Boltzmann machines and their applications

Aarts, Ehl Emile; Korst, Jan

doi:10.1007/3-540-17943-7_119

Cited by 36 publications

(20 citation statements)

References 16 publications

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“…De nition 1 For xed r, k and , with k < v and > 0, we say that A is the Parameters and descriptors are related by the following multiplicity conditions, r = u=v k = u=b = r(k ; 1) v ; 1 = u(u ; b) bv(v ; 1) with r, k and integers, therefore restricting the range of admissible parameter sets.…”

Section: The Problem: Block Designsmentioning

confidence: 99%

“…The cost functions considered in this work 5] are de ned as the linear combination of a set of distribution measures for each of the properties of a block design. (1) with U P t P h P v Q and Q de ned next, and ( u t h v q q ), the coecients of the linear combination, de ning the composition of a particular cost function. When the parameter set (v b u) is admissible the optimal values of the previous measures are derived by assuming that properties i) to iv) in de nition 1 hold (optimality assumption), even if the corresponding design does not exist.…”

Section: The Tool: Optimizing Neural Networkmentioning

confidence: 99%

“…Connection weights codify the composition coe cients of the cost function chosen. Therefore, optimal energy values, current energy values and local elds are given by equations (3), (1), and (2), respectively.…”

Section: Search Strategiesmentioning

confidence: 99%

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Neural Cost Functions and Search Strategies for the Generation of Block Designs An Experimental Evaluation

Bofill¹

2001

International Journal of Neural Systems

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A constraint satisfaction problem, namely the generation of Balanced Incomplete Block Designs (v b r k )-BIBDs, is casted in terms of function optimization. A family of cost functions that both suit the problem and admit a neural implementation is de ned. An experimental comparison spanning this repertoire of cost functions and three neural relaxation strategies (Down-Hill search, Simulated Annealing and a new Parallel Mean Search procedure), as applied to all BIBDs of up to 1000 entries, has been undertaken. The experiments were performed on a Connection Machine CM-200 and their analysis required a careful study of performace measures. The simplest cost function standed out as the best one for the three strategies. Parallel Mean Search, with several processors searching cooperatively in parallel, could solve a larger number of problems than the same number of processors working independently, but Simulated Annealing yielded overall the best results. Other conclusions, as detailed in the paper, could be drawn from the comparison, BIBDs remaining a challenging problem for neural optimization algorithms.

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Section: The Problem: Block Designsmentioning

confidence: 99%

Section: The Tool: Optimizing Neural Networkmentioning

confidence: 99%

See 1 more Smart Citation

Neural Cost Functions and Search Strategies for the Generation of Block Designs An Experimental Evaluation

Bofill¹

2001

International Journal of Neural Systems

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“…In the Artificial Intelligence field, relaxation has been mainly used in computer visionsince it is where it was first used-to address problems such as corner and edge recognition or line and image smoothing (Richards, Landgrebe, & Swain, 1981;Lloyd, 1983). Nevertheless, many traditional AI problems can be stated as a labeling problem: the traveling salesman problem, n-queens, or any other combinatorial problem (Aarts & Korst, 1987).…”

Section: Relax: a Relaxation Labeling Based Taggermentioning

confidence: 99%

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Abstract.We have applied the inductive learning of statistical decision trees and relaxation labeling to the Natural Language Processing (NLP) task of morphosyntactic disambiguation (Part Of Speech Tagging). The learning process is supervised and obtains a language model oriented to resolve POS ambiguities, consisting of a set of statistical decision trees expressing distribution of tags and words in some relevant contexts. The acquired decision trees have been directly used in a tagger that is both relatively simple and fast, and which has been tested and evaluated on the Wall Street Journal (WSJ) corpus with competitive accuracy. However, better results can be obtained by translating the trees into rules to feed a flexible relaxation labeling based tagger. In this direction we describe a tagger which is able to use information of any kind (n-grams, automatically acquired constraints, linguistically motivated manually written constraints, etc.), and in particular to incorporate the machine-learned decision trees. Simultaneously, we address the problem of tagging when only limited training material is available, which is crucial in any process of constructing, from scratch, an annotated corpus. We show that high levels of accuracy can be achieved with our system in this situation, and report some results obtained when using it to develop a 5.5 million words Spanish corpus from scratch.

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“…In this paper, our aim is to generalize the distribution assumption used in the traditional language modelling approach, based on fully-observable Boltzmann Machine (BM) [1] that can yield a kind of Boltzmann distribution. In statistical mechanics, the Boltzmann distribution (also known as Gibbs distribution) is used as probability distribution over possible states of a system.…”

Section: Introductionmentioning

confidence: 99%

Document Boltzmann Machines for Information Retrieval

Qian

Zhang

Hou

et al. 2015

Lecture Notes in Computer Science

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Abstract. Probabilistic language modelling has been widely used in information retrieval. It estimates document models under the multinomial distribution assumption, and uses query likelihood to rank documents. In this paper, we aim to generalize this distribution assumption by exploring the use of fully-observable Boltzmann Machines (BMs) for document modelling. BM is a stochastic recurrent network and is able to model the distribution of multi-dimensional variables. It yields a kind of Boltzmann distribution which is more general than multinomial distribution. We propose a Document Boltzmann Machine (DBM) that can naturally capture the intrinsic connections among terms and estimate query likelihood efficiently. We formally prove that under certain conditions (with 1-order parameters learnt only), DBM subsumes the traditional document language model. Its relations to other graphical models in IR, e.g., MRF model, are also discussed. Our experiments on the document reranking demonstrate the potential of the proposed DBM.

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Boltzmann machines and their applications

Cited by 36 publications

References 16 publications

Neural Cost Functions and Search Strategies for the Generation of Block Designs An Experimental Evaluation

Neural Cost Functions and Search Strategies for the Generation of Block Designs An Experimental Evaluation

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Document Boltzmann Machines for Information Retrieval

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