Boltzmann machines

E7922

energy-based model probabilistic graphical model stochastic neural network architecture unsupervised learning model

Boltzmann machines are stochastic recurrent neural networks used for learning complex probability distributions, foundational in unsupervised learning and energy-based models.

Aliases (9)

restricted Boltzmann machines ×2
Boltzmann machine ×1
Boltzmann machine learning ×1
Deep Boltzmann machines ×1
Learning and Relearning in Boltzmann Machines ×1
Restricted Boltzmann machines ×1
deep Boltzmann machines ×1
deep belief networks ×1
restricted Boltzmann machine ×1

Statements (48)

Predicate	Object
instanceOf	energy-based model → probabilistic graphical model → stochastic neural network architecture → unsupervised learning model →
approximationMethod	mean-field approximation → variational inference →
basedOn	Boltzmann distribution → statistical mechanics →
definesProbability	P(s) = exp(-E(s))/Z →
difficulty	partition function computation is exponential in number of units →
hasComponent	bias parameters → hidden units → visible units →
hasConnectionType	fully connected between all units in general form →
hasEnergyFunctionForm	E(v,h) = -∑_i a_i v_i -∑_j b_j h_j -∑_{i,j} v_i w_{ij} h_j -∑_{i<k} v_i u_{ik} v_k -∑_{j<l} h_j v_{jl} h_l →
hasLearningRule	contrastive divergence approximation → persistent contrastive divergence → stochastic gradient descent on log-likelihood →
hasNetworkType	recurrent neural network →
hasPartitionFunction	Z = ∑_s exp(-E(s)) →
hasProperty	Gibbs distribution over states → Markov random field structure → asynchronous stochastic updates → binary-valued units → converges to thermal equilibrium distribution → energy function → intractable exact learning for large networks → stochastic units → symmetrical weights → undirected connections →
hasSamplingMethod	Gibbs sampling → Markov chain Monte Carlo →
inspired	Deep Boltzmann machines → Deep belief networks → Restricted Boltzmann machines →
introducedBy	Geoffrey Hinton → Terrence Sejnowski →
introducedInPublication	Learning and Relearning in Boltzmann Machines →
introducedInYear	1985 →
relatedTo	Hopfield networks → Ising models →
trainingObjective	maximize data log-likelihood →
usedFor	associative memory → combinatorial optimization → density estimation → modeling complex probability distributions → representation learning → unsupervised feature learning →

Referenced by (12)

Subject (surface form when different)	Predicate
Geoffrey Hinton → Geoffrey Hinton ("restricted Boltzmann machines") → Geoffrey Hinton ("deep belief networks") → Ruslan Salakhutdinov ("restricted Boltzmann machines") → Terrence Sejnowski ("Boltzmann machine learning") →	knownFor
Boltzmann machines ("Restricted Boltzmann machines") → Boltzmann machines ("Deep Boltzmann machines") →	inspired
A fast learning algorithm for deep belief nets → Deep belief networks ("deep Boltzmann machines") →	relatedTo
Boltzmann machines ("Learning and Relearning in Boltzmann Machines") →	introducedInPublication
Hopfield network ("Boltzmann machine") →	isRelatedTo
A fast learning algorithm for deep belief nets ("restricted Boltzmann machine") →	usesModel