Seminar for Statistics

Research Seminar


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

Autumn Semester 2014


Date Speaker Title Time Location
26-sep-2014 (fri)
Eleni Sgouritsa
Identifying confounders and telling cause from effect using latent variable models 15:15-16:00 HG G 19.1
Abstract: Drawing causal conclusions from observed statistical dependencies is a fundamental problem. Conditional-independence based causal discovery (e.g., PC or FCI) cannot be used in case there are no observed conditional independences. Alternative methods investigate a different set of assumptions, namely restricting the model class, e.g., additive noise models. In this talk, I will present two causal inference methods employing different kind of assumptions than the above.
The first is a method to infer the existence and identify a finite confounder attaining a small number of values. It is based on a kernel method to identify finite mixtures of nonparametric product distributions. The number of mixture components is found by embedding the joint distribution into a reproducing kernel Hilbert space. The mixture components are then recovered by clustering according to an independence criterion.
In the second part I will focus on the problem of causal inference in the two-variable case (assuming causal sufficiency). The proposed method is based on the assumption that, if X causes Y, the marginal distribution P(X) contains no information about P(Y|X). In contrast, P(Y) may contain information about P(X|Y). Consequently, semi-supervised and unsupervised learning (inferring the conditional from the marginal) should be possible in the latter but not in the former case. Accordingly, a method is proposed to decide upon the causal structure.

Eleni Sgouritsa (MPI for Intelligent Systems, Tuebingen)

10-oct-2014 (fri)
Hannes Leeb
On conditional moments of high-dimensional random vectors given lower-dimensional projections 15:15-16:00 HG G 19.1
Abstract: One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional variances are constant. We here show that this property is also shared, in an approximate sense, by a large class of non-Gaussian distributions. We allow for several conditioning variables and we provide explicit non-asymptotic results,whereby we extend earlier findings of Hall and Li (1993) and Leeb (2013).

(This is joint work with Lukas Steinberger.)


Hannes Leeb (Universität Wien)

14-nov-2014 (fri)
Harrison Zhou
Sparse Canonical Correlation Analysis: Minimaxity and Adaptivity 15:15-16:00 HG G 19.1
Abstract: Canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables. In this talk we consider the problem of estimating the leading canonical correlation directions in high dimensional settings. Recently, under the assumption that the leading canonical correlation directions are sparse, various procedures have been proposed for many high dimensional applications involving massive data sets. However, there has been few theoretical justification available in the literature. In this talk, we establish rate-optimal non-asymptotic minimax estimation with respect to an appropriate loss function for a wide range of model spaces. Two interesting phenomena are observed. First, the minimax rates are not affected by the presence of nuisance parameters, namely the covariance matrices of the two sets of random variables, though they need to be estimated in the canonical correlation analysis problem. Second, we allow the presence of the residual canonical correlation directions. However, they do not influence the minimax rates under a mild condition on eigengap. A generalized sin-theta theorem and an empirical process bound for Gaussian quadratic forms under rank constraint are used to establish the minimax upper bounds, which may be of independent interest.

If time permits, we will discuss a computationally efficient two-stage estimation procedure which consists of a convex programming based initialization stage and a group Lasso based refinement stage, and show some encouraging numerical results on simulated data sets and a breast cancer data set.

Harrison Zhou (Yale University, New Haven, CT)

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