Restricted Boltzmann Machine based on a Fermi sea

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/ac331d ◽

2021 ◽

Author(s):

Yana Lyakhova ◽

Evgeny Alexandrovich Polyakov ◽

Alexey N Rubtsov

Keyword(s):

Degrees Of Freedom ◽

Cold Atoms ◽

Laws Of Nature ◽

Restricted Boltzmann Machine ◽

Data Sets ◽

Boltzmann Machine ◽

Log Likelihood ◽

Observable Data ◽

Lattice Fermions ◽

Machine Learning Models

Abstract In recent years, there has been an intensive research on how to exploit the quantum laws of nature in the machine learning. Models have been put forward which employ spins, photons, and cold atoms. In this work we study the possibility of using the lattice fermions to learn the classical data. We propose an alternative to the quantum Boltzmann Machine, the so-called Spin-Fermion Machine (SFM), in which the spins represent the degrees of freedom of the observable data (to be learned), and the fermions represent the correlations between the data. The coupling is linear in spins and quadratic in fermions. The fermions are allowed to tunnel between the lattice sites. The training of SFM can be eciently implemented since there are closed expressions for the log- likelihood gradient. We nd that SFM is more powerful than the classical Restricted Boltzmann Machine (RBM) with the same number of physical degrees of freedom. The reason is that SFM has additional freedom due to the rotation of the Fermi sea. We show examples for several data sets.

Download Full-text

Interdependences of Products in Market Baskets: Comparing the Conditional Restricted Boltzmann Machine to the Multivariate Logit Model

Review of Marketing Science ◽

10.1515/roms-2020-0074 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Harald Hruschka

Keyword(s):

Hidden Variables ◽

Restricted Boltzmann Machine ◽

Future Research ◽

Data Sets ◽

Boltzmann Machine ◽

Consumer Durables ◽

Product Categories ◽

Simulation Based ◽

Out Of Sample ◽

Average Probability

AbstractWe analyze market baskets of individual households in two consumer durables categories (music, computer related products) by the multivariate logit (MVL) model, its finite mixture extension (FM-MVL) and the conditional restricted Boltzmann machine (CRBM). The CRBM attains a vastly better out-of-sample performance than MVL and FM-MVL models. Based on simulation-based likelihood ratio tests we prefer the CRBM to the FM-MVL model. To interpret hidden variables of conditional Boltzmann machines we look at their average probability differences between purchase and non-purchases of any sub-category across all baskets. To measure interdependences we compute cross effects between sub-categories for the best performing FM-MVL model and CRBM. In both product categories the CRBM indicates more or higher positive cross effects than the FM-MVL model. Finally, we suggest appropriate future research based on larger and more detailed data sets.

Download Full-text

Context-aware restricted Boltzmann machine meets collaborative filtering

Online Information Review ◽

10.1108/oir-02-2017-0069 ◽

2018 ◽

Vol 44 (2) ◽

pp. 455-476

Author(s):

Jingshuai Zhang ◽

Yuanxin Ouyang ◽

Weizhu Xie ◽

Wenge Rong ◽

Zhang Xiong

Keyword(s):

Collaborative Filtering ◽

Contextual Information ◽

Restricted Boltzmann Machine ◽

Combination Method ◽

Data Sets ◽

Context Aware ◽

Boltzmann Machine ◽

Content Type ◽

Recommendation Accuracy ◽

Hybrid Recommendation

Purpose The purpose of this paper is to propose an approach to incorporate contextual information into collaborative filtering (CF) based on the restricted Boltzmann machine (RBM) and deep belief networks (DBNs). Traditionally, neither the RBM nor its derivative model has been applied to modeling contextual information. In this work, the authors analyze the RBM and explore how to utilize a user’s occupation information to enhance recommendation accuracy. Design/methodology/approach The proposed approach is based on the RBM. The authors employ user occupation information as a context to design a context-aware RBM and stack the context-aware RBM to construct DBNs for recommendations. Findings The experiments on the MovieLens data sets show that the user occupation-aware RBM outperforms other CF models, and combinations of different context-aware models by mutual information can obtain better accuracy. Moreover, the context-aware DBNs model is superior to baseline methods, indicating that deep networks have more qualifications for extracting preference features. Originality/value To improve recommendation accuracy through modeling contextual information, the authors propose context-aware CF approaches based on the RBM. Additionally, the authors attempt to introduce hybrid weights based on information entropy to combine context-aware models. Furthermore, the authors stack the RBM to construct a context-aware multilayer network model. The results of the experiments not only convey that the context-aware RBM has potential in terms of contextual information but also demonstrate that the combination method, the hybrid recommendation and the multilayer neural network extension have significant benefits for the recommendation quality.

Download Full-text

A Hybrid Imputation Method Based on Denoising Restricted Boltzmann Machine

International Journal of Grid and High Performance Computing ◽

10.4018/ijghpc.2018040101 ◽

2018 ◽

Vol 10 (2) ◽

pp. 1-13

Author(s):

Jiang Xu ◽

Siqian Liu ◽

Zhikui Chen ◽

Yonglin Leng

Keyword(s):

Incomplete Data ◽

Imputation Method ◽

Restricted Boltzmann Machine ◽

Data Sets ◽

Data Imputation ◽

Boltzmann Machine ◽

Machine Model ◽

Robust Feature Extraction ◽

Effectiveness And Efficiency ◽

Occurrence Matrix

Data imputation is an important issue in data processing and analysis which has serious impact on the results of data mining and learning. Most of the existing algorithms are either utilizing whole data sets for imputation or only considering the correlation among records. Aiming at these problems, the article proposes a hybrid method to fill incomplete data. In order to reduce interference and computation, denoising restricted Boltzmann machine model is developed for robust feature extraction from incomplete data and clustering. Then, the article proposes partial-distance and co-occurrence matrix strategies to measure correlation between records and attributes, respectively. Finally, quantifiable correlation is converted to weights for imputation. Compared with different algorithms, the experimental results confirm the effectiveness and efficiency of the proposed method in data imputation.

Download Full-text