All Questions
Tagged with nonlinear-optimization markov-chains
9 questions
3
votes
0
answers
202
views
Maximize an $L^p$-functional subject to a set of constraints
Let
$(E,\mathcal E,\lambda)$ and $(E',\mathcal E',\lambda')$ be measure spaces
$f\in L^2(\lambda)$
$I$ be a finite nonempty set
$\varphi_i:E'\to E$ be bijective $(\mathcal E',\mathcal E)$-measurable ...
- 167
3
votes
0
answers
121
views
Finding a mixture of 1st and 0'th order Markov models that is closest to an empirical distribution
I am interested in finding the distribution "$p^*$" closest to an empirical distribution $\hat{p}$ where $p^*$ is a mixture of first and zeroth order Markov models. That is, I want to find $$
p^* = \...
- 283
2
votes
2
answers
1k
views
Stochastic gradient descent convergence for non-convex smooth functions
I'm looking for a proof of convergence of stochastic gradient descent applied to a non-convex smooth function. I'm generally interested in just asymptotic convergence, preferably to a critical point, ...
- 219
2
votes
2
answers
338
views
Of all probability matrix $P$ having stationary distribution $\pi$, find the one having smallest diagonal
I am requesting your help today trying to solve a somewhat odd problem. Is there a way to find through some numerical algorithm such as Newton's method the stochastic matrix $\boldsymbol{P}$ having ...
- 23
2
votes
0
answers
174
views
Fitting a Markov Model with Linear Transition Probabilities
I asked this yesterday on math.stackexchange. It didn't get any attention so I'm reposting here. Hope this is in line with policy.
I have data which I model as $50$ rounds of a Markov chain with ...
- 21
1
vote
0
answers
79
views
Markov Chain that maximises the entropy creation rate
I am working on MERW (Maximal entropy random walk) for a project.
I want to show that given a graph G, there is $\textbf{only one}$ aperiodic markov chain on G that maximises the entropy creation rate ...
- 11
1
vote
0
answers
116
views
Showing existence of a solution to an underdetermined system of equations with non-negativity constraints
Let $K$ be a positive integer, let $p\in (0,1)$, and let $\{W(k,i),W^B(k,i), \varphi_k(i)\}_{1\leq i\leq k\leq K}$ be variables.
I need to prove that there exists a solution to the following system ...
- 63
1
vote
0
answers
73
views
Reduce the asymptotic variance for a class of Metropolis-Hasting estimates
I'm running the Metropolis-Hastings algorithm with state space $E$, target distribution $\mu=p\lambda$ and proposal kernel $Q$ to estimate $\mu(hf)$ for a fixed function $f:E\to[0,\infty)^3$ and a ...
- 167
1
vote
0
answers
106
views
Show a Poincaré inequality for a Markov kernel and minimize the Poincaré constant
Let $\tilde\kappa$ denote the transition kernel of the Markov chain generated by the Metropolis-Hastings algorithm with proposal kernel $\tilde Q$ and target distribution $\tilde\mu$ (see definitions ...
- 167