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Results tagged with pr.probability
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user 17589
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
3
votes
1
answer
237
views
Concentration of a modified random walk
Let $\varepsilon$ be a number in $(0, 1)$, consider the following random walk on the real line $X^{(0)}, X^{(1)}, \dots$, where
$X^{(0)}=0$
If $X^{(t)} > 0$, then with probability $.5$, $X^{(t+1)} …
- 143
3
votes
3
answers
460
views
$H(p) \le H(q) + KL(p, q)$?
Let $H(p) = \sum_i p_i\log\frac{1}{p_i}$ be the entropy of $p$
and $KL(p, q) = \sum_i p_i\log\frac{p_i}{q_i}$ be the KL divergence between $p$ and $q$. Does it hold that $H(p) \le H(q) + KL(p, q)$?
I …
- 143
0
votes
1
answer
490
views
Optimal solution to cross entropy loss in the continuous case
This could be a simple question but I don't have a satisfying answer.
Setup. Suppose that we have $K$ different classes, and consider cross entropy loss which maps a probability vector in the probabi …
- 143