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data_mining:neural_network:hopfield [2017/04/09 11:03] – [Improve search with stochastic units] phreazer | data_mining:neural_network:hopfield [2017/04/09 11:10] (current) – [Boltzman machine] phreazer | ||
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$p(s_i=1) = \frac{1}{1+e^{-\Delta E_i/T}}$ | $p(s_i=1) = \frac{1}{1+e^{-\Delta E_i/T}}$ | ||
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+ | ===== Thermal equilibrium ===== | ||
+ | Thermal equi. at temperature of 1 | ||
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+ | Reaching thermal equilibrium is difficult concept. Probability distribution over configurations settles down to statonary distribution. | ||
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+ | Intuitively: | ||
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+ | Approaching equilibrium: | ||
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+ | * Start with any distribution over all identical systems | ||
+ | * Apply stochastic update rule, to pick next configuration for each individual system | ||
+ | * May reach situation where fraction of systems in each configuration remains constant. | ||
+ | * This stationary distribution is called thermal equilibrium. | ||
+ | * Any given system keeps changing its configuration, | ||
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+ | ===== Boltzman machine ===== | ||
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+ | Given: Training set of binary vectors. Fit model that will assign a probability to every possible binary vector. | ||
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+ | Useful for deciding if other binary vectors come from some distribution (e.g. to detect unusual behavious). |