Russell and Norvig, Chapter 19: Learning in Neural and Belief Networks

19.1 How the Brain Works
- neuron (Fig19.1, p565)
- axon-dendrite connections (10-10^5) between neurons are called synapses
- synapses propagate electrochemical signals
- number, placement and strength of connections changes over time
  - learning ?
- conclude the brain (or "mysticism") causes the mind

19.2 Neural Networks
- unit [Fig19.4, p568]
  - input and output units
- activation functions [Fig19.5, p569]
- network structures
  - feed-forward
    - perceptron
    - multilayer network [Fig19.7, p572]
      - hidden units
      - one big enough hidden layer approximates any continuous function
  - recurrent (brain)
  - optimal structure ?

19.3 Perceptrons [Fig19.8, p574]
- learns linearly-separable functions [Fig19.9, p575]
- algorithm [Fig19.11, p577]
- update: Wj = Wj + alpha * Ij * Err
  - Wj = weight on link from input Ij
  - alpha = learning rate (0.1 - 0.3)
  - Err = difference between desired and observed output
- symbolic inputs
  - local encoding
    - one input unit per attribute
    - each attribute value assigned a real value (0.0-1.0)
  - distributed encoding
    - one unit for each attr/value pair
- comparison of perceptron to decision tree [Fig19.12, p578]

19.4 Multilayer Feed-Forward Networks
- backpropagation
  - generic network [Fig19.13, p579]
  - hidden to output
    - Wji = Wji + alpha * a_j * delta_i
      - delta_i = Err_i * g'(in_i)
  - input to hidden
    - Wkj = Wkj + alpha * Ik * delta_j
      - delta_j = g'(in_j) sum_i Wji * delta_i
- algorithm [Fig19.14, p581]
- gradient descent search in weight space [Fig19.16, p582]
- see comparison to belief networks at end

19.5 Applications of Neural Networks
- pronunciation of English words (NETtalk)
  - input: 7 char window over text, 26+3 (punctuation) inputs per char
  - hidden: 80
  - output: phonemes
  - 95% on training, 78% on testing
- handwritten character recognition (zip codes)
  - input: 16x16 for a digit
  - 3 hidden layers: 768, 192, 30 units (not fully connected)
  - output: 10 units, one per digit
  - 99% on testing
  - hardware version in use
- driving
  - autonomous land vehicle in a neural network (alvinn)
  - input: 30x32 pixel image
  - hidden: 5, fully connected
  - output: 20 units for each possible steering direction
  - up to 90 miles, up to 70 mph
  - extensive learning for each road type/condition

19.6 Bayesian Methods for Learning Belief Networks
- bayesian learning
  - use hypotheses as intermediary between data and predictions
  - given data D and competing hypotheses Hi predicting X
    - P(X|D) = P(X|Hi)*P(Hi|D) is best choice (distribution)
      - but, P(Hi|D) is usually intractable
    - find Hi maximizing P(Hi|D)
      - maximum a posteriori (MAP) hypothesis
      - P(X|D) ~ P(X|Hmap)*P(Hmap|D)
      - applying Bayes rule
        - P(Hi|D) = P(D|Hi)*P(Hi) / P(D)
          - P(D) fixed
          - choose P(Hi) as uniform or Ockham bias
            - uniform: P(D|Hi) maximum liklihood (ML) hypothesis
- belief network learning
  - types
    - known structure, fully observable
      - learn CPTs
    - unknown structure, fully observable
      - learn network topology (model-based)
      - then know structure problem
    - known structure, hidden variables
      - similar to neural network learning
    - unknown structure, hidden variables (?)
  - adaptive probabilistic networks
    - given @P(D)/@CPT, use gradient descent (NN) learning
      - (@P(D_j)/@w_i)/P(D_j) = P(x_i,u_i | D_j) / w_i
        - where w_i = CPT_i and D_j are the examples
  - belief networks vs neural networks
    - BN representation semantically meaningful
    - BN representation local, NN distributed
    - continuous variables handled better by NN, but no relations
    - BNs can be automatically created
    - NNs have fast inference at the expense of limited training
      - each epoch takes |examples|*|weights|
        - exponential number of epochs possible
    - BNs have slow inference, but more expressive representation
    - no specific inputs and outputs in BNs
    - easier to include prior knowledge into BNs
    - NNs more sensitive to noise