Reconstructing the Energy Landscape of a Distribution from Monte Carlo Samples

  title={Reconstructing the Energy Landscape of a Distribution from Monte Carlo Samples},
  author={Qing Zhou and Wing Hung Wong},
Defining the energy function as the negative logarithm of the density, we explore the energy landscape of a distribution via the tree of sublevel sets of its energy. This tree represents the hierarchy among the connected components of the sublevel sets. We propose ways to annotate the tree so that it provides information on both topological and statistical aspects of the distribution, such as the local energy minima (local modes), their local domains and volumes, and the barriers between them… 

Mapping the Energy Landscape

This chapter introduces a novel MCMC method for identifying macroscopic structures in locally noisy energy landscapes and explores and visualizes the model space for clustering, bi-clustering, and grammar learning.

Mapping Energy Landscapes of Non-Convex Learning Problems

A way to measure the difficulties (or complexity) of these learning problems and study how various conditions affect the landscape complexity, such as separability of the clusters, the number of examples, and the level of supervision is proposed.

Optimisation via Slice Sampling

A simulation-based approach to optimisation with multi-modal functions using slice sampling that specifies the objective function as an energy potential in a Boltzmann distribution and uses auxiliary exponential slice variables to provide samples for a variety of energy levels.

Multi-Domain Sampling With Applications to Structural Inference of Bayesian Networks

The multi-domain sampler is applied to structural learning of protein-signaling networks from high-throughput single-cell data, where a signaling network is modeled as a causal Bayesian network and improves the accuracy and the predictive power of estimated networks.

Effect of sequences on the shape of protein energy landscapes

This study designed a clustering method based on graph theory to analyze the conformations sampled using a recently developed Monte Carlo method, FRESS, and found that the way protein motions are modeled (the move sets) has a significant effect on the shape of protein energy landscapes.

Topological methods for exploring low-density states in biomolecular folding pathways.

A computational approach to explore the relatively low populated transition or intermediate states in biomolecular folding pathways, based on a topological data analysis tool, MAPPER, with simulation data from large-scale distributed computing, inspired by classical Morse theory in mathematics.

Parallel tempering with equi-energy moves

This work proposes an adaptation of the Equi-Energy Sampler that combines PT with the principle of swapping between chains with the same level of energy, and keeps the original idea of the EES while ensuring good theoretical properties, and practical implementation.

Convergence of the Equi-Energy Sampler and Its Application to the Ising Model.

A complete proof of the convergence of a recently developed sampling algorithm called the equi-energy (EE) sampler in the case that the state space is countable is provided, showing that in a countable state space, each sampling chain in the EE sampler is strongly ergodic.

The landscape of complex networks: Critical nodes and a hierarchical decomposition

Inspired by the classical Morse theory, a new notion, critical nodes of functions on networks, are introduced, based on the gradient flow of these functions, which enables a concise topological landscape of functions in networks.

Split Sampling: Expectations, Normalisation and Rare Events

This paper develops a methodology that is called split sampling methods to estimate high dimensional expectations and rare event probabilities using an auxiliary variable MCMC simulation and derives the estimator from a Rao-Blackwellised estimate of a marginal auxiliary variable distribution.



Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

  • S. GemanD. Geman
  • Physics
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 1984
The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.

Continuous Contour Monte Carlo for Marginal Density Estimation With an Application to a Spatial Statistical Model

The problem of marginal density estimation for a multivariate density function f(x) can be generally stated as a problem of density function estimation for a random vector λ(x) of dimension lower

A Generalized Wang–Landau Algorithm for Monte Carlo Computation

The generalized algorithm, motivated by the successes of the Wang–Landau algorithm in discrete systems, is generalized to continuous systems and provides a new method for Monte Carlo integration based on stochastic approximation and is an excellent tool for Monte Monte optimization.

Stochastic Approximation in Monte Carlo Computation

The stochastic approximation Monte Carlo (SAMC) algorithm is proposed, which overcomes the shortcomings of the WL algorithm and establishes a theorem concerning its convergence.

Equi-energy sampler with applications in statistical inference and statistical mechanics

Kou, Zhou and Wong have introduced a novel sampling method, the equi-energy sampler, which could contribute significantly to the field of structural prediction, and a very closely related method, multicanonical sampling (MCS).

The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics

Topological characteristics of multidimensional potential energy surfaces are explored and the full conformation space is mapped on the set of local minima. This map partitions conformation space

Monte Carlo Sampling Methods Using Markov Chains and Their Applications

SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and

Bayesian inference on biopolymer models

This paper presents a tutorial style description of a Bayesian inference procedure for segmentation of a sequence based on the heterogeneity in its composition, and shows how this goal can be achieved for most bioinformatics methods that use dynamic programming.

Nested sampling for general Bayesian computation

Nested sampling estimates directly how the likelihood function relates to prior mass. The evidence (alternatively the marginal likelihood, marginal den- sity of the data, or the prior predictive) is

Efficient, multiple-range random walk algorithm to calculate the density of states.

A new Monte Carlo algorithm is presented that permits us to directly access the free energy and entropy, is independent of temperature, and is efficient for the study of both 1st order and 2nd order phase transitions.