Sunday, July 29, 2007

Evolutionary Artwork

David Oranshak is using evolutionary algorithms to create aesthetically pleasing artwork

Also, "human vs computer" design awards for 2007

Saturday, July 28, 2007

Computers beat humans at face recognition task

The top performing system exhibited better performance than human evaluators when matching faces under varying lighting conditions in NIST large scale face recognition benchmark.

See Figure 8 in

Thursday, July 26, 2007

matrix-vector multiplication complexity

Suppose A,B are nxn matrices, and x is an nx1 vector. Need to compute M1M2...Mm x where each Mi is either A or B. The straightforward approach is to start multiplying from the right, which takes O(n^2 m) operations. Is it possible to have an O(n^2 m) algorithm that solves the problem above, but has a lower time complexity than the baseline?

The lower bound is O(n^2+m) because that's how long it takes to input the problem. If you could improve on the standard approach, you could solve the problem of inference in Markov-1 hidden markov model with binary observations faster than the Forward algorithm

Thursday, July 19, 2007

UCI datasets updated

Looks like UCI website has been updated with some new data, including some sequential/relational datasets

Friday, July 13, 2007

HMM's and Linear classifiers

I've across the following question recently -- suppose you have a fully specified Markov-1 Hidden Markov Model with binary observations {Xi} and binary states {Yi}. You observe X1,...,Xn and have to predict Yn. Is the Bayes optimal classifier linear? Empirically, the answer seems to be "yes", but it's not clear to how show it.

Update actually looks like they are not linear in general, which can be seen a contour-plot of P(Yn|X1,X2,X3) where each axis parametrizes P(Xi|Yi)

Monday, July 09, 2007

Next 10 years of Structured Learning

ILP 07 had a discussion panel on next 10 years of structured learning. The video is now posted on Video Lectures

Here are couple of things that caught my eye

1. Bernhard Pfahringer -- someone should work on a centralized repository like, except for structured learning

2. Thomas Dietterich -- need a way to combine benefits of high-performance discriminative learning with semantics of generative models (for the purpose of being able to train various modules separately and then combine them)

3. Pedro Domingos -- current systems (logistic regression, perceptron, SVM) have 1 level of internal structure, need to work out ways to learn multi-tiered compact internal structure effectively

4. Pedro Domingos - - should craft algorithms for which tractable inference is the learning bias -- in other words, the algorithm is explicitly tailored to prefer models that are easy to do inference in

Tuesday, July 03, 2007

Regularizing with arbitrary quadratic forms

People often fit the model to data by minimizing J(w)+w'Bw where J is the objective function and B is some matrix. Normally people use diagonal or symmetric positive definite matrices for B, but what happens if you use other types?

Here's a Mathematica notebook using Manipulate functionality to let you visualize the shrinkage that happens with different matrices, assuming J(w)'s Hessian is the identity matrix. Drag the locators to modify eigenvectors of B.

One thing to note is that if B is badly conditioned, strange things happen, for instance for some values of w*, they may get pushed away from zero. For negative-definite or indefinite matrices B you may get all w*'s getting shrunk away from zero, or they may get flipped across origin, where w* is argmax_w J(w)

Positive Definite


Negative Definite