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Mar
14
awarded  Enlightened
Mar
14
awarded  Nice Answer
Oct
23
awarded  Yearling
Jun
25
awarded  Yearling
Aug
11
revised How to compute KL-divergence when PMF contains 0s?
added 362 characters in body
Aug
11
answered How to compute KL-divergence when PMF contains 0s?
Jul
13
comment Conic hulls and cones
BTW I believe there is a typo in your description: primal certificates mean no extreme point, and dual certificates mean some extreme point amongst the remaining input points.
Jul
13
comment Conic hulls and cones
Welcome to MO! That is a very nice algorithm! Just a note--I can't figure out how to directly convert this to conic hulls, so it seems necessary to use a conic-to-convex reduction as remarked by Jean-Marc Schlenker in the comments above. (To be specific about the problem: it is possible that a non-extremal point has the largest projection onto the dual certificate, simply because it is "farthest down" that polyhedral face. I tried a couple quick fixes, but all failed. Anyway, the projection solution by Jean-Marc is fast and sufficient.)
Jul
12
revised Conic hulls and cones
math parse error
Jul
12
answered Conic hulls and cones
May
9
awarded  Nice Answer
Apr
6
revised Existence of nonnegative solutions to an underdetermined system of linear equations
sampling for pos & neg
Apr
6
answered Existence of nonnegative solutions to an underdetermined system of linear equations
Dec
17
awarded  Yearling
Aug
22
comment Kernel width in Kernel density estimation
About using neighbors--although this seems like a reasonable idea, there is very little work in this direction. Luc Devroye has a few papers on this topic http://cg.scs.carleton.ca/~luc/devs.html , and you'll see that just looking at the closest is inadequate. In general, cross-validation is the standard technique. If you are interested in L1 density estimates, there is an excellent book by Devroye and Lugosi titled "Combinatorial Methods in Density Estimation".
Aug
19
revised Why were matrix determinants once such a big deal?
added 227 characters in body
Aug
19
answered Why were matrix determinants once such a big deal?
Jul
23
answered Is quadratic programming still NP-hard if you have bounds and a feasible point?
Mar
18
comment Are Bregman divergences quasi-convex?
(and set $x= (0,0)$.) in the bad example, since $f$ is linear along $x-y$ and $x-z$, then $b_x(y) = b_x(z) = 0$. On the other hand, since it is quadratic along $x-w$, the Bregman divergence is nonzero; in fact, it is $1/2$. I have an argument that $f$ is convex, but it is vague. I have to run, but tomorrow hopefully I can come back with something better.
Mar
18
comment Are Bregman divergences quasi-convex?
thanks for clarifying. If you can verify the following example (in cylindrical coordinates) is convex, then the general case does not work. Set $\lambda(\theta) = \frac {4}{\pi}\left | \theta - \frac \pi 4\right|$, $S= [0,1] \times [0,\pi/2]$, and $f : S\to \mathbb{R}$ to $f(r,\theta) = \lambda(\theta)r + (1-\lambda(\theta))r^2$. Since $\lambda(\cdot)$ goes between 0 (at $\theta \in \{0,\pi/2\}$) and 1 (at $\theta = \pi/4$), $f$ interpolates (rotationally) between linear and quadratic. The bad choice is $y = (1,0)$, $z =(1,\pi/2)$, and $w = (y+z)/2 = (\sqrt{2}/2,\pi/4)$.