Wed Sep 22: Financial Modeling II: On-Line, Worst-Case Models

This week, Sham Kakade and Ryan Porter will take us through some recent works in a much more adversarial model of price movement, along with the kinds of results one can obtain in such models.

Wed Sep 29: Financial Modeling III: Trading in Markovian Price Models

We will finish up our financial wanderings with two topics:

Wed Oct 6:

Guest Speaker Yee Whye Teh, UC Berkeley

Hierarchical Dirichlet processes: A Bayesian approach to sharing clusters among related groups

Abstract: We consider problems involving groups of data, where each observation within a group is drawn from a mixture model, and where it is desirable to share mixture components both within and between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from data. Such problems occur often in practice, e.g. in the problem of topic discovery in document corpora, each document is treated as a group of data items (bag of words), and each topic corresponds to a mixture component. In this setting, sharing components between groups simply means that topics can occur across a number of documents, allowing dependencies across documents (groups) to be modeled effectively as well as conferring generalization to new documents (groups).

The hierarchical Dirichlet process (HDP) is a Bayesian solution to this problem, utilizing both hierarchical and nonparametric modeling ideas. Each group is modeled using a Dirichlet process (DP) mixture, which provides a nonparametric prior for the number of components within each group. To facilitate sharing components between groups, we consider a hierarchical extension where the common base distribution for the DPs is itself distributed according to a DP. Such a base distribution being discrete, the group specific DPs necessarily share atoms, hence the mixtures for different groups necessarily share components.

We discuss a variety of representations for the HDP, as well as Markov chain Monte Carlo algorithms for posterior inference. We report experimental results on three text corpora showing the effective and superior performance of the HDP over previous models.

Technical Report: Hierarchical Dirichlet processes. Teh, Jordan, Beal and Blei (2004). UC Berkeley Department of Statistics, TR 653. Can be obtained at: http://www.cs.berkeley.edu/~ywteh/research/npbayes

Wed Oct 13:

Seminar participant and CIS doctoral student Timothee Cour will take us through the Bach-Jordan paper below, and related recent research that Timothy has been doing with Jianbo Shi.

Wed Oct 20:

Seminar participant Ted Sandler will lead us through some recent work in the theory community on spectral and graph clustering:

Wed Oct 27:

Seminar participant Ben Packer will tell us about some recent dimensionality reduction work he has done with Kilian Wienberger, as well as related background and connections to kernel methods. Further readings may be posted as well.

Wed Nov 3:

Once again the inimitable Sham Kakade steps to the plate, this time to speak on some recent work he has been doing:

Online Bounds for Bayesian Algorithms

Abstract: I'll provide some competitive online bounds for a number of Bayesian algorithms, without making any assumptions on the data generation process. These bounds show that some of the most popular Bayesian algorithms (such as least squares regression and Bayesian logistic regression) perform favorably when compared, in retrospect, to the single best model in the model class. I'll also provide bounds for some widely used maximum a posteriori (MAP) estimation algorithms, including regularized logistic regression.

Finally, I'll present some results (on work in progress) on online bounds for Gaussian Processes. The bound here have an interesting dependence on an intrinsic notion of dimensionality.

Wed Nov 10: Seminar participant Axel Bernal will lead us through work on conditional random fields, including the application of such models to gene finding.

Wed Nov 17:

Guest Speaker Prof. Amy Greenwald, Brown University (held this week in Levine 307)

Game-Theoretic Learning

No-regret learning algorithms have attracted a great deal of attention in the game-theoretic and machine learning communities. Whereas rational agents act so as to maximize their expected utilities, no-regret learners are boundedly rational agents that act so as to minimize their ``regret''. In this talk, we discuss the behavior of no-regret learning algorithms in repeated games.

Specifically, we introduce a general class of algorithms called no-$\Phi$-regret learning, which includes common variants of no-regret learning such as no-external-regret and no-internal-regret learning. Analogously, we introduce a class of game-theoretic equilibria called $\Phi$-equilibria. We show that no-$\Phi$-regret learning algorithms converge to $\Phi$-equilibria. In particular, no-external-regret learning converges to minimax equilibrium in zero-sum games; and no-internal-regret learning converges to correlated equilibrium in general-sum games. Although our class of no-regret algorithms is quite extensive, no algorithm in this class learns Nash equilibrium.

Here are Amy's slides.

Wed Nov 24: NO MEETING, THANKSGIVING BREAK

Wed Dec 1:

Gaurav Chakravorty will lead us through several papers of Vladimiar Vovk, who has systematically removed probabilistic assumptions from probability theory:

Wed Dec 8:

This week seminar participant Rong Chen, a postdoc in the Penn radiology department, will talk about his work applying graphical models to medical image analysis.

We'll start with a little bit of relevant background on Bayes networks and belief propagation:

Then we'll move on to Rong's work, including some slides to be provided later.

THE BULLPEN

In this area, I will place links to papers and topics that may eventually promoted to the actual schedule. I will try to group them by rough "modules" of semi-related material. The initial set of modules is strongly based on the suggestions made during our first meeting. As these modules are fleshed out with specific readings and volunteers, they will be promoted to the formal schedule above.

A number of us expressed interest in looking at papers in the general areas of spectral clustering, factor analysis, and blind source separation including potential applications to image processing and vision, and financial data. Some suggested topics in this area were:

There was also interest in probabilistic models for document representation. Suggested topics:

There was healthy interest in the latest in graphical models and its relatives. Suggested topics:

Though a bit of it will be folded into our finance wanderings, there may be interest in developments in on-line learning and statistics, including:

Two other topic areas suggested were machine learning in medical imaging where we may have some local expertise and source of interesting problems; and Joe Halpern's extensive line of work on the foundations of probabilistic reasoning.

I continue to be interested in learning more about the work on property testing going on in the theory community, and its potential connections to topics in machine learning.

Have wanted to read this for a while: