## Research Seminar

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

### Autumn Semester 2013

Organiser(s)

Date Speaker Title Time Location
2-sep-2013 (mon)
Julien Gagneur
Model-based Gene Set Analysis and Systems genetics with environment 11:15-12:00 HG G 19.1
 Abstract: 1. The interpretation of data-driven experiments in genomics often involves a search for biological categories that are enriched for the responder genes identified by the experiments. With Model-based Gene Set Analysis (MGSA), we tackle the problem by turning the question differently. Instead of searching for all significantly enriched groups, we search for a minimal set of groups that can explain the data. 2. Systems genetics with environment. We show how non-additive effects between genotype and environment can be exploited for causal inference in molecular networks. Using genome-wide perturbation assays in yeast, we experimentally demonstrate the validity of the approach. Bio: Julien Gagneur has a background in applied mathematics. His contribution includes the development of computational methods for a wide range of genomic application (metabolic and protein network, gene set enrichment, transcription) and insights into gene regulation mechanisms from genome-wide data (cis-regulatory modules, antisense expression). His lab, started in July 2012 at the gene center in Munich, focuses on computational approaches to understand mechanisms of gene regulation and their phenotypic impact from genome-wide assays. http://www.gagneur.genzentrum.lmu.de Speakers: Julien Gagneur (Ludwig Maximilian University of Munich (LMU))
20-sep-2013 (fri)
Robin Evans
Distinguishing between different causal models 15:15-16:00 HG G 19.1
 Abstract: Causal models based upon directed acyclic graphs (DAGs, or Bayesian networks) have gained wide attention over the past 20 years, but accounting for the effect of hidden variables in this context has proved extremely challenging. The resulting marginalized DAG models (mDAGs) fail to display many of the nice properties of ordinary DAGs, and they are difficult to describe mathematically. We introduce these models and gives some recent results on their characterization. The nested Markov models of Richardson et al (2013) provide approximations to the mDAG models which are much easier to work with; we show that the nested model is 'complete', in that it gives a complete algebraic description of the mDAG. If there is time, we will also discuss some methods for finding inequality constraints in mDAG models, and how these may be used (in principle) to distinguish between different causal hypotheses, even using only observational data. Speakers: Robin Evans (University of Cambridge, UK)
27-sep-2013 (fri)
Sylvain Sardy
Blockwise and coordinatewise thresholding to combine tests of di fferent natures in modern ANOVA 15:15-16:00 HG G 19.1
 Abstract: I derive new tests for fi xed and random ANOVA based on a thresholded point estimate. The pivotal quantity is the threshold that sets all the coefficients of the null hypothesis to zero. Thresholding can be employed coordinatewise or blockwise, or both, which leads to tests with good power properties under alternative hypotheses that are either sparse or dense. Speakers: Sylvain Sardy (Université de Genève)
22-oct-2013 (tue)
Po-Ling Loh
Local optima of nonconvex regularized M-estimators 12:15-13:00 HG G 19,1
 Abstract: We present recent results concerning local optima of various regularized M-estimators, where both loss and penalty functions are allowed to be nonconvex. We show that whenever the loss function satisfies restricted strong convexity and the penalty function satisfies suitable regularity conditions, all local optima of the composite objective function lie within statistical precision of the true parameter vector. Applications of interest include the corrected Lasso for errors-in-variables models and regression in generalized linear models with nonconvex regularizers such as SCAD and MCP. We also show that a simple adaptation of composite gradient descent may be used to efficiently optimize such nonconvex objectives. This is joint work with Martin Wainwright. ***** Speakers: Po-Ling Loh (Seminar für Statistik, ETH Zürich)
8-nov-2013 (fri)
Fabian Wauthier
A Comparative Framework for Preconditioned Lasso Algorithms 15:15-16:00 HG G 19.1
 Abstract: The Lasso is a cornerstone of modern multivariate data analysis, yet its performance suffers in the common situation in which covariates are correlated. This limitation has led to a growing number of Preconditioned Lasso algorithms that pre-multiply X and y by matrices P_X, P_y prior to running the standard Lasso. A direct comparison of these and similar Lasso-style algorithms to the original Lasso is difficult because the performance of all of these methods depends critically on an auxiliary penalty parameter \lambda. In this paper we propose an agnostic, theoretical framework for comparing Preconditioned Lasso algorithms to the Lasso without having to choose \lambda. We apply our framework to three Preconditioned Lasso instances. Speakers: Fabian Wauthier (University of Oxford, Department of Statistics)
15-nov-2013 (fri)
Dennis Kristensen
Limited information likelihood inference in stochastic volatility jump-diffusion models 15:15-16:00 HG G 19.1
