Definition
A Boltzmann machine is a network of symmetrically connected, neuron-like units that make stochastic decisions about whether to be on or off. Boltzmann machines have a simple learning algorithm (Hinton and Sejnowski 1983) that allows them to discover interesting features that represent complex regularities in the training data. The learning algorithm is very slow in networks with many layers of feature detectors, but it is fast in “restricted Boltzmann machines” that have a single layer of feature detectors. Many hidden layers can be learned efficiently by composing restricted Boltzmann machines, using the feature activations of one as the training data for the next.
Boltzmann machines are used to solve two quite different computational problems. For a search problem, the weights on the connections are fixed and are used to represent a cost function. The stochastic dynamics of a Boltzmann machine then allow it to sample binary state vectors that have low values of the cost...
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Ackley D, Hinton G, Sejnowski T (1985) A Learning algorithm for Boltzmann machines. Cognit Sci 9(1):147–169
Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6(6):721–741
Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci U S A 79:2554–2558
Hinton GE (2002) Training products of experts by minimizing contrastive divergence. Neural Comput 14(8):1711–1800
Hinton GE, Osindero S, Teh YW (2006) A fast learning algorithm for deep belief nets. Neural Comput 18:1527–1554
Hinton GE, Salakhutdinov RR (2006) Reducing the dimensionality of data with neural networks. Science 313:504–507
Hinton GE, Sejnowski TJ (1983) Optimal perceptual inference. In: Proceedings of the IEEE conference on computer vision and pattern recognition, Washington, DC, pp 448–453
Jordan MI (1998) Learning in graphical models. MIT, Cambridge
Kirkpatrick S, Gelatt DD, Vecci MP (1983) Optimization by simulated annealing. Science 220(4598):671–680
Lafferty J, McCallum A, Pereira F (2001) Conditional random fields: Probabilistic models for segmenting and labeling sequence data. In: Proceedings of the 18th international conference on machine learning, Williamstown, pp 282–289. Morgan Kaufmann, San Francisco
Peterson C, Anderson JR (1987) A mean field theory learning algorithm for neural networks. Complex Syst 1(5):995–1019
Sejnowski TJ (1986) Higher-order Boltzmann machines. AIP Conf Proc 151(1):398–403
Smolensky P (1986) Information processing in dynamical systems: foundations of harmony theory. In: Rumelhart DE, McClelland JL (eds) Parallel distributed processing. Foundations, vol 1. MIT, Cambridge, pp 194–281 Press.
Welling M, Rosen-Zvi M, Hinton GE (2005) Exponential family harmoniums with an application to information retrieval. In: Lawrence K. Saul, Yair Weiss and Leon Bottou (eds) Advances in neural information processing systems, vol 17. MIT, Cambridge, pp 1481–1488
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Hinton, G. (2017). Boltzmann Machines. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7687-1_31
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