Probabilistic inference is an attractive approach to uncertain reasoning and empirical learning in artificial intelligence. Computational difculties arise, however, because probabilistic models with the necessary realism and flexibility lead to complex distributions over high-dimensional spaces. Related problems in other fields have been tackled using Monte Carlo methods based on sampling using Markov chains, providing a rich array of techniques that can be applied to problems in artificial intelligence. The "Metropolis algorithm" has been used to solve difficult problems in statistical physics for over forty years, and, in the last few years, the related method of "Gibbs sampling" has been applied to problems of statistical inference. Concurrently, an alternative method for solving problems in statistical physics by means of dynamical simulation has been developed as well, and has recently been unified with the Metropolis algorithm to produce the "hybrid Monte Carlo" method. In computer science, Markov chain sampling is the basis of the heuristic optimization technique of "simulated annealing", and has recently been used in randomized algorithms for approximate counting of large sets. In this review, I outline the role of probabilistic inference in artificial intelligence, and present the theory of Markov chains, and describe various Markov chain Monte Carlo algorithms, along with a number of supporting techniques. I try to present a comprehensive picture of the range of methods that have been developed, including techniques from the varied literature that have not yet seen wide application in artificial intelligence, but which appear relevant. As illustrative examples, I use the problems of probabilitic inference in expert systems, discovery of latent classes from data, and Bayesian learning for neural networks.

Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative models, each pattern can be generated in exponentially many ways. It is thus intractable to adjust the parameters to maximize the probability of the observed patterns. We describe a way of finessing this combinatorial explosion by maximizing an easily computed lower bound on the probability of the observations. Our method can be viewed as a form of hierarchical self-supervised learning that may relate to the function of bottom-up and top-down cortical processing pathways.

Evolutionary computation (EC) consists of the design and analysis of probabilistic algorithms inspired by the principles of natural selection and variation. Genetic Programming (GP) is one subfield of EC that emphasizes desirable features such as the use of procedural representations, the capability to discover and exploit intrinsic characteristics of the application domain, and the flexibility to adapt the shape and complexity of learned models. Approaches that learn monolithic representations are considerably less likely to be effective for complex problems, and standard GP is no exception. The main goal of this dissertation is to extend GP capabilities with automatic mechanisms to cope with problems of increasing complexity. Humans succeed here by skillfully using hierarchical decomposition and abstraction mechanisms. The translation of such mechanisms into a general computer implementation is a tremendous challenge, which requires a firm understanding of the interplay between repr...

In the first genetic programming (GP) book John Koza noticed that fitness histograms give a highly informative global view of the evolutionary process (Koza, 1992). The idea is further developed in this paper by discussing GP evolution in analogy to a physical system. I focus on three inter-related major goals: (1) Study the the problem of search effort allocation in GP; (2) Develop methods in the GA/GP framework that allow adaptive control of diversity; (3) Study ways of adaptation for faster convergence to optimal solution. An entropy measure based on phenotype classes is introduced which abstracts fitness histograms. In this context, entropy represents a measure of population diversity. An analysis of entropy plots and their correlation with other statistics from the population enables an intelligent adaptation of search control. 1 INTRODUCTION One important problem in search control is the allocation of search effort. In general, search effort should be spent to maximize the proba...

Abstract: We analyse the low temperature phase of ferromagnetic Kac-Ising models in dimensions d ≥ 2. We show that if the range of interactions is γ −1, then two disjoint translation invariant Gibbs states exist, if the inverse temperature β satisfies β − 1 ≥ γ κ, where κ = d(1−ǫ), for (2d+1)(d+1) any ǫ> 0. The prove involves the blocking procedure usual for Kac models and also a contour representation for the resulting long-range (almost) continuous spin system which is suitable for the use of a variant of the Peierls argument.

We derive precise Ornstein-Zernike asymptotic formula for the decay of the two-point function Pp(0 ! x) of the Bernoulli bond percolation on the integer lattice Z d in any dimension d > 2, in any direction x and for any sub-critical value of p < pc(d).

this paper, we introduce a new algorithm called `bits-back coding' that makes stochastic source

The general features of Microcanonical Thermodynamics as applied to the fragmentation of atomic clusters are discussed. Here we first develop the thermodynamics of microcanonical phase transitions of first and second order in systems which are thermodynamically stable in the sense of van Hove. We show how both kinds of phase transitions can unambiguously be identified in small isolated systems of ∼ 100 atoms by the shape of the microcanonical caloric equation of state T(E) and not so well by the coexistence of two spatially clearly separated phases. In contrast to ordinary (canonical) thermodynamics Microcanonical Thermodynamics gives an insight into the coexistence region. Here the form of the specific heat c(E/N) connects transitions of first and second order in a natural way. The phase transition towards fragmentation is introduced. The similarities and differences to the boiling of macrosystems are pointed out. 1

We derive precise Ornstein-Zernike asymptotic formula for the decay of the two-point function (rr0rr)z in the general context of finite range Ising type models on Z a.

We review what we have learned about the "Renormalization Group peculiarities" which were discovered about twenty years ago by Griffiths and Pearce, and which questions they asked are still widely open. We also mention some related developments.