Note: This is the day for the MSB open house.
We will be discussing the following paper:
N. Gershenfeld, B. Schoner and E. Metois
Cluster-weighted modelling for time-series analysis,
Nature 397:329-332 (1999).
Link to paper.
No presentation, short planning meeting.
» Slides. «
Reading:
NOTE: Time change to Tuesday May 16th, 2pm!!!
Reading:
J. Machta
Complexity, parallel computation and statistical physics,
cond-mat/0510809 (2005).
»
Link to paper.
«
»»POSTPONED - NO MEETING THIS WEEK.««
updated May 29th, 2006.
Reading:
A.K. Jain, M.N. Murty, and P.J. Flynn
Data Clustering: A Review,
ACM Computing Surveys 31(3): 264-323 (1999).
»
Link to paper.
«
We apply an information theoretic treatment of action potential time series measured with multi-electrode arrays to estimate the detailed connectivity of mammalian neuronal cell assemblies grown in vitro. We infer causal correlations between neurons both through standard linear time correlations and more generally via the mutual information between their spike trains. In addition we implement the mutual information between any two spike trains conditional on the response of a third cell, as a means to identify and distinguish classes of correlations among three neurons. The conditional three-cell information measures the extent to which consideration of a third cell's activity increases (synergy) or not (redundancy or independence) knowledge of the statistical state of the pair under study. The use of a conditional three-cell measure leads to greater accuracy and sheds light into the functional connectivity arrangements of any three cells. We quantify the structure of the resultant connectivity graphs in the light of other complex networks and demonstrate that, despite their ex vivo development the connectivity maps derived from cultured neural assemblies display nontrivial structure in clustering coefficient, path length and assortative mixing relative to randomized graphs with the same average connectivity.
Around the turn of the 20th century, Poincar\'e formulated the idea of studying nature via the qualitative, geometric study of spaces of mappings we use to model nature. Since then, much of mathematical dynamics as well as nonlinear dynamics in many applied fields has worked to achieve partial solution to this problem. In this talk I will discuss a construction that provides both a means of attacking Poincar\'e's original problem as well as providing a language for mathematical and scientific results to "speak" to each other. In a practical way, this goal will be achieved using a function space (neural networks) that admits a measure. Using the chosen function space, a Monte Carlo analysis relative to this measure of the macroscopic geometric features will be presented. In particular, the geometric quantification will consist of analyzing a function that measures the number of positive Lyapunov exponents (and hence expanding directions) with parameter variation. This function is then rescaled to remove a dependence on dimension and the number of parameters such that an analysis can be performed in the asymptotic limit of a large number of dimensions.
» Slides from Chris E. « updated: Jul 17, 2006.
Slides available above.
A discussion of the paper available at: link to paper.
» Slides from Sean «
Links from Sean:
» java implementation of sequitur
» hierarchical representation of music
Sean also said he would be willing to share his implementation of the algorithm with those in the group who are interested.
Bring your comments and ideas on the paper to the meeting:
» If possible, have comments in writing for Karoline and Jim - thanks! «
The paper is available online - doi: 10.1063/1.1531823.
The paper is available online - doi: 10.1103/PhysRevLett.91.084102.
The paper is available online - doi: 10.1103/PhysRevLett.85.3524.
The paper is available online - http://www.pnas.org/cgi/content/full/99/7/4748.
We will be going over primarily chapter 2, but chapter 1 offers some explanations, background terminology, and history. It's not necessary to read all of chapter 1, but for background, I would suggest sections 1.1 and 1.3. Both chapters are available online at
http://cse.ucdavis.edu/~brown/reinforce
It is a fair amount of reading (although not terribly mathy), so we will probably be going over chapter 2 for the next couple of meetings.
--Benny.
Continue discussion from last week, starting at section 2.4.
We might start on Chapter 3 if time allows. Benny will put this chapter up sometime this week:
Continue discussion from last week, starting at section 2.8 and possibly continuing into Chapter 3. Chapters are still available at the link below:
http://cse.ucdavis.edu/~brown/reinforce
Dr. Richard Sutton also has a website for the book at:
http://www.cs.ualberta.ca/%7Esutton/book/the-book.html
This site is of particular interest because there is Lisp code which was used to generate some of the plots from the book. Also, the full text is available in html format. This might be useful to those of us who don't mind reading online.
--> Don't forget the new meeting time. <--
Continue discussion from last week, starting at chapter 3. Chapters are still available at the link below:
Continue discussion from last week, starting at chapter 3. Chapters are still available at the link below:
Continue discussion from last week, starting at (approximately) section 3.6.
Chapters are still available at the link below:
Chapters are still available at the link below:
Ongoing discussion will start from section 3.8 this week. Chapters are still available at the link below:
There is no group meeting this week. Please attend
Dr. Sergey Gavrilets - The dynamics of Machiavellian intelligence
For further details see CSE website http://cse.ucdavis.edu/calendars
We will start the meeting with a discussion of an optimal policy for a simple task designed by Benny: [ pdf ].
Given time, discussion will then continue on to chapter 4. Chapters 4 and 5 are now available at the link below:
Have a nice Thanksgiving break.
In these group meetings I will walk us through the methods of Bayesian inference of k-th order Markov chains from finite data samples. In addition to inference of parameters for a particular order k, I will discuss model comparison for a range of orders, selecting the order which best describes the data. Finally, I will discuss connections between inference, statistical mechanics and information theory. This connection allows us to estimate entropy rates of the process which created the data sample under consideration.
Ongoing discussion will start from section 4.2 this week. Chapters are still available at the link below:
In these group meetings I will walk us through the methods of Bayesian inference of k-th order Markov chains from finite data samples. In addition to inference of parameters for a particular order k, I will discuss model comparison for a range of orders, selecting the order which best describes the data. Finally, I will discuss connections between inference, statistical mechanics and information theory. This connection allows us to estimate entropy rates of the process which created the data sample under consideration.