Project

Proposal

  Your proposal should address each of the following elements:

  1. What is the problem?  Are you trying confirm an existing theory
     by testing a computational model or running a set of experiments?
     Are you trying to replicate some previously published results?
     Do you have a new hypothesis to test?  Are you demonstrating how
     a biologically inspired model performs on a given dataset?  Be
     explicit. You may not know how to solve the problem yet, but you
     should be able to state the problem clearly.

  2. How will you address the problem?  Will you write code and run it
     on a set of existing benchmarks comparing your performance with
     published results?  Will you run experiments and compare your
     data with published results?  Will you compare two or more
     algorithms on a dataset meant to contrast the algorithms relative
     to their biological plausibility?  Where appropriate tell me how
     you will obtain the necessary resources: equipment, lab animals,
     existing code and datasets, etc.

  3. How does your project address biological issues?  Is your model
     biologically plausible?  Are you making a claim about what
     biological organisms are capable of (or not) or about how such
     organisms perform particular tasks (or do poorly on particular
     tasks)?  How will you substantiate such claims?

  4. How does you project address computational issues? Is your model
     computationally feasible?  Can you instantiate your theory in a
     working program?  Is your algorithm such that it could be run on
     biological hardware?

  5. How much time do you expect this project will take you?

  Send your proposal to tld@cs.brown.edu before 5PM Wednesday, November 8.

Example projects

Here's a sketch of a project (actually three projects):

1. Problem description:

   Implement a special-purpose version of the hierarchical replication
   model described in the Ullman and Soloviev paper to solve a variant
   of Dileep George's pictionary problem using invariant features.

   OR

   Implement a special-purpose version of Olshaussen et al's routing
   algorithm simulating a biologically plausible routing circuit and
   demonstrate it working on the pictionary problem.

   OR

   Implement a version of slow features using the formulation in Dean,
   Wiskott and Sejnowski or one of your own devising (I'll be glad to
   suggest a couple of interesting directions) and then test it on the
   pictionary problem.

   The pictionary dataset is shown here and I can provide you with
   some tools for manipulating the pictionary images in Matlab:
   http://www.cs.brown.edu/~tld/projects/cortex/pictionary.png

2. Experimental framework:

   Let P be the set of 48 simple black-on-white patterns in the
   pictionary dataset each approximately 16 X 16 pixels.  Let D be a
   subset P corresponding to 24 patterns randomly chosen from P.
   You'll be given D and expected to learn a hierarchy of invariant
   features.  You can take as long as you want on this, but the
   resulting recognition algorithm has be biologically plausible;
   you might implement this as simple circuit or feature trellis.

   Then you'll be given a set of labeled pairs where each pair
   consists of an integer 1-48 and an image with one of the 48
   patterns (or a scaled version) displayed within a 32 X 32 pixel
   canvas.  You'll be expected to learn to recognize each of the
   patterns in the training set with at most a few trials and at
   locations (demonstrating translation invariance) and in sizes
   (demonstrating scale invariance) not present in the training data.

Suggestions

Here were some initial suggestions (from October 19 email).

  Feature Extraction and Representation in Early Vision (Subspace Methods)

  The brain extracts information from highly redundant sensory
  signals. The goal of sensory coding is to transform the input
  reducing the redundancy among elements in the sensory stream - Barlow

 - implement and experiment with different approaches to modeling
   the representational output of the lateral geniculate / input
   to V1 - Daubechies wavelets such as Gabor functions and methods
   for learning bases including independent components analysis;

 - information theoretic and combinatorial analysis concerning the
   feasibility of different proposals for memorizing image patches
   and then composing them hierarchically as suggested by Ullman,
   Risenhuber and Poggio, and others;

 - take two methods for constructing subspaces characterizing the
    input to V1, one generative method, e.g., ICA, and one
    discriminitive method, e.g., LDA, and analyze their possible
    use as the geometric frame buffer that Mumford talks about.

  Reconstructive/Generative Methods
    - E.g., Principal Components Analysis (PCA)
            Independent Components Analysis (ICA)
    -       Nonnegative Matrix Factorization (NMF) for recovering HMMs
    - Enable (partial) reconstruction of input images.
    - Enable bottom on and top down (feedback) inference.

  Discriminative Methods
    - E.g., Support Vector Machines (SVM)
            Latent Dirichlet Allocation (LDA)
            Canonical Correlation Analysis (CCA)
    - Tend to be supervised learning techniques.
    - Do not allow (partial) reconstruction of images.
    - Less informative, more specialized, task specific.

  Illumination Invariance

   - David Heeger has a good model of divisive contrast normalization
     in cats which is widely accepted as a good model [Heeger, 1992].

  Scale Invariance

   - David Lowe's Scale Invariant Feature Transform (SIFT-PCA)
     This is not meant as a neural model so read about scale
     invariance in the brain and compare one or more of the
     neural models with SIFT.

  Sparse Overcomplete Representations

   - various


  Hierarchical Models

 - implement the particle filtering approach outlined in Lee and
   Mumford emphasizing how timing might work as new input arrives
   at the lowest level even as earlier input is just reaching the
   highest levels and being propagated back down the hierarchy;

 - examine evidence for a hierarchy of geometric representations
   beyond V1 using Steve Zucker's work as a starting point;


Learning Invariant Features

 - experiment with different graphical model topologies that
   implement the inertial models described in the Dean paper;

 - implement a version of Wiskott and Sejnoski's slow features
   that uses subscribes to the input output requirements for
   modules within Lee and Mumford's hierarchical Bayesian model;


  Attentional Mechanisms

   - computational theory of attention in early vision - how might
     we extend the approach described in Itti and Baldi to explain
     some of the results in Lee and Mumford that pertain to how we
     focus attention to resolve ambiguity; don't limit yourself to
     just Itti's paper - there are other more compelling models.

   - adapt Itti's code to drive saccadic eye movements using the
     cortical modeling software and the pictionary dataset;