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| data_mining:neural_network:model_combination [2017/04/01 15:20] – [Approximating full Bayesian learning in a NN] phreazer | data_mining:neural_network:model_combination [2017/08/19 22:11] – phreazer | ||
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| * Expensive, but works much better than ML learning, when posteriror is vague or multimodal (data is scarce). | * Expensive, but works much better than ML learning, when posteriror is vague or multimodal (data is scarce). | ||
| + | Monte Carlo method | ||
| Idea: Might be good enough to sample weight vectors according to their posterior probabilities. | Idea: Might be good enough to sample weight vectors according to their posterior probabilities. | ||
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| $p(y_{\text{test}} | \text{input}_\text{test}, | $p(y_{\text{test}} | \text{input}_\text{test}, | ||
| - | Monte Carlo method | + | Sample weight vectors $p(W_i|D)$. |
| + | |||
| + | In Backpropagation, | ||
| + | |||
| + | With sampling: Add some gaussion noise to weight vector, after each update. | ||
| + | |||
| + | Markov Chain Monte Carlo: | ||
| + | |||
| + | If we use just the right amount of noise, and if we let thei weight vector wander around for long enough before we take a sample, we will get an ubiased sample form the true posterior over weight vectors. | ||
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| + | More complicated and effective methods than MCMC method: Don't need to wander the space long. | ||
| - | Random weights | + | If we compute gradient of cost function on a **random mini-batch**, |