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Seminar for Statistics
 
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Research Seminar

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Time/Place: every Friday at 3.15 pm in the Main Building of ETH, HG G 19.1

Spring Semester 2014

Organiser(s)

Date Speaker Title Time Location
21-feb-2014 (fri)
Valen Johnson
Uniformly most powerful Bayesian tests and the reproducibility of scientific research 15:15-16:00 HG G 19.1
Abstract: Uniformly most powerful Bayesian tests are defined and compared to
classical uniformly most powerful tests. By equating the rejection
regions of these two tests, an equivalence between Bayes factors based on these tests and frequentist p-values is illustrated. The implications of this equivalence for the reproducibility of scientific research are examined. Approximately uniformly most powerful Bayesian tests are described for t tests, and the power of these tests are compared to ideal Bayes factors (defined by determining the best test alternative for each true value of the parameter), as well as to Bayes
factors obtained using the true parameter value as the alternative.
Interpretations and asymptotic properties of these Bayes factors are also discussed.
Speakers:

Valen Johnson (Texas A&M University)

28-feb-2014 (fri)
Tom Claassen
FCI+ or Why learning sparse causal models is not NP-hard 15:15-16:00 HG G 19.1
Abstract: Causal discovery lies at the heart of most scientific research today. It is the science of identifying presence or absence of cause-effect relations between certain variables in a model. Building up such a causal model from (purely) observational data can be hard, especially when latent confounders (unobserved common causes) may be present. For example, it is well-known that learning a minimal Bayesian network (BN) model over a (sub)set of variables from an underlying causal DAG is NP-hard, even for sparse networks with node degree bounded by k. Given that finding a minimal causal model is more complicated than finding a minimal DAG it was often tacitly assumed that causal discovery in general was NP-hard as well. Indeed the famous FCI algorithm, long the only provably sound and complete algorithm in the presence of latent confounders and selection bias, has worst-case running time that is exponential in the number of nodes N, even for sparse graphs.
Perhaps surprisingly then it turns out that we can exploit the structure in the problem to reconstruct the correct causal model in worst case N^(2k+4) independence tests, i.e. polynomial in the number of nodes. In this talk I will present the FCI+ algorithm as the first sound and complete causal discovery algorithm that implements this approach. It does not solve an NP-hard problem, and does not contradict any known hardness results: it just shows that causal discovery is perhaps more complicated, but not as hard as learning a minimal BN. In practice the running time remains close to the PC limit (without latent confounders, order k*N^(k+2), similar to RFCI). Current research aims to tighten complexity bounds and further optimize the algorithm.
Speakers:

Tom Claassen (Radboud University Nijmegen, The Netherlands)

21-mar-2014 (fri)
Eric Gautier
Uniform confidence sets for high dimensional regression and instrumental regression via linear programming 15:15-16:00 HG G 19.1
Abstract: In this talk we present a one-stage method to compute joint confidence sets for the coefficients of a high-dimensional regression with random design under sparsity. The confidence sets have finite sample validity and are robust to non-Gaussian errors of unknown variance and heteroscedastic errors. Nonzero coefficients can be arbitrarily close to zero. This extends previous work with Alexandre Tsybakov where we rely on a conic program to obtain joint confidence sets and estimation for this pivotal linear programming procedure. The method we present only relies on linear programming which is important for dealing with high-dimensional models. We will explain how this method extends to linear models with regressors that are correlated with the error term (called endogenous regressors) as is often the case in econometrics. The procedure relies on the use of so-called instrumental variables. The method is then robust to identification and weak instruments.
Speakers:

Eric Gautier (ENSAE-CREST, Paris)

4-apr-2014 (fri)
Alessio Sancetta
A Nonparametric Estimator for the Covariance Function of Functional Data 15:15-16:00 HG G 19.1
Abstract: Many quantities of interest in economics and finance can be represented as partially observed functional data. Examples include structural business cycles estimation, implied volatility smile, the yield curve. Having embedded these quantities into continuous random curves, estimation of the covariance function is needed to extract factors, perform dimensionality reduction, and conduct inference on the factor scores. A series expansion for the covariance function is considered. Under summability restrictions on the absolute values of the coefficients in the series expansion, an estimation procedure that is resilient to overfitting is proposed. Under certain conditions, the rate of consistency for the resulting estimator is nearly the parametric rate when the observations are weakly dependent. When the domain of the functional data is K(> 1) dimensional, the absolute summability restriction of the coefficients avoids the so called curse of dimensionality. As an application, a Box-Pierce statistic to test independence of partially observed functional data is derived. Simulation results and an empirical investigation of the efficiency of the Eurodollar futures contracts on the Chicago Mercantile Exchange are included.

Speakers:

Alessio Sancetta (Royal Holloway, University of London)

9-may-2014 (fri)
Iain Currie
GLAM: Generalized Linear Array Models 15:15-16:00 HG G 19.1
Abstract: A Generalized Linear Array Model (GLAM) is a generalized linear model where the data lie on an array and the model matrix can be expressed as a Kronecker product. GLAM is conceptually attractive since its high-speed, low-footprint algorithms exploit the structure of both the data and the model. GLAMs have been applied in mortality studies, density estimation, spatial-temporal smoothing,variety trials, etc. In this talk we

(1) describe the GLAM ideas and algorithms in the setting of the original motivating example, two-dimensional smooth model of mortality,

(2) give an extended discussion of a recent application to the Lee-Carter model, an important model in the forecasting of mortality.

