Matthew T. Harrison
M. Harrison. (2005) "Discovering compositional structures." Ph.D. Dissertation, Brown University.
Compositionality is an important aspect of human cognition, perhaps responsible for the remarkably fast visual learning demonstrated by humans and other animals. Hierarchical representations with reusable parts that increase in selectivity and invariance are a particularly compelling framework for compositional vision. In the first part of this thesis we experiment with learning such representations from data. In the second part we focus on statistical methods that might be useful for investigating how the brain implements compositionality.
Part 1. In Chapter 2 we describe an iterative, unsupervised learning heuristic that can create large, hierarchical, probabilistic graphical models. Barlow's notion of suspicious coincidence detection arises quite naturally from this heuristic. In Chapter 3 we experiment with incorporating spatial dependencies into the model using natural images. This creates hierarchies of increasing selectivity, but not invariance. In Chapter 4 we experiment with incorporating temporal dependencies into the model using natural video. This creates hierarchies of increasing invariance, but not selectivity. In Chapter 5 we discuss issues like the binding problem that are likely to arise when we combine the two approaches.
Part 2. In Chapter 6 we illustrate how natural image statistics can, in principle, facilitate agnostic methods for modeling the receptive fields of visual neurons. The only experiments are with simulated data. In Chapter 7 we describe a large class of statistical methods called jitter methods which are useful for analyzing the timescale of neural spike trains. These methods control for slow rate variations and also for certain spike history effects, like refractory periods and bursting. They can be used for hypothesis testing or for creating rate- and history-controlled measures of neural synchrony. We present some limited results on actual neural data, mostly for illustrative purposes. Chapter 8 concludes both parts of the thesis and briefly describes some future work.
The whole thing. 205 pages. 2.6 MB.
Contents. 7 pages. 63 KB.
Chapter 1. 7 pages. 159 KB. Introduction.
Part 1. 105 pages. 967 KB. This includes the contents, the intro (Ch. 1), the vision parts (Ch. 2-5), and the conclusion (Ch. 8).
Chapter 2. 16 pages. 213 KB.
Chapter 3. 35 pages. 388 KB. (This is basically an older tech report that has been circulated as Harrison & Geman, 2003, in progress.)
Chapter 4. 38 pages. 651 KB.
Chapter 5. 5 pages. 102 KB.
Part 2. 110 pages. 1.8 MB. This includes the contents, the intro (Ch. 1), the neuroscience parts (Ch 6-7), and the conclusion (Ch. 8).
Chapter 6. 20 pages. 1.1 MB. (This is the tech report Harrison, Geman & Bienenstock. Using statistics ... 2004.)
Chapter 7. 77 pages. 812 KB.
Chapter 8. 2 pages. 42 KB. Conclusion.