354 karma · joined July 17, 2012
It helps that elementary functions are in some sense dense in the set of all other functions. Results like Stone-Weierstrass show that on a compact interval, any function can be arbitrarily-well approximated by a polynomial.
Other things that might interest you-- how one might know if a function even has an antiderivative that can be expressed as an elementary function: http://en.wikipedia.org/wiki/Liouville%27s_theorem_(differen...
(* - this guilt is a weird thing I can't really describe. It also lessens as I advance further in my career and am more sure of myself.)
The Manhattan and Euclidean distance on finite spaces both generalize to "l_p norms" (1 and 2, respectively) on an n-dimensional Euclidean space, where ||x||_p = (|x_0|^p + |x_1|^p + ... + |x_n|^p)^(1/p). You can even naturally define it in the limit where p goes to infinity!
Quite efficient even for something silly, like casting a long_int -> short_int mapping by first converting the keys to strings. Hurrah, prefix trees!
But when an acquihire with retention bonus is almost equivalent in net payout to you as a successful acquisition or IPO might be, it is difficult to be super-invested instead of merely daydreaming and working toward starting your own company. At best you can hope to be flush from a quick and healthy payout, which might pay off student loans or capitalize the first steps of your own risky venture.
Is the game of Silicon Valley just to structurally encourage everyone to eventually devote their time to fully creating their own pet technologies and products? Who works for anyone else except for fools and transients?
(I'm currently a fool or transient.)
East Bay is charming and inexpensive. There are residents and young people who discuss more than option-pool restructuring and PHP/Rails. As long as I can continue to work in San Francisco, and as long as rents stay as high as they are in that city, I'll choose to live here.
(Then bust out R again when you want to play with stochastic processes and Brownian motion.)
Would love to hear more about entrepreneurs who live on the edge and try to start a business while also needing to make rent and student loan payments.
( - Pretty sure that learning Logo, QBasic, DOS, and Telnet/Winsock during grade school in 90's is the only reason I'm an employed programmer now.)
But for high-dimensional text problems that're pure classification, I tend to rely simply on 1NN classifiers (against a single centroid of training data of a target category, of which there tend to be many). I've spent a lot of time with NMF, for its potential as an incredibly interesting data-exploration tool ("There's a pronoun cluster! There's a Spanish cluster! There's a 404 Error axis!") or low-dimension projection step. I've even spent a good amount of time on implementing the algorithm in a number of memory-efficient ways.
Could you expand a bit on how you used NMF for these problems in practice (similar to how a sparse autoencoder captures reduced-dimensional features en route to supervised learning), or how others used ensemble methods?
Great practice for 2.7 that's probably quashed in 3.0. For large dicts, no need to create a giant set en route when iterating over keys, values, or both. Use "for k in d.iterkeys()", "for v in d.itervals", "for k,v in d.iteritems."
While I'm at it-- if you're ever finding yourself using a huge amount of awfully rigid objects from a single class, use __slots__ to allocate needed variables! Python will otherwise define the object's namespace in a dict (called __dict__) which allocates a whole kilobyte per object. Bad news if you have several hundred thousand... Guessing this is why Guido loves namedtuples so much for basic attributed storage.
Honestly, part of this mania began when I looked at my statements for just one provider (Chase) and realized the minimum payments they were asking for (~$300) covered ONLY the monthly interest. That sort of freaked me out, and I got spooked at the prospect of allowing that bank to rent-seek on my back for the next few decades, while I lack any sort of consumer rights to even ask a court for bankruptcy protection.
A lot of the simple analogies and explanations I can use to talk about determinants or Fourier transforms now I can only conjure because of the complex study taking years to soak through.
(To be explicit, that person is me, and I tend to throw all buffer money right at student loans before they grow like a hydra, faster than I can kill them.)
You can, however, calculate importance scores for the features used. Brennan's original paper gives a good algorithm for doing this (in short: for each tree, permuting the data along some feature for an out of bag sample and seeing how much worse it does.)
Really looking forward to his future discussion of computational topology and persistent homologies.