 Abstract: We develop a novel method for estimation and filtering of continuous-time models with stochastic volatility and jumps using so-called Approximate Bayesian Computation which build likelihoods based on limited information. The proposed estimators are computationally attractive relative to standard likelihood-based estimators since they rely on low-dimensional auxiliary statistics and so avoid computation of high-dimensional integrals. We also develop a simple filtering algorithm that allows one to track the latent volatility process in real time without any heavy computational burden. Despite their computational simplicity, we find that estimators and filters perform well in practice and lead to precise estimates of model parameters and latent variables. We show how the methods can incorporate intra-daily information to improve on the estimation and filter- ing. In particular, the availability of realized volatility measures help us in learning about parameters and latent states. The method is employed in the estimation of a flexible stochastic volatility model for the dynamics of the Stoxx50 equity index. We find evidence of the presence of jumps and in favor of a structural break in parameters. During the recent financial crisis, volatility has a higher mean and variance, and is less persistent than before the crisis. Jumps occur slightly less frequently, and are more likely to be negative when they do occur. Speakers: Dennis Kristensen (University College London)
26-nov-2013 (tue)
Volkan Cevher
Composite self-concordant minimization 16:15-17:00 HG G 19.2
 Abstract: We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function endowed with a computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth part. An important highlight of our work is a new set of analytic step-size selection and correction procedures based on the structure of the problem. We describe concrete algorithmic instances of our framework for several interesting large-scale applications, such as graph learning, Poisson regression with total variation regularization, and heteroscedastic LASSO. Here is a link to the document that contains technical parts of the presentation: http://arxiv.org/abs/1308.2867 Speakers: Volkan Cevher (EPFL, Lausanne)
29-nov-2013 (fri)
Simon Broda
On distributions of ratios 15:15-16:00 HG G 19.1
 Abstract: A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random variables. If in addition, the joint characteristic function of numerator and denominator is known, then standard Fourier inversion techniques can be used to reconstruct the distribution function from it. Most research in this field has been based on this correspondence, but which breaks down when both numerator and denominator are supported on the entire real line. The present manuscript derives inversion formulae and saddlepoint approximations that remain valid in this case, and reduce to known results when the denominator is almost surely positive. Applications include the IV estimator of a structural parameter in a just-identified equation. Speakers: Simon Broda (University of Amsterdam)
29-nov-2013 (fri)
Thomas Mikosch
Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series 16:15-17:00 HG G 19.1
 Abstract: We give an asymptotic theory for the eigenvalues of the sample covariance matrix of a multivariate time series. The time series constitutes a linear process across time and between components. The input noise of the linear process has regularly varying tails with index $\alpha\in (0,4)$; in particular, the time series has infinite fourth moment. We derive the limiting behavior for the largest eigenvalues of the sample covariance matrix and show point process convergence of the normalized eigenvalues. The limiting process has an explicit form involving points of a Poisson process and eigenvalues of a non-negative definite matrix Based on this convergence we derive limit theory for a host of other continuous functionals of the eigenvalues, including the joint convergence of the largest eigenvalues, the joint convergence of the largest eigenvalue and the trace of the sample covariance matrix, and the ratio of the largest eigenvalue to their sum. This is joint work with Richard A. Davis (Columbia NY) and Oliver Pfaffel (Munich). Speakers: Thomas Mikosch (University of Copenhagen)
6-dec-2013 (fri)
Jun Mikyoung
Matérn-based nonstationary cross-covariance models for global processes 15:15-16:00 HG G 19.1
 Abstract: Many spatial processes in environmental applications, such as climate variables and climate model errors on a global scale, exhibit complex nonstationary dependence structure, not only in their marginal covariance but their cross-covariance. Flexible cross-covariance models for processes on a global scale are critical for accurate description of each spatial processes as well as their cross-dependence and for improved prediction. We propose various ways for producing cross-covariance models, based on Matérn covariance model class, that are suitable for describing prominent nonstationary characteristics of the global processes. In particular, we seek nonstationary version of Matérn covariance models whose smoothness parameters vary over space, coupled with differential operators approach for modeling large-scale nonstationarity. We compare their performances to some of existing models in terms of the aic and spatial prediction in two applications problems: joint modeling of surface temperature and precipitation, and joint modeling of errors of climate model ensembles. Speakers: Jun Mikyoung (Texas A&M University)

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