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Autumn Semester 2015

Note: The highlighted event marks the next occurring event.

Date / Time Speaker Title Location
18 September 2015
Robin Evans
University of Oxford
Causal Models and How to Refute Them  HG G 19.1 
Abstract: Directed acyclic graph models (DAG models, also called Bayesian networks) are widely used in the context of causal inference, and they can be manipulated to represent the consequences of intervention in a causal system. However, DAGs cannot fully represent causal models with confounding; other classes of graphs, such as ancestral graphs and ADMGs, have been introduced to deal with this using additional kinds of edge, but we show that these are not sufficiently rich to capture the range of possible models. In fact, no mixed graph over the observed variables is rich enough, however many edges are used. Instead we introduce mDAGs, a class of hyper-graphs which is appropriate for representing causal models when some of the variables are unobserved. Results on the Markov equivalence of these models show that when interpreted causally, mDAGs are the minimal class of graphs which can be sensibly used. Understanding such equivalences is critical for the use of automatic causal structure learning methods, a topic in which there is considerable interest. We elucidate the state of the art as well as some open problems.
25 September 2015
Damian Kozbur
Seminar für Statistik
Testing-Based Forward Model Selection  HG G 19.1 
Abstract: This work develops theory for a Testing-Based Forward Model Selection procedure in linear regression and m-estimation problems. Forward Selection is a greedy procedure which inductively selects covariates which reliably add predictive power into a statistical model. A testing procedure, whose properties resemble traditional statistical hypothesis testing, is assumed as a primitive. It is used as a tool for guiding the forward selection by deciding which variable to include next and when to stop including variables. This offers a flexible and data- driven way to estimate models and construct predictions in high dimensional statistical problems. Probabilistic bounds for prediction error and number of selected covariates are proved for the proposed Testing- Based Forward Selection. The regularity conditions assumed on the set of hypothesis tests are verified for several example problems. The per- formance of Testing-based Forward Selection is compared to Lasso and Post-Lasso in Simulation studies.
28 September 2015
Claudia Klüppelberg
Technische Universität München
Extremes on directed acyclic graphs  HG G 19.1 
Abstract: We consider a new max-linear structural equation model, where all random variables can be written as a max-linear function of their parents and noise terms. For the corresponding graph we assume that it is a DAG. We present basic probabilistic results of our model; in particular we characterise those max-linear random vectors, which originate in a max-linear structural equation model and are, hence, max-linear distributions on DAGs. We also determine the minimal DAG corresponding to the max-linear structural equation model. As an example we consider the structural equation model with max-stable noise variables, resulting in a max-stable max-linear DAG. This is joint work with Nadine Gissibl.
23 October 2015
Alessandra Luati
University of Bologna
Generalised Linear Cepstral Models for the Spectrum of a Time Series  HG G 19.1 
Abstract: The paper introduces the class of generalised linear models with Box-Cox link for the spectrum of a time series. The Box-Cox transformation of the spectral density is represented as a finite Fourier polynomial, with coefficients, that we term generalised cepstral coefficients, providing a complete characterisation of the properties of the random process. The link function depends on a power transformation parameter and encompasses the exponential model (logarithmic link), the autoregressive model (inverse link), and the moving average model (identity link). One of the merits of this model class is the possibility of nesting alternative spectral estimation methods under the same likelihood-based framework, so that the selection of a particular parametric spectrum amounts to estimating the transformation parameter. We also show that the generalised cepstral coefficients are a one to one function of the inverse partial autocorrelations of the process, which can be used to evaluate the mutual information between the past and the future of the process.
6 November 2015
Egil Ferkingstad
NTNU Trondheim, Norway
Title T.B.A. HG G 19.1 
20 November 2015
Guido Consonni
Università Cattolica del Sacro Cuore
Objective Bayes Covariate-Adjusted Sparse Graphical Model Selection  HG G 19.1 
Abstract: We present an objective Bayes method for covariance selection in Gaussian multivariate regression models whose error term has a covariance structure which is Markov with respect to a Directed Acyclic Graph (DAG). The scope is covariate-adjusted sparse graphical model selection, a topic of growing importance especially in the area of genetical genomics (eQTL analysis). Specically, we provide a closed-form expression for the marginal likelihood of any DAG (witsmallh small parent sets) whose computation virtually requires no subjective elicitation by the user and involves only conjugate matrix normal Wishart distributions. This is made possible by a specic form of prior assignment, whereby only one prior under the complete DAG model need be specied, based on the notion of fractional Bayes factor. All priors under the other DAG models are derived using prior modularity, and global parameter independence, in the terminology of Geiger & Heckerman (2002). Since the marginal likelihood we obtain is constant within each class of Markov equivalent DAGs, our method naturally specializes to covariate-adjusted decomposable graphical models. Keywords: Bayesian model selection; Covariate-adjusted graphical model; Covariance selection; Decomposable graphical model; Directed acyclic graphical model; Fractional Bayes factor; Gaussian graphical model; Gaussian multivariate regression; Marginal likelihood; Sparse model selection.
4 December 2015
Benedikt Pötscher
University of Vienna
Title T.B.A.  HG G 19.1 
Abstract: tba

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