arXiv subjects

Chii-Ruey Hwang

Publications and source records attributed to Chii-Ruey Hwang.

4 recordsLinked to original sources

arXiv2015

Disorder chaos in the spherical mean-field model

We consider the problem of disorder chaos in the spherical mean-field model. It is concerned about the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters. The prediction states that if the disorders in the Hamiltonians are slightly decoupled, then the overlap will be concentrated near a constant value. Following Guerra's replica symmetry breaking scheme, we establish this at the level of the free energy as well as the Gibbs measure irrespective the presence or absence of the external field.

math.PR↗

arXiv2014

On the Weak Convergence and Central Limit Theorem of Blurring and Nonblurring Processes with Application to Robust Location Estimation

This article studies the weak convergence and associated Central Limit Theorem for blurring and nonblurring processes. Then, they are applied to the estimation of location parameter. Simulation studies show that the location estimation based on the convergence point of blurring process is more robust and often more efficient than that of nonblurring process.

math.ST↗

arXiv2014

Variance reduction for diffusions

The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of the diffusion after a long time provides a good sample from the desired distribution. There exist many diffusions with a common equilibrium, and one would naturally like to choose those that make the convergence to equilibrium faster. One way to do this is to consider a reversible diffusion, and add to it an antisymmetric drift which preserves the invariant measure. It has been proven that, in general, the irreversible algorithm performs better than the reversible one, in that the spectral gap is larger. In the present work, asymptotic variance is used as the criterion to compare these algorithms. We first provide a general comparison result, and then apply it to the specific cases of a diffusion on $\mathbb{R}^d$, or on a compact Riemannian manifold. We prove that, in general, adding an antisymmetric drift to a reversible diffusion reduces the asymptotic variance. We also provide some extensions of this result concerning strict inequality, the worst-case analysis, and the behavior of the asymptotic variance when the drift goes to infinity.

math.PR↗

arXiv2005

Accelerating diffusions

Let U be a given function defined on R^d and π(x) be a density function proportional to \exp -U(x). The following diffusion X(t) is often used to sample from π(x), dX(t)=-\nabla U(X(t)) dt+\sqrt2 dW(t),\qquad X(0)=x_0. To accelerate the convergence, a family of diffusions with π(x) as their common equilibrium is considered, dX(t)=\bigl(-\nabla U(X(t))+C(X(t))\bigr) dt+\sqrt2 dW(t),\qquad X(0)=x_0. Let L_C be the corresponding infinitesimal generator. The spectral gap of L_C in L^2(π) (λ(C)), and the convergence exponent of X(t) to πin variational norm (ρ(C)), are used to describe the convergence rate, where λ(C)= Sup{real part of μ\dvtxμis in the spectrum of L_C, μis not zero}, {-2.8cm}ρ(C) = Inf\biggl{ρ\dvtx\int | p(t,x,y) -π(y)| dy \le g(x) e^{ρt}\biggr}.Roughly speaking, L_C is a perturbation of the self-adjoint L_0 by an antisymmetric operator C\cdot\nabla, where C is weighted divergence free. We prove that λ(C)\le λ(0) and equality holds only in some rare situations. Furthermore, ρ(C)\le λ(C) and equality holds for C=0. In other words, adding an extra drift, C(x), accelerates convergence. Related problems are also discussed.

math.PR↗