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--- data_mining:neural_network:belief_nets [2017/04/29 10:24] – phreazer
+++ data_mining:neural_network:belief_nets [2017/07/30 16:05] (current) – [Structure] phreazer
@@ Line 56: / Line 56: @@
 ===== Learning layers of features by stacking RBMs =====
+RBM can be learned fairly efficient. Stacking RBMs can learn lots of features. By stacking you get an indefinitely deep belief net.
+Combine 2 RBMs to make a DBN.
+v <=W_1=> h_1 copy binary state for each v: h_1 <=W_2=>h_2.
+==== Compose two RBM models ====
+v <=W_1= h_1 <=W_2=> h_2
+Bottom layer is unidirectional. => Not a Boltzman machine. It's a deep belief net.
+==== 3 layers ====
+data <=W_1= h_1 <=W_2= h_2 <=W_3=> h_3
+Generate data:
+  * Equilibrium sample from **top-level** RBM (h_2,h_3), by Gibbs sampling for a long time. Defines prior distr. of h_2.
+  * Top-Down pass from h_2 to get states for other layers.
+=== Averaging factorial distributions ===
+By averaging 2 fact. distr. you don't get a fact. distr. => Mixture distr.
+In RBM the posterior over 4 hidden units is factorial for each visible vector
+  * Posterior for v1: 0.9, 0.9, 0.1, 0.1
+  * Posterior for v2: 0.1, 0.1, 0.9, 0.9
+  * Aggregated: 0.5, 0.5, 0.5, 0.5
+Consider binary vec (1,1,0,0)
+  * Posterior for v1 p(1,1,0,0) = 0.9^4 = 0.43
+  * Posterior for v2 p(1,1,0,0) = 0.1^4 = 0.0001
+  * Aggregated posterior p(1,1,0,0) = 0.215
+      * Factorial would be p = 0.5^4
+==== Why does learning work? ====
+Weights of bottom level RBM:
+p(v|h); p(h|v); p(v,h); p(v); p(h);
+Can express RBM model as $p(v) = \sum_h p(h) p(v|h)$
+If leave $p(v|h)$ alon, but improve $p(h)$, we improve $p(v)$. To improve $p(h)$ we need it be a **better model than $p(h;W)$** of the **aggregated** posterior distr. over hidden vectors produced by applying W transposed to the data.
+==== Constrastive version of wake-sleep algorithm ====
+==== Discriminative fine-tuning for DBNs ====
+  * First learn one layer at a time by stacking RBMs.
+  * Use this pre-training (found initial weights), which can be fine-tuned by a local search procedure.
+  * Perviously: Constrastive wake-sleep fine-tuning the model to be better at generation.
+  * Now: Use Backprop to fine-tune the model to be better at discrimination.
+Backprop works better with greedy pre-training:
+* Works wll ans scales to big networks, esp. when we have locality in each layer.
+* We do not start backpropagation until we have sensible feature detectors.
+    * Initial gradients are sensibel, backprop only needs to perform a local search from a sensible start point.
+Fine-tuning only modifies features slightly to get category boundaries right (does not need to discover new features).
+Objection: Many features are learned that are useless for a particular discrimination.
+Example model (MNIST): Add 10-way softmax at the top and do backprop.
+More layers => lower error with pretraining.
+Solutions are qualitative different.
+==== Model real-valued data with RBMS ====
+Mean-field logistic units cannot represent precise inetermediate values (e.g. pixel intensity in image).
+Model pixels as Gaussian variables. Alternating Gibbs sampling, with lower learning rate.
+Parabolic containment function. (keep visible unit close to b_i).
+Energy-gradient.
+Stepped sigmoid units. Many copies of a stochastic binary unist. All copies have same weiths and bias, b, but they have different fixed offsets to the bias (b-0.5, b-1.5, ...).
+==== Structure ====
+Autoencoder, then feed forward NN