CURRENT RESEARCH TOPICS


Compositional Vision 

Compositionality refers to the ability of humans to represent entities as hierarchies of reusable parts.  The parts themselves are meaningful entities and are reusable in a near-infinite assortment of meaningful combinations. Compositional hierarchies can be fitted with a probability distribution and used as prior models in a scene interpretation system.

Neural Representation 

Certain predictions about the nature of the neural code follow from the principle of compositionality. In particular, there must be a mechanism for rapidly and reversibly binding otherwise uncorrelated spatio-temporal patterns of neural activities. Evidence of binding may be present in the fine-temporal structure of neural discharges. Statistical methods are being devised for a systematic search for fine-temporal structure in stable multi-unit recordings.

Neural Modeling 

Common inputs to multiple neurons promote synchronous firing.  And synchronous firing among presynaptic neurons promotes postsynaptic activity.  Therefore, a neuron's activity reflects in part the extent of common active input to its active presynaptic neurons.  Common active input is circumstantial and therefore carries information.  I am exploring the hypothesis that the nervous system represents binding by commonality of inputs.  The assumption is that all predicates can be reduced to the overlapping of representations of constituent parts.  Overlapping generates common inputs, common inputs generate synchrony, and synchrony generates activity in selected postsynaptic neurons.  Activity in these postsynaptic neurons thereby signals a composition of parts.

 


PAPERS BY TOPIC

Compositionality in computer vision

Summary:  The “ROC gap,” that separates biological from machine vision performance is largely due to the problem of reusability — parts and subparts of objects of interest form parts and subparts of “background” objects.  Hierarchical models can avoid most false detections by explaining background in terms of the parts and subparts of the objects of interest.  In hierarchical models, objects come equipped with their own background models.  

Essays and ideas about neurobiology

Summary: The important questions are about structure and representation, not about learning per se.  

Statistics of neural spike trains

Summary: There is no such thing as a repeated trial in cortical neurophysiology; hence we can test for an excess, but never a lack, of precision.  

Computational linguistics

Summary: Some tutorials, some results about estimation, some extensions of probabilistic context-free grammars to context-sensitive grammars. 

Image processing, image analysis, Markov random fields, and MCMC

Summary: Some ideas about using Markov random fields for Bayesian image analysis, and Monte Carlo methods for computing, including a first proof of convergence for simulated annealing. 

Graphs and computing

Summary: A straight-forward look at dynamic programming on general dependency graphs, with applications in image processing and algebraic coding. 

Information theory

Summary: A theoretical justification of the much-used mode estimator in predictive coding. 

Natural scene statistics

Summary: Natural images scale because the world is flat. 

Mathematical statistics

Summary: Some results on non-parametric (tabula rasa) estimation, including a first proof of consistency for estimators regularized by cross-validation.

Some limit theorems for random matrices and for some large dynamical systems

Summary: First strong limits for the norm and spectral radius of random matrices; applications to regular behavior in random systems, such as (near) limit cycles in a high-dimensional dynamical system with random coefficients.

   

APMA 2610 - Recent Applications of Probability and Statistics

Curriculum Vita

 

Division of Applied Mathematics - Brown University - Providence - Rhode Island 02912

stuart_geman brown.edu