***Faculty Search Candidate Talk***
Abstract: Our research program focuses on learning Recursive Compositional Models (RCMs) for visual patterns such as articulated deformable objects like horses and human body, image scenes, etc. The methodology of our work is based on the assumption of recursive compositionality of visual world which naturally takes into account both the representation and computation complexity of image models. Visual patterns are represented by RCMs in a hierarchical form which makes use of both recursion and composition. The complex visual patterns are recursively decomposed into multiple layers of simpler sub-patterns. Learning (or inference) the RCMs can be recursively divided into learning simpler sub-RCMs, subsub-RCMs and so on. We have shown the representation and computation power of recursive compositionality by the developments of certain types of RCMs, learning methods and inference algorithms for several computer vision tasks including articulated deformable object detection, parsing and segmentation, and image segmentation and scene understanding.
***Faculty Search Candidate Talk***
Abstract:
I will describe work on the Columbia/Con Edison Manhole Events project. An
important goal of the project is to produce a ranked list of manholes and
service boxes in Manhattan, in order of vulnerability to serious events such
as fires, explosions, and smoking manholes. This list will assist Con Edison
with prioritization of repair work. Of over 50,000 manholes and service boxes,
only 0.1 to 1 percent are implicated in a given event each year, so the top
of the ranked list needs to be very accurate. Several sources of Con Edison
data are used for this task, the most important of which is the ECS (Emergency
Control Systems) database, consisting of historical trouble tickets from
past events that are mainly recorded in free text by Con Edison
dispatchers.
For the ranking task, I will describe a supervised ranking algorithm that
concentrates at the top of a ranked list, called the "P-Norm Push." The
problem of supervised ranking is to order a set of objects based on a sample
of labeled preference data. Such problems arise not only for the manhole
event prediction problem, but also for many other industrial prioritization
problems, information retrieval tasks such as document retrieval, and other
applications in natural language processing such as name tagging. In many of
these applications, the ranking accuracy at the top of the list is more
important than farther down the list.
I will introduce the problem of manhole
event prediction and derive the P-Norm Push algorithm along with some
theoretical properties. Results on a blind prediction test indicate the
usefulness of this approach for mitigation of future manhole events in
Manhattan.
Papers relating to this talk can be found at:
http://www1.ccls.columbia.edu/~rudin/main.html, listed under "Manhole Events"
and "P-Norm Ranking." This work is in collaboration with Rebecca Passonneau,
Axinia Radeva, Robert Schapire, Ingrid Daubechies, Heng Ji, Ralph Grishman,
and several others.
Stochastic Systems Seminar
Abstract: the beta ensembles of random matrix theory are natural generalizations of the Gaussian Orthogonal, Unitary, and Symplectic Ensembles, these classical cases corresponding to beta = 1, 2, and 4. We prove that the extremal eigenvalues for the general ensembles have limit laws described by the low lying spectrum of certain raandom Schroedinger operators, as conjectured by Edelman-Sutton. As a corollary, a second characterization of these laws is made the explosion probability of a simple one-dimensional diffusion. A complementary pictures is developed for beta versions of random sample-covariance matrices. (Based on work with J. Ramirez and B. Virag.)
Lefschetz Center for Dynamical Systems Seminar
Abstract: Correlated activity in neural tissue can impact the information carried by neural populations. However, there are few results that provide a mechanistic understanding of their generation and propagation. I will examine this question using versions of the integrate and fire model, extending previous results for single neurons to populations. I will also present new numerical methods for the simulation of networks of stochastic integrate and fire neurons which are orders of magnitude faster than Monte Carlo simulations.
Center for Computational Molecular Biology Seminar
Abstract:
The topology of metabolic networks may provide important insights not only into
the metabolic capacity of species, but also into the habitats in which they
evolved. In this talk I will present several analyses of metabolic networks
and show how various ecological insights can be obtained from genomic-based
data.
I will first introduce various factors that affect the structure of metabolic
networks, and specifically the environmental and genetic determinants that
affect network modularity. I will then present the first large-scale
computational reconstruction of metabolic growth environments, analyzing the
metabolic networks of hundreds of species and using a graph-theory based
algorithm to identify for each species a set of seed compounds that must be
exogenously acquired. Such seed sets form ecological "interfaces" between
metabolic networks and their surroundings, approximating the effective
biochemical environment of each species. The seed sets' composition
significantly correlates with several properties characterizing the species'
environments and agrees with biological observations concerning major
adaptations. Computational reconstruction of metabolic networks of ancestral
species and phylogenetic analysis of the seed sets reveal the complex
dynamics governing gain and loss of biosynthetic capacity across the
phylogenetic tree.
I will further present an extension of this framework, accounting for
interactions between species, by introducing a pair-wise, topology-based
measure of biosynthetic support, which reflects the extent to which the
nutritional requirements of one species could be satisfied by the
biosynthetic capacity of another. I will show that this measure is aligned
with host-parasite interactions and facilitates successful prediction of
such interactions on a large-scale.
Finally, I will discuss the application of this approach to the analysis of
microbial communities and metagenomic data of the human microbiota and outline
future research directions; The "reverse ecology" approach demonstrated in
these analyses lays the foundations for further studying the complex web of
interactions characterizing various ecosystems and the evolutionary interplay
between organisms and their habitats on a large scale.
Scientific Computing Seminar
PDE Seminar
Abstract: We describe the asymptotic behavior in energy space of Palais-Smale sequences for an anisotropic problem on a domain in the Euclidian space. This description is well-known in the isotropoic case. In the general case, we emphasize the crucial role played by the geometry of the domain.