References
Currie, I. D., Durban, M. and Eilers, P. H. C. (2006) Generalized linear array models with applications to multidimensional smoothing.
Journal of the Royal Statistical Society, Series B, 68, 259-280.
DOI reference: http://doi:10.1111/j.1467-9868.2006.00543.x

Currie, I. D. (2013) Smoothing constrained generalized linear models with an application to the Lee-Carter model. Statistical Modelling, 13,69-93.
DOI reference: http://doi:10.1177/1471082X12471373
Speakers:

Iain Currie (Heriot-Watt University, Edinburgh)

16-may-2014 (fri)
Mohammad Sadeh
Considering Unknown Unknowns - Reconstruction of Non-confoundable Causal Relations in Biological Networks 15:15-16:00 HG G 19.1
Abstract: Our current understanding of virtually all cellular signaling pathways is almost certainly incomplete. We miss important but sofar unknown players in the pathways. Moreover, we only have a partial account of the molecular interactions and modi cations of the known players. When analyzing the cell, we look through narrow windows leaving potentially important events in blind spots. Much network reconstruction
methods are based on investigating unknown relations of known players assuming there are not any unknown
players. This might severely bias both the computational and manual reconstruction of underlying biological networks.
Here we ask the question, which features of a network can be confounded by incomplete observations and which cannot. In the context of nested e ect model based network reconstruction, we show that in the presence of missing observations or hidden factors with their unknown e ects (unknown-unknowns), a reliable
reconstruction of the full network is not feasible. Nevertheless, we can show that certain characteristics of signaling networks like the existence of cross talk between certain branches of the network can be inferred in a not-confoundable way. We derive a simple polynomial test for inferring such not-confoundable characteristics
of signaling networks. We also define a set of edges to partially reconstruct the signaling networks when the unknown players exist. Finally, we evaluate the performance of the proposed method on simulated data and two biological studies, a first application to embryonic stem cell diff erentiation in mice and a recent study on the Wnt signaling pathway in colorectal cancer cells. We demonstrate that taking unknown hidden mechanisms into account changes our account of real biological networks.
References
[1] Sadeh, M. J., Mo a, G. and Spang, R. (2013). Considering Unknown Unknowns - Reconstruction of Non-confoundable Causal Relations in Biological Networks. In RE- COMB 234248.
[2] Anchang B, Sadeh M, Jacob J, Tresch A, Vlad M, et al. (2009) Modeling the temporal interplay of molecular signaling and gene expression by using dynamic nested e ects models. Proceedings of the National Academy of Sciences 106: 6447.
[3] Tresch A, Markowetz F (2008) Structure learning in nested e ects models. Stat Appl Genet Mol Biol 7.
[4] Markowetz, F and Bloch, J and Spang, R (2005) Non-transcriptional pathway features reconstructed from
secondary e ects of RNA interference Bioinformatics 21:4026-32.
[5] Markowetz, F and Kostka, D and Troyanskaya, O G and Spang, R (2007) Nested e ects models for high-dimensional phenotyping screens Bioinformatics 13:i305-12.
1Max Planck Institute for Molecular Genetics. Ihnestrae 63-73, D-14195 Berlin, (Germany).
Speakers:

Mohammad Sadeh (Max Planck Institute for Molecular Genetics)

23-may-2014 (fri)
Gassiat Elisabeth
Non parametric hidden Markov models. 15:15-16:00 HG G 19.1
Abstract: In this talk I will present recent results about non parametric identifiability of hidden Markov models, and some consequences in non parametric estimation.

References:
E. Gassiat, A. Cleynen, S. Robin
Finite state space non parametric hidden Markov models are in general identifiable
arxiv preprint, 2013.

E. Gassiat, J. Rousseau
Non parametric finite translation mixtures with dependent regime
Bernoulli, à paraitre.

E.Vernet
Posterior consistency for nonparametric Hidden Markov Models with finite state space

T. Dumont and S. Le Corff
Nonparametric regression on hidden phi-mixing variables: identifiability and consistency of a pseudo-likelihood based estimation procedure

Speakers:

Gassiat Elisabeth (Université Paris-Sud)

23-may-2014 (fri)
Jane L. Hutton
Chain Event Graphs for Informative Missingness 16:30-17:15 HG G 19.1
Abstract: Chain event graphs (CEGs) extend graphical models to address situations in which, after one variable takes a particular value, possible values of future variables differ from those following alternative values (Thwaites et al 2010). These graphs are a useful framework for modelling discrete processes which exhibit strong asymmetric dependence structures, and are
derived from probability trees by merging the vertices in the trees
together whose associated conditional probabilities are the same.

We exploit this framework to develop new classes of models where
missingness is influential and data are unlikely to be missing at random (Barclay et al 2014). Context-specific symmetries are captured by the CEG. As models can be scored efficiently and in closed form, standard Bayesian selection methods can be used to search over a range of models.
The selected maximum a posteriori model can be easily read back to the client in a graphically transparent way.

The efficacy of our methods are illustrated using survival of people with cerebral palsy, and a longitudinal study from birth to age 25 of children in New Zealand, analysing their hospital admissions aged 18-25 years with
respect to family functioning, education, and substance abuse aged 16-18 years.

P Thwaites, JQ Smith, and E Riccomagno (2010) "Causal Analysis with Chain Event Graphs" Artificial Intelligence, 174, 889-909.

LM Barclay, JL Hutton and JQ Smith, (2014) "Chain Event Graphs for Informed Missingness", Bayesian Analysis, Vol. 9, 53-76.
Speakers:

Jane L. Hutton (University of Warwick, UK)


Further information: sekretariat@stat.math.ethz.ch

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