Alex Ramirez: June 21th

Alex will be presenting a short version of this paper. In it the authors consider loss functions, for many estimators, that obey certain smoothness and convexity requirements and prove a global, geometric convergence (fast) rate of convergence under Nestorv's Gradient descent method up to a level of Statistical precision.

There will be no meeting on June 14th.

Kamiar Rahnama Rad: June 7th

Information rates and Optimal decoding in Large Populations

Many fundamental questions in theoretical neuroscience involve optimal decoding and the computation of Shannon information rates in populations of spiking neurons. In this paper, we apply methods from the asymptotic theory of statistical inference to obtain a clearer analytical understanding of these quantities. We find that for large neural populations carrying a finite total amount of information, the full spiking population response is asymptotically as informative as a single observation from a Gaussian process whose mean and covariance can be characterized explicitly in terms of network and single neuron properties. The Gaussian form of this asymptotic sufficient statistic allows us in certain cases to perform opti- mal Bayesian decoding by simple linear transformations, and to obtain closed-form expressions of the Shannon information carried by the network. One technical advantage of the theory is that it may be applied easily even to non-Poisson point process network models; for example, we find that under some conditions, neural populations with strong history-dependent (non-Poisson) effects carry exactly the same information as do simpler equivalent populations of non-interacting Poisson neurons with matched firing rates. We argue that our findings help to clarify some results from the recent literature on neural decoding and neuroprosthetic design.

Eric Shea-Brown : May 31st

Eric Shea-Brown who has come all the way from U of Washington will be speaking about:

A mechanistic approach to multi-spike patterns in neural circuits:
There is a combinatorial explosion in the number of possible activity patterns in neural circuits of increasing size, enabling an enormous complexity in which patterns occur and how this depends on incoming stimuli.  However, recent experiments show that this complexity is not always accessed -- the activity of many neural populations is remarkably well captured by simpler descriptions that rely only on the activity of single neurons and neuron pairs.  

What is especially intriguing is that these pairwise descriptions succeed even in cases where circuit architecture seems likely to create a far more complex set of outputs.  We seek a mechanistic understanding of this phenomenon -- and predictions for when it will break down -- based on simple models of spike generation, circuit connectivity, and stimuli.  This also offers a chance to explore how much (and how little) beyond-pairwise spike patterns can matter to coding in different circuits.

As a specific application, we consider the empirical success of pairwise models in capturing the activity of ON-parasol retinal ganglion cells. We first use intracellular recordings to fully constrain a model of the underlying circuit dynamics.  Our theory then provides an explanation for experimental findings based on ON-parasol stimulus filtering and spike generation properties.  

This is joint work with Andrea Barreiro, Julijana Gjorgjieva, and Fred Rieke.

Max Nikitchenko: May 10

This Tuesday, on 2011/05/10, I will discuss methods for the acceleration of the convergence of algorithms with linear convergence near the fixed point, such as EM, which are known to be notoriously slow in that area. Two approaches are possible: modify the iterative algorithm itself (PX-EM (by parameter-expansion), ECM (by maximizing the maximizer individually for each parameter, keeping the others fixed), etc), or use the recent history of the iterations to extrapolate them closer to the fixed point (in which case you keep all your machinery intact and only plug in an auxiliary function for extrapolating the already computed iteration steps). I will talk about the second class of the accelerators.

I will start with the method I derived myself, which is visual, but powerful at the same time. I will then focus on two papers which seem to become the gold standard in the acceleration techniques: Varadhan, R. & Roland, C. "Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm" (dx.doi.org/10.1111/j.1467-9469.2007.00585.x) from 2008 and Zhou, H.; Alexander, D. & Lange, K. "A quasi-Newton acceleration for high-dimensional optimization algorithms" (dx.doi.org/10.1007/s11222-009-9166-3) from 2011. I have just found out about the second paper and it seems to overlap heavily with the method I derived. I hope we will clear this question up!

class presentations may 3 at 3:00

hi all - this tuesday we won't have normal group meeting. instead, the
students in my class will be giving presentations about the projects they
have been working on this semester. talk titles are here:
http://www.stat.columbia.edu/~liam/teaching/neurostat-spr11/talks.txt

presentations will begin at 3, and each one should last 15 min or so.
everyone's welcome to attend - hope to see you there.
L

Jianing Shi : April 26th

I will discuss Nesterov's optimal gradient method at the group meeting.  I will talk about Nesterov's method for minimizing composite objective function, together with its implication for L1 minimization. 

There is unfortunately no short story on Nesterov's method, however you can find his work at

http://www.core.ucl.ac.be/~nesterov/

Jianing's nicely done slides can be found here.

Jonathan Huggins : April 19

Submodularity part II, starting at 5:45pm.

After a brief review of two weeks ago, I will describe Queyranne's efficient and fully combinatorial algorithm for minimizing symmetric submodular functions. Next, I will give the details of the convex Lovasz extension of submodular functions, including a sketch of the proof of how to efficiently calculate the extension. Finally, I'll discuss portions of a recent paper on decomposable submodular functions by Stobbe and Krause, emphasizing its application to Markov Random Fields and the connections to the Lovasz extension and concave functions