We describe a Metropolis-Hastings algorithm for sampling formal concepts, i.e., closed (item-) sets, according to any desired strictly positive distribution. Important applications are (a) estimating the number of all formal concepts as well as (b) discovering any number of interesting, non-redundant, and representative local patterns. Setting (a) can be used for estimating the runtime of algor...

This paper deals with the asymptotic properties of the Metropolis-Hastings algorithm, when the distribution of interest is unknown, but can be approximated by a sequential estimator of its density. We prove that, under very simple conditions, the rate of convergence of the Metropolis-Hastings algorithm is the same as that of the sequential estimator when the latter is introduced as the reversib...

We present a novel Metropolis-Hastings method for large datasets that uses small expected-size minibatches of data. Previous work on reducing the cost of MetropolisHastings tests yield variable data consumed per sample, with only constant factor reductions versus using the full dataset for each sample. Here we present a method that can be tuned to provide arbitrarily small batch sizes, by adjus...

The case study documented in this tutorial exercises the capabilities of the Metropolis Design Environment with an industrial-sized design. As a typical design example in Metropolis, this case study consists of a functional network, an architectural network, and a mapping network. The functional network models a simple application where data is obtained from two independent sources, manipulated...

We give the first analysis of a systematic scan version of the Metropolis algorithm. Our examples include generating random elements of a Coxeter group with probability determined by the length function. The analysis is based on interpreting Metropolis walks in terms of the multiplication in the Iwahori-Hecke algebra.

This paper presents a geometric approach to estimating subspaces as elements of complex Grassmann-manifold, with each subspace represented by its unique, complex projection matrix. Variation between the subspaces is modeled by rotating their projection matrices via the action of unitary matrices [elements of the unitary group U( )]. Subspace estimation or tracking then corresponds to inferences...

We give the first analysis of a systematic scan version of the Metropolis algorithm. Our examples include generating random elements of a Coxeter group with probability determined by the length function. The analysis is based on interpreting Metropolis walks in terms of the multiplication in the Iwahori-Hecke algebra.

In complex systems such as spin systems and protein systems, conventional simulations in the canonical ensemble will get trapped in states of energy local minima. We employ the generalized-ensemble algorithms in order to overcome this multiple-minima problem. Two wellknown generalized-ensemble algorithms, namely, multicanonical algorithm and replica-exchange method, are described. We then prese...

(First draft March 2005; revised November 2005) Abstract This paper extends some adaptive schemes that have been developed for the Random Walk Metropolis algorithm to more general versions of the Metropolis-Hastings (MH) algorithm, particularly to the Metropolis Adjusted Langevin algorithm of Roberts and Tweedie (1996). Our simulations show that the adaptation drastically improves the performan...