Left as an exercise to the student: Rapid psychical optimal basis choices?

December 7, 2005 at 6:35 pm · Filed under Uncategorized

I must away. Time presses. Gravity presses. Clothes presses.

But first, in telegraphic style:

• Suppose I give you a lot of linear programming problems. I specify the objective function in standard form, the matrix of coefficients, the right-hand-side vector. For this question, there will be exactly 10 unknowns, and 20 equality constraints, so I will give you one 10×20 matrix, one 10-element vector (the objective) and one 20-element vector (the right-hand-side). Every such problem I give you will be feasible.

  You can ask me for as many such problems as you want, and every exemplar will be different [technically, the Euclidean distance from any other you've seen will be at least 10^–8 units], with a unique combination of coefficients and vectors. OK? You can see it?

  I want you to tell me, as often as possible, what the optimum basis is. I want a binary vector of n bits, each a 1 if the variable is in the optimal basis, and a 0 if it is not.

  You may not explicitly solve the problem. Rather, you must train a… thing. Think neural network. Think regression model. Think genetic programming system. Some machine learning thing that learns from data. I will give you as much data as you want, but every time you ask for more, I will demand your prediction of the optimal basis membership, and I will grade it. +1 point when you’re right on all elements, and 0 points when you’re wrong on any element of the vector [though keep in mind that multiple bases may have optimal cost; any of those will be worth a point].

  What’s the highest score you can get with a feed-forward multilayer perceptron? A generalized linear model? A GP system using arithmetic and simple if-then statements only?

Comments

It’ll be quiet for a bit

December 5, 2005 at 8:11 am · Filed under Project

End of semester. Project, project, homework, test, test, test, grant.

I am jotting things to share with you. They may pop up now and then, as a fist waved at my crowded iCal.

Nuff said.

Comments (2)

Automated Inference and the Future of Econometrics

December 4, 2005 at 10:06 am · Filed under Uncategorized

via Mahalanobis:

Peter C.B. Phillips: This [free] issue of Econometric Theory marks 20 full years of publication of the journal ET and the beginning of our third decade. To celebrate the occasion, I invited a group of econometricians, including all the present and past co-editors of ET, to reflect on the future of econometrics. To focus discussion, I selected a theme that relates to a recent trend in the practical use of econometric methodology, one that seems destined to play an increasing role in the future of the subject%u2014automated modeling and inference. Accordingly, this issue contains contributions on various aspects of the theme of automation, introducing the notion of automated discovery, analyzing the validity of selection procedures, and discussing the practical utility of these automated methods in econometric modeling exercises.

Comments