1,601 reputation
615
bio website suitdummy.blogspot.com
location Cambridge, MA
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visits member for 2 years, 5 months
seen 2 days ago

I once launched swi-prolog and asked it a question:

ely:~/home$ prolog
Welcome to SWI-Prolog (Multi-threaded, 64 bits, Version 5.10.1)
Copyright (c) 1990-2010 University of Amsterdam, VU Amsterdam
SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
and you are welcome to redistribute it under certain conditions.
Please visit http://www.swi-prolog.org for details.

For help, use ?- help(Topic). or ?- apropos(Word).

?- love(math) is unrequited.
true.

Mar
22
answered Gradient of a Mahalanobis distance
Mar
22
revised Real analysis question
edited body
Mar
22
answered Real analysis question
Mar
22
comment Finding displacement from origin of SVM hyperplane
Scikits.learn, which is a Python layer over LIBSVM, does return the bias parameter within SVM objects. It's easy to use; I would consider it.
Mar
22
comment How do you filter through published papers and find the ones you should read?
Yeah, like Cross-Validated, Sci-Comp, and Theoretical Computer Science for example.
Mar
22
comment Do non-mathematical fields use the appropriate level of analytic/probabilistic rigor?
Regarding your comments on probability theory, I think Jaynes wrote the definitive rebuke of dogmatic dependence on measure theory, in Appendix B of his "Probability Theory: The Logic of Science." Reading Jaynes in grad school revived my love of math. Measure theory is important, insofar as it is an expedient tool, and if other folks like it for aesthetic reasons, that's fine. But in general, I think graduate-level education in probability has forgotten that applied math is supposed to be in the service of something...
Mar
22
comment P vs NP and Gödel
As an interesting aside, Godel wrote a letter to Von Neumann once expressing how, if P=NP, it will be the end of human mathematics, excepting possibly the postulation of axioms. The remark is in this paper (which is well worth a read for most folks here anyway).
Mar
22
answered How do you filter through published papers and find the ones you should read?
Mar
22
answered Do non-mathematical fields use the appropriate level of analytic/probabilistic rigor?
Mar
21
revised Combining independent probabilities of an event
added 9 characters in body
Mar
21
answered Combining independent probabilities of an event
Mar
21
answered Conditional Probability Problem (drawing chips from an urn)
Mar
20
comment How to estimate the number of articles on Wikipedia using the “random article” function?
This seems like a good problem for a latent random graph model. Given a model of some graph parameters (which will control the number of nodes and the diameter, etc.), you could use some Bayesian model fitting methods to decide which graph likely gives rise to your observed number of pages-before-repeat. That is how I would start, at least. Unlike the German tank problem, this one is sensitive to the graph structure you assume. There are well-confirmed network models of wiki-like graphs, though. Check out M.E.J. Newman's recent book on networks for some examples.
Mar
20
comment probability of sequential events
Note that it can fail either right away at point 1 (you know the probability of that) or (with probability that it does not fail at point 1) it can fail at point 2 with a probability that you know. Add these to get total probability of failure, F, then 1-F is the probability of success.
Mar
20
answered Is it possible to prove that a problem $P$ is decidable in $O(\phi)$ without providing an algorithm that decides $P$ in $O(\phi)$?
Mar
20
revised General properties of eigenvalues of a Jacobian matrix when premultiplied by a symmetric, positive definite matrix?
added 595 characters in body
Mar
20
asked General properties of eigenvalues of a Jacobian matrix when premultiplied by a symmetric, positive definite matrix?
Mar
20
revised How to find the conditional expectation for this pdf
added 784 characters in body
Mar
20
comment How to find the conditional expectation for this pdf
You're right. The mistake though is not quite what you mentioned. It is that in my first conditional expectation, I forgot to divide by the marginal probability $P(X_{1} = x_{1})$. Then, multiplying by that again will cancel it to make the last formula correct. I am updating to reflect this.
Mar
20
comment How to find the conditional expectation for this pdf
But the first term of the product is just for a single value of $x_{1}$. You have to multiply by the probability of that value of $x_{1}$ and sum over all potential choices for $x_{1}$.