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Additional NN Models

Additional NN Models. Reinforcement learning (RL) Basic ideas: Supervised learning: (delta rule, BP) Samples (x, f(x)) to learn function f(.) precise error can be determined and is used to drive the learning. Unsupervised learning: (competitive, BM)

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Additional NN Models

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  1. Additional NN Models Reinforcement learning (RL) • Basic ideas: • Supervised learning: (delta rule, BP) • Samples (x, f(x)) to learn function f(.) • precise error can be determined and is used to drive the learning. • Unsupervised learning: (competitive, BM) • no target/desired output provided to help learning, • learning is self-organized/clustering • reinforcement learning: in between the two • no target output for input vectors in training samples • a judge/critic will evaluate the output good: reward signal (+1) bad: penalty signal (-1)

  2. RL exists in many places • Originated from psychology( training animal) • Machine learning community, different theories and algorithms major difficulty: credit/blame distribution chess playing: W/L (multi-step) soccer playing: W/L(multi-player) • In many applications, it is much easier to determine good/bad, right/wrong, acceptable/unacceptable than to provide precise correct answer/error. • It is up to the learning process to improve the system’s performance based on the critic’s signal.

  3. Principle of RL • Let r = +1 reword (good output) r = -1 penalty (bad output) • If r = +1, the system is encouraged to continue what it is doing If r = -1, the system is encouraged not to do what it is doing. • Need to search for better output • because r = -1 does not indicate what the good output should be. • common method is “random search”

  4. critic z(k) y(k) x(k) • ARP: the associative reword-and-penalty algorithm for NN (Barton and Anandan, 1985) • Architecture input: x(k) output: y(k) stochastic units: z(k) for random search

  5. Random search by stochastic units zi or let zi obey a continuous probability distribution function. or let is a random noise, obeys certain distribution. Key: z is not a deterministic function of x, this gives z a chance to be a good output. • Prepare desired output (temporary)

  6. Compute the errors at z layer where E(z(k)) is the expected value of z(k) because z is a random variable How to compute E(z(k)) • take average of z over a period of time • compute from the distribution, if possible • if logistic sigmoid function is used, • Training: BP or other method to minimize the error

  7. Recurrent BP • Recurrent networks: network with feedback links • State (output) of the network evolves along the time. • may or may not have hidden nodes. • may or may not stabilize when • how to learn w so that an initial state (input) will lead to • a stable state with the desired output. 2. Unfolding • for any recurrent network with finite evolution time, there is an equivalent feedforward network. • problems: too many repetitions too many layers when the network need a long time to

  8. reach stable state. standard BP needs to be relized to hard duplicate weights. 3. Recurrent BP (1987) system: assume at least one fixed point exists for the system with the given initial state when a fixed point is reduced can be obtained. error

  9. take the gradient descent approach to minimize E by update W direct derivation will have

  10. Computing is very time consuming. Pineda and Almeida/s proposal: can be computed by another recurrent net with identical structure of the original RN direction of each are is reversed( transposed network) in the original network: weight for node j to i: Wij in the transposed network, weight for node j to i:

  11. Weight-update procedure for RBP with a given input and its desired output • Relax the original network to a fixed point • Compute error • Relax the transposed network to a fixed point • Update the weight of the original network

  12. The complete learning algorithm incremental/sequential W is updated by the preseting of each learning pair using the weight-update procedure. to ensure the dearned network is stable, learning rate must be small(much smaller than the rate for standard BP learning) time consuming: two relaxation processes are involved for each step of weight update better performance than BP in some applications

  13. (III) Probabilistic Neural Networks 1. Purpose: classify a given input pattern x into one of the pre-defined classes by Bayesian decision rule. Suppose there are k predefined classes s1, …sk P(si): prior probability of class si P(x|si): conditional probability of class si P(x): probability of x P(si|x): posterior probability of si, given x example: S=s1Us2Us3….Usk, the set of all patients si: the set of all patients having disease I x: a description of a patient(manifestation)

  14. P(x|si): prob. One with disease I will have description x P(si|x): prob. one with description x will have disease i. by Bayes’ theorem:

  15. 2. PNN architecture: feed forward with 2 hidden layers learning is not used to minimize error but to obtain P(x|si) 3. Learning assumption: P(si) are known, P(x|si) obey Gaussian distr. estimate

  16. 4.Comments: (1) Bayesian classification by (2) fast classification( especially if implemented in parallel machine). (3) fast learning (4) trade nodes for time( not good with large training samaples/clusters).

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