David Pfau: March 27th (at 5PM)

I'll be presenting on work in progress in collaboration with Bijan Pesaran's group (Yan Wong, Mariana Vigeral, David Putrino) and Josh Merel on building a high degree-of-freedom brain-machine interface.  I'll focus on the Bayesian paradigm for decoding, and two practical problems for pushing that paradigm beyond the commonly-used Kalman filtering approach: building better likelihoods, and building better priors.  The first amounts to fitting tuning curves for various neurons.  Other groups have shown a nonlinear dependence of firing rate on hand position in 3D space, here I will show some preliminary results on fitting tuning curves for large numbers of joint angles.  The second amounts to building better generative models of reach and grasp motions.  As a first step in that direction, I've looked at PCA and ICA for reducing the dimension of reach-and-grasp signals.

Gustavo Lacerda: March 20th

Title: spatial regularization

Consider modeling each neuron as a 2-parameter logistic model (spiking probability as a function of stimulus intensity), and suppose we perform independent experiments on each neuron. Now imagine that the data isn't very informative, so we need to regularize our estimates. We can do spatial regularization by adding a quadratic penalty on the difference of estimates for nearby neurons. Now, suppose that there are *two* types of neurons, and that you only want to shrink together neurons of the same type. We don't want our estimate to be influenced by "false neighbors", i.e. neurons that are spatially close but of a different type. We discuss how to optimize this model. Finally, we explore the idea of Fused Group Lasso.

Kamiar Rahnama Rad: Feb. 21

Two following questions will be discussed:  1. How does embedding low dimensional structures in high dimensional spaces decreases the learning complexity significantly? I will consider the simplest model, that is a linear transformation with additive noise.  2. Modern datasets are accumulated (and in some cases even stored) in a distributed or decentralized manner. Can distributed algorithms be designed to fit a global model over such datasets while retaining the performance of centralized estimators?   

The talk will be based on the following two papers: 

http://www.columbia.edu/~kr2248/papers/ieee-sparse.pdf  

http://www.columbia.edu/~kr2248/papers/CDC2010-1.pdf

Bryan Conroy: Fed. 14th

Bryan Conroy will talk about a fast method for computing many related l2-regularized logistic regression problems, and about possible extensions to other GLMs, and l1-regularizers.

Eftychios P.: Jan. 31st and Feb. 7th

I am planning to lead a very informal discussion on some neat techniques for convex and semidefinite relaxation that can be used to transform intractable optimization problems into approximate but convex ones. I'll also discuss a few applications to statistical neuroscience that we are currently pursuing.

Some background material (although I'm not planning to go over any of these in detail) includes:

http://www.se.cuhk.edu.hk/~manchoso/papers/sdrapp-SPM.pdf
http://arxiv.org/abs/1012.0621
http://www-stat.stanford.edu/~candes/papers/PhaseRetrieval.pdf
http://users.cms.caltech.edu/~jtropp/papers/MT11-Two-Proposals-EJS.pdf

David Pfau: Dec. 20th

David will be giving a fly-by view of a number of cool papers from NIPS.

First is Empirical Models of Spiking in Neural Populations by Macke, Büsing, Cunningham, Yu, Shenoy and Mahani, where they evaluate the relative merits of GLMs with pairwise coupling and state space models on multielectrode recording in motor cortex.

Next, Quasi-Newton Methods for Markov Chain Monte Carlo by Zhang and Sutton looks at how to use approximate second-order methods like L-BFGS for MCMC while still preserving detailed balance.

Then, Demixed Principal Component Analysis is an extension of PCA which demixes the dependence of different latent dimensions on different observed parameters, and is used to analyze neural data from PFC

Finally, Learning to Learn with Compound Hierarchical-Deep Models, which combines a deep neural network for learning visual features with a hierarchical nonparametric Bayesian model for learning object categories to make one cool-looking demo.

Previous Group Meetings (for archival purposes)

Universal MAP Estimation in Compressed Sensing, by Baron and Duarte

Quantifying Statistical Interdependence by Message Passing on Graphs, by Dauwels, Vialatte, Weber and Chichocki. Part I and Part II

The No-U_Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo, by Hoffman and Gelman.