User raskol - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T18:03:53Z http://mathoverflow.net/feeds/user/29611 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/124686/equivalent-markov-random-fields Equivalent Markov Random Fields raskol 2013-03-16T11:42:44Z 2013-05-10T09:22:00Z <p>Hi,</p> <p>Is it possible to have topologically different Markov Random Fields (few different edges) and yet yielding the same inference results ?</p> <p>Thanks!</p> http://mathoverflow.net/questions/125884/kl-divergences-comparison KL divergence(s) comparison, raskol 2013-03-29T07:39:45Z 2013-03-29T22:31:00Z <p>Hi,</p> <p>$P_1$, $P_2$, $P_3$ are probability distributions defined on the same support.</p> <p>Knowing that $H(P_1) &lt; H(P_2) &lt; H(P_3)$, can we compare $D_{KL}(P_2,P_1)$ and $D_{KL}(P_3,P_1)$ ?</p> <p>(H is the Shannon Entropy and $D_{KL}$ is the Kullback–Leibler divergence)</p> <p>Thank you.</p> http://mathoverflow.net/questions/121159/equilibrium-of-random-zero-sum-game Equilibrium of random zero-sum game, raskol 2013-02-08T07:27:07Z 2013-02-08T08:45:54Z <p>Hi,</p> <p>How to find, or at least express, the equilibrium of a zero-sum game with an $n*n$ payoff matrix (each player has $n$ strategies) and the payoff of the entry $(i,j)$ is $u(i,j)$. $u$ a random function of the strategies $i$ and $j$.</p> <p>What about the case where $n \rightarrow \infty$.</p> <p>Any reference or code is welcome.</p> <p>Thanks a lot!</p> http://mathoverflow.net/questions/115270/how-to-work-with-infinite-random-graphs How to work with infinite random graph(s) ? raskol 2012-12-03T10:54:28Z 2012-12-03T14:50:14Z <p>Hi,</p> <p>In the case where we are dealing with an infinite random graph (RG with infinite nodes).</p> <p>How do we model/work with notions like degrees, degree distribution ? How are they defined ?</p> <p>Thanks!</p> http://mathoverflow.net/questions/115258/softmax-activation-function-with-infinite-support softmax activation function with infinite support ? raskol 2012-12-03T07:39:43Z 2012-12-03T07:39:43Z <p>Hi,</p> <p>How do we calculate the terms of a <a href="http://en.wikipedia.org/wiki/Softmax_activation_function" rel="nofollow">softmax activation function</a> with an infinite support ?</p> <p>That is, finding the $\{p_i\}_i$ with <a href="http://en.wikipedia.org/wiki/Softmax_activation_function" rel="nofollow">$p_i = {{e^{q_i}} \over {\sum_{j=1}^\infty e^{q_j} }}$</a> (how to estimate the infinite sum?)</p> <p>Any proposition or idea is welcome.</p> <p>Thanks a lot!</p> http://mathoverflow.net/questions/125884/kl-divergences-comparison/125948#125948 Comment by raskol raskol 2013-04-01T15:54:12Z 2013-04-01T15:54:12Z Thank you. If we specify that KL is continuous at $(S_2, S_1)$ (respectively $(S_3, S_1)$) and that the distributions $S_1$, $S_2$, $S_3$ are strictly positive over all the support elements. Is it possible to characterize $D_{KL}(P_2,P_1)/D_{KL}(P_3,P_1)$ ? http://mathoverflow.net/questions/125884/kl-divergences-comparison/125948#125948 Comment by raskol raskol 2013-04-01T15:52:31Z 2013-04-01T15:52:31Z Thank you. If we specify that KL is continuous at $(S_2, S_1)$ (respectively $(S_3, S_1)) and that the distributions$S_1$,$S_2$,$S_3$are strictly positive over all the support elements, is it possible to characterize$D_{KL}(P_2,P_1)/D_{KL}(P_3,P_1)$? http://mathoverflow.net/questions/124686/equivalent-markov-random-fields Comment by raskol raskol 2013-03-18T10:32:43Z 2013-03-18T10:32:43Z In the case of Bayesian networks: &quot;It has been noted that different Bayesian networks may be equivalent in the sense that they actually represent the same joint probability distribution (and thus conditional independency information as well), even though they have different graphical structures.&quot; (<a href="http://www.cs.uregina.ca/Research/Techreports/2002-02.ps" rel="nofollow">cs.uregina.ca/Research/Techreports/2002-02.ps</a>). I am asking the same question for MRFs. http://mathoverflow.net/questions/115258/softmax-activation-function-with-infinite-support Comment by raskol raskol 2012-12-05T07:05:36Z 2012-12-05T07:05:36Z Forgive me. Supposing that we have an infinite network$G_{\infty}$with vertices$V=[1, \infty]$. Herein,$q_i$is the value of the node$i \in V$. The$q_i\$ are determined by a random walk that starts from a node.