulation of mutations using conjunctive Bayesian networks, an
exponential family of waiting time models in which the occurrence of
mutations is constrained by a partial order. Two opposing limit cases
arise if mutations either follow a linear order or occur
independently. We derive analytical expressions for the waiting time
until a specific number of mutations have accumulated and show how the
waiting time relates to the dependency structure among mutations.
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| Datum | Ort | Thema | VortragendeR |
| 25.4. |
FU Berlin, A3 Raum 005 |
10:00 Modellauswahl bei Transkriptionsfaktor-Bindungsstellen-Analyse |
Benjamin Georgi, MPI molekulare Genetik Berlin |
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11:00 An introduction to coalescent theory: the next hunting ground for algebraic statistics? |
David Bryant, Dept. Mathematics University of Auckland |
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Kaffeepause |
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13:00 Studeny's Analysis graphischer Modelle auf wenigen Variablen |
Thomas Kahle, MPI Mathematik in den Naturwissenschaften, Leipzig |
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14:00 Algebraic Statistics for model selection: an outlook |
Alexander Schliep, MPI molekulare Genetik Berlin |
| 8.5. |
MPI Leipzig |
10:30 Construction of Toric Gröbner Bases |
Christian Haase, FU Berlin |
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11:45 Consistency of information criteria |
Mathias Drton, University of Chicago |
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14:00 Geometry and Biology | Jürgen Jost, MPI Mathematics in the Sciences Leipzig |
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15:00 Discussion on Markov Bases / Inequalities | Johannes Rauh, MPI Mathematics in the Sciences Leipzig |
| 10.6. |
MPI Berlin Anreise Lecture Hall, Ground floor |
10:30 From Arabidopsis roots to bilinear
equations |
Dustin Cartwright, UC Berkeley |
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11:45 Lattice point problems arising from model selection
problems |
Raymond Hemmecke, Otto-von-Guericke University
Magdeburg |
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Lunch |
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14:00 Statistical Analysis of Digital Gene Expression |
Hugues Richard, MPI molekulare Genetik Berlin |
| 11.7. |
OvGU Magdeburg
Gebäude 2, Raum 311 |
10.30-11.30 Model discrimination using multiple steady
state information |
Carsten Conradi, MPI Magdeburg |
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11.45-12.15 Static versus Dynamic Logic and Integer Programming
> Models for Signaling Networks |
Kathrin Niermann, OvGU Magdeburg |
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12.15-12.45 Reconstructing biological models from experimental data |
Markus Durzinsky, OvGU Magdeburg |
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Lunch |
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14.15-15.15 Denoising and Dimension Reduction in Kernel Feature Space |
Klaus-Robert Müller, TU Berlin |
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15.30-16.30 Open Problems in Algebraic Statistics |
Bernd Sturmfels, UC Berkeley, TU Berlin |
| 23.7. |
TU Berlin, MA 649 |
11:00 Tropical Geometry in Applied Mathematics |
Michael Joswig, TU Darmstadt |
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Lunch |
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13:30 Markov Bases in Statistical Genetics |
Caroline Uhler, UC Berkeley |
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14:30 Solving Constraint Optimization Problems via Importance
Sampling in the Grand Canonical Ensemble |
Karl-Heinz Zimmermann, Technische Universität Hamburg-Harburg |
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Coffee | |
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16:00 Toric Dynamical Systems |
Anne Shiu, UC Berkeley |
