Related papers: Sampling Biased Monotonic Surfaces using Exponenti…
The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…
The switch chain is a well-known Markov chain for sampling directed graphs with a given degree sequence. While not ergodic in general, we show that it is ergodic for regular degree sequences. We then prove that the switch chain is rapidly…
Considering a Markov chain defined on a cycle, near-quadratic improvement of mixing is shown when only a subtle perturbation is introduced to the structure and non-reversible transition probabilities are used. More precisely, a mixing time…
We provide an optimally mixing Markov chain for 6-colorings of the square lattice on rectangular regions with free, fixed, or toroidal boundary conditions. This implies that the uniform distribution on the set of such colorings has strong…
We study Markov chains for $\alpha$-orientations of plane graphs, these are orientations where the outdegree of each vertex is prescribed by the value of a given function $\alpha$. The set of $\alpha$-orientations of a plane graph has a…
Lifted Markov chains are Markov chains on graphs with added local "memory" and can be used to mix towards a target distribution faster than their memoryless counterparts. Upper and lower bounds on the achievable performance have been…
Sampling from Gibbs distribution is a central problem in computer science as well as in statistical physics. In this work we focus on the k-colouring model} and the hard-core model with fugacity \lambda when the underlying graph is an…
We analyze the general biased adjacent transposition shuffle process, which is a well-studied Markov chain on the symmetric group $S_n$. In each step, an adjacent pair of elements $i$ and $j$ are chosen, and then $i$ is placed ahead of $j$…
In a series of recent works, Boyd, Diaconis, and their co-authors have introduced a semidefinite programming approach for computing the fastest mixing Markov chain on a graph of allowed transitions, given a target stationary distribution.…
A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions,…
We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and…
TThe prototypical problem we study here is the following. Given a $2L\times 2L$ square, there are approximately $\exp(4KL^2/\pi )$ ways to tile it with dominos, i.e. with horizontal or vertical $2\times 1$ rectangles, where $K\approx 0.916$…
Zigzags in graphs embedded in surfaces are cyclic sequences of edges whose any two consecutive edges are different, have a common vertex and belong to the same face. We investigate zigzags in randomly constructed combinatorial tetrahedral…
We show how to combine Fourier analysis with coupling arguments to bound the mixing times of a variety of Markov chains. The mixing time is the number of steps a Markov chain takes to approach its equilibrium distribution. One application…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
We survey existing techniques to bound the mixing time of Markov chains. The mixing time is related to a geometric parameter called conductance which is a measure of edge-expansion. Bounds on conductance are typically obtained by a…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
We prove rapid mixing for certain Markov chains on the set $S_n$ of permutations on $1,2,\dots,n$ in which adjacent transpositions are made with probabilities that depend on the items being transposed. Typically, when in state $\sigma$, a…
Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the…
We study local Markov chains for sampling 3-colorings of the discrete torus $T_{L,d}={0,..., L-1}^d$. We show that there is a constant $\rho \approx .22$ such that for all even $L \geq 4$ and $d$ sufficiently large, certain local Markov…