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The math blog of Dmitry OstrovskyMon, 21 Nov 2016 12:17:36 +0000hourly1http://wordpress.com/Comment on Subexponential distributions I — Bernstein inequality and quadratic forms by Dmitry Ostrovsky
https://ostrodmit.blog/2015/05/08/subexponential-random-variables/comment-page-1/#comment-67
Mon, 21 Nov 2016 12:17:36 +0000http://ostrodmit.wordpress.com/?p=1001#comment-67Csaba, you’re right of course, and thank you for the feedback.
The union bound here is for the “methodological purpose”, as seen by the next display (passing from \Chi_1^2 to \Chi_n^2). Basically, the whole first paragraph is just to introduce the idea that one can use the union bound to control the sum of i.i.d. r.v.’s. Of course, union bounding alone is not enough, one needs Chernoff on top, as shown in the remaining part of the post.
]]>Comment on Subexponential distributions I — Bernstein inequality and quadratic forms by csabaszepesvari
https://ostrodmit.blog/2015/05/08/subexponential-random-variables/comment-page-1/#comment-66
Sat, 19 Nov 2016 23:35:26 +0000http://ostrodmit.wordpress.com/?p=1001#comment-66At the very beginning why do you need the union bound? You could simply calculate: $P(X \ge t) = P( \xi^2 \ge t ) = P( |\xi| \ge \sqrt{t}) \le \exp( -(\sqrt{t})^2/2 ) = \exp(-t)$.
]]>Comment on ‘Shear’ convex polyhedra by ‘Shear’ convex polyhedra: solution | Look at the corners!
https://ostrodmit.blog/2015/09/25/tight-convex-polyhedra/comment-page-1/#comment-39
Sat, 17 Oct 2015 11:05:43 +0000http://ostrodmit.wordpress.com/?p=3436#comment-39[…] ← ‘Shear’ convex polyhedra […]
]]>Comment on Sandwiching smooth convex functions by Subgradient projection method III — Strong convexity | Look at the corners!
https://ostrodmit.blog/2015/01/21/lipschitz-gradient-upper-bound/comment-page-1/#comment-37
Tue, 28 Jul 2015 22:52:17 +0000http://ostrodmit.wordpress.com/?p=338#comment-37[…] Strong convexity provides an improved lower bound for a convex function; therefore are in our right to expect the improvement of the rate of convergence of SPM. In this post we will find out how much we actually gain. […]
]]>Comment on Projection on a convex set is closer to any point of the set by Subgradient Projection method II — smooth objective | Look at the corners!
https://ostrodmit.blog/2015/01/22/piphagorean-inequality-for-a-projection-on-a-convex-set/comment-page-1/#comment-36
Tue, 28 Jul 2015 15:39:18 +0000http://ostrodmit.wordpress.com/?p=345#comment-36[…] where the third inequality follows from the Euclidean projection lemma. […]
]]>Comment on Sandwiching smooth convex functions by Subgradient Projection method II — smooth objective | Look at the corners!
https://ostrodmit.blog/2015/01/21/lipschitz-gradient-upper-bound/comment-page-1/#comment-35
Sun, 26 Jul 2015 16:48:55 +0000http://ostrodmit.wordpress.com/?p=338#comment-35[…] In the last post of the course, we showed how oracle complexity of SPM can be bounded for Lipschitz functions. Now, the question is whether this bound can be enhanced, if the objective is smooth, meaning that it is differentiable with a Lipschitz gradient. Intuitively, it means that not only the objective function is globally lower bounded by a linear form (“prop”) given by the subgradient (now just gradient), but also it is upper bounded: it lies within the parabolic envelope from the “prop”. Moreover, it turns that the lower bound can also be improved. In other words, we can “sandwich” the function (all this is described in this post). […]
]]>Comment on Black box approach to optimization by Subgradient Projection method | Look at the corners!
https://ostrodmit.blog/2015/01/25/first-order-methods-i-subgradient-projection/comment-page-1/#comment-34
Sat, 06 Jun 2015 22:28:25 +0000http://ostrodmit.wordpress.com/?p=369#comment-34[…] ← Black box model Fourier transforms → […]
]]>Comment on Projected Gradient Descent I — Lipschitz functions by “Pythagorean inequality” | Look at the corners!
https://ostrodmit.blog/2015/01/25/subradient-projection-method/comment-page-1/#comment-33
Fri, 05 Jun 2015 01:01:54 +0000http://ostrodmit.wordpress.com/?p=408#comment-33[…] lemma is used in the analysis of the Subgradient Projection Method, a basic method for large-scale […]
]]>Comment on Azuma-Hoeffding inequality by Martingale method II — McDiarmid’s inequality | Look at the corners!
https://ostrodmit.blog/2015/05/24/azuma-hoeffding-inequality/comment-page-1/#comment-32
Wed, 27 May 2015 23:27:04 +0000http://ostrodmit.wordpress.com/?p=1777#comment-32[…] the previous post of the course, we obtained Azuma–Hoeffding inequality by cleverly working with conditional […]
]]>Comment on Subexponential distributions I — Bernstein inequality and quadratic forms by Azuma-Hoeffding inequality | Look at the corners!
https://ostrodmit.blog/2015/05/08/subexponential-random-variables/comment-page-1/#comment-31
Tue, 26 May 2015 12:13:47 +0000http://ostrodmit.wordpress.com/?p=1001#comment-31[…] concentrates above its mean, with a remarkable special case when are bounded. We then obtained another result (concentration of quadratic forms) for Gaussian when is a quadratic form of a Gaussian […]
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