Research Seminar

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Spring Semester 2016

Note: The highlighted event marks the next occurring event.

Date / Time Speaker Title Location
22 February 2016
Nadler Boaz
Weizmann Institute of Science
Unsupervised Ensemble Learning   HG  G 19.1 
Abstract: Abstract: In various applications, one is given the advice or predictions of several classifiers of unknown reliability, over multiple questions or queries. This scenario is different from the standard supervised setting where classifier accuracy can be assessed from available labeled training or validation data, and raises several questions: given only the predictions of several classifiers of unknown accuracies, over a large set of unlabeled test data, is it possible to a) reliably rank them, and b) construct a meta-classifier more accurate than any individual classifier in the ensemble? In this talk we'll show that under various independence assumptions between classifier errors, this high dimensional data hides simple low dimensional structures. In particular, we'll present simple spectral methods to address the above questions, and derive new unsupervised spectral meta-learners. We'll prove these methods are asymptotically consistent when the model assumptions hold, and also present their empirical success on a variety of unsupervised learning problems.
4 March 2016
Ryan Tibshirani
Carnegie Mellon University, USA
Trend Filtering: Some Recent Advances and Challenges  HG G 19.1 
Abstract: I will discuss trend filtering, a newly proposed tool of Steidl et al. (2006), Kim et al. (2009) for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute kth order discrete derivatives over the input points. I will give an overview of some interesting connections between these estimates and adaptive spline estimation, in particular, a connection to locally adaptive regression splines of Mammen and van de Geer (1997). If time permits, I will discuss some extensions of trend filtering, namely, to high-dimensional data and (separately) to graph-based data. I will also discuss some of the challenges I see in each of these settings. This represents joint work with Veeranjaneyulu Sadhanala, Yu-Xiang Wang, James Sharpnack, and Alex Smola.
18 March 2016
Jonathan Rosenblatt
Ben Gurion University of the Negev
On the Optimality of Averaging in Distributed Statistical Learning  HG G 19.1 
Abstract: A common approach to statistical learning on big data is to randomly split it among m machines and calculate the parameter of interest by averaging their m individual estimates. Focusing on empirical risk minimization, or equivalently M-estimation, we study the statistical error incurred by this strategy. We consider two asymptotic settings: one where the number of samples per machine n->inf but the number of parameters p is fixed, and a second high-dimensional regime where both p,n-> inf with p/n-> kappa. Most previous works provided only moment bounds on the error incurred by splitting the data in the fixed p setting. In contrast, we present for both regimes asymptotically exact distributions for this estimation error. In the fixed-p setting, under suitable assumptions, we thus prove that to leading order, averaging is as accurate as the centralized solution. In the high-dimensional setting, we show a qualitatively different behavior: data splitting does incur a first order accuracy loss, which we quantify precisely. In addition, our asymptotic distributions allow the construction of confidence intervals and hypothesis testing on the estimated parameters. Our main conclusion is that in both regimes, averaging parallelized estimates is an attractive way to speedup computations and save on memory, while incurring a quantifiable and typically moderate excess error.
8 April 2016
Rainer von Sachs
Université catholique de Louvain
Functional mixed effect models for spectra of subject-replicated time series  HG G 19.1 
Abstract: Abstract: In this work in progress we treat a functional mixed effects model in the setting of spectral analysis of subject-replicated time series data. We assume that the time series subjects share a common population spectral curve (functional fixed effect), additional to some random subject-specific deviation around this curve (functional random effects), which models the variability within the population. In contrast to existing work we allow this variability to be non-diagonal, i.e. there may exist explicit corre- lation between the different subjects in the population. To estimate the common population curve we project the subject-curves onto an appropriate orthonormal basis (such as a wavelet basis) and continue working in the coefficient domain instead of the functional domain. In a sampled data model, with discretely observed noisy subject-curves, the model in the co- efficient domain reduces to a finite-dimensional linear mixed model. This allows us, for estimation and prediction of the fixed and random effect coefficients, to apply both traditional linear mixed model meth- ods and, if necessary by the spatially variable nature of the spectral curves, work with some appropriate non-linear thresholding approach. We derive some theoretical properties of our methodology highlighting the influence of the correlation in the subject population. To illustrate the proposed functional mixed model, we show some examples using simulated time series data, and an analysis of empirical subject-replicated EEG data. We conclude with some possible extensions, among which we allow situations where the data show po- tential breakpoints in its second order (spectral) structure over time. The presented work is joint with Joris Chau (ISBA, UCL).
29 April 2016
Christian Brownless
Universität Pompeu Fabra, Barcelona
Community Detection in Partial Correlation Network Models  HG G 19.1 
Abstract: Real world networks often exhibit a community structure, in the sense that the vertices of the network are partitioned into groups such that the concentration of linkages is high among vertices in the same group and low otherwise. This moti- vates us to introduce a class of Gaussian graphical models whose network structure is determined by a stochastic block model. The stochastic block model is a random graph in which vertices are partitioned into communities and the existence of a link between two vertices is determined by a Bernoulli trial with a probability that de- pends on the communities the vertices belong to. A natural question that arises in this framework is how to detect communities from a random sample of observations. We introduce a community-detection algorithm called Blockbuster, which consists of applying spectral clustering to the sample covariance matrix, that is, it applies k-means clustering to the eigenvectors corresponding to its largest eigenvalues. We study the properties of the procedure and show that Blockbuster consistently de- tects communities when the network dimension and the sample size are large. The methodology is used to study real activity clustering in the United States and Eu- rope. Keywords: Partial Correlation Networks, Random Graphs, Community Detection, Spec- tral Clustering, Graphical Models JEL: C3, C33, C55
20 May 2016
Asger Lunde
Aarhus University
Realizing Commodity Correlations  HG G 19.1 
Abstract: We propose to use the Realized Beta GARCH model of Hansen et al. (2014) to exploit the potential of using high-frequency data in commodity markets for the modeling of correlations. The model produces accurate forecasts of pairwise correlations between commodities which can be used to construct a composite covariance matrix. We eval- uate the attractiveness of this matrix in a portfolio context and compare it to models more commonly used in the industry. We demonstrate significant economic gains in a realistic setting including short selling constraints and transaction costs. Keywords: Commodities, financialization, futures market. JEL Classification: C53, C58, G12, G13, G15, G17, G32.
23 June 2016
Dan Roy
University of Toronto Scarborough
Models and Estimation for Sparse Network Data under Exchangeability  HG G 19.2 
Abstract: We introduce a class of random graphs on the reals R defined by the exchangeability of their vertices. A straightforward adaptation of a result by Kallenberg yields a representation theorem: every such random graph is characterized by three (potentially random) components: a nonnegative real I, an integrable function S : R+ to R+, and a symmetric measurable function W: R+^2 to [0,1] that satisfies several weak integrability conditions. We call the triple (I,S,W) a graphex, in analogy to graphons, which characterize the (dense) exchangeable graphs on N. I will present some results about the structure and consistent estimation of these random graphs. Joint work with Victor Veitch

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