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Exploring Neural Networks and Bayesian Learning in Machine Learning

Dive into neural networks and Bayesian learning in machine learning, understanding brain function, neural structure, and learning mechanisms. Explore the power of neural networks compared to computers.

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Exploring Neural Networks and Bayesian Learning in Machine Learning

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  1. CMSC 671Fall 2001 Class #25-26 – Tuesday, November 27 / Thursday, November 29

  2. Today’s class • Neural networks • Bayesian learning

  3. Machine Learning: Neural and Bayesian Chapter 19 Some material adapted from lecture notes by Lise Getoor and Ron Parr

  4. Neural function • Brain function (thought) occurs as the result of the firing of neurons • Neurons connect to each other through synapses, which propagate action potential (electrical impulses) by releasing neurotransmitters • Synapses can be excitatory (potential-increasing) or inhibitory (potential-decreasing), and have varying activation thresholds • Learning occurs as a result of the synapses’ plasticicity: They exhibit long-term changes in connection strength • There are about 1011 neurons and about 1014 synapses in the human brain

  5. Biology of a neuron

  6. Brain structure • Different areas of the brain have different functions • Some areas seem to have the same function in all humans (e.g., Broca’s region); the overall layout is generally consistent • Some areas are more plastic, and vary in their function; also, the lower-level structure and function vary greatly • We don’t know how different functions are “assigned” or acquired • Partly the result of the physical layout / connection to inputs (sensors) and outputs (effectors) • Partly the result of experience (learning) • We really don’t understand how this neural structure leads to what we perceive as “consciousness” or “thought” • Our neural networks are not nearly as complex or intricate as the actual brain structure

  7. Comparison of computing power • Computers are way faster than neurons… • But there are a lot more neurons than we can reasonably model in modern digital computers, and they all fire in parallel • Neural networks are designed to be massively parallel • The brain is effectively a billion times faster

  8. Neural networks • Neural networks are made up of nodes or units, connected by links • Each link has an associated weight and activation level • Each node has an input function (typically summing over weighted inputs), an activation function, and an output

  9. Layered feed-forward network Output units Hidden units Input units

  10. Neural unit

  11. “Executing” neural networks • Input units are set by some exterior function (think of these as sensors), which causes their output links to be activated at the specified level • Working forward through the network, the input function of each unit is applied to compute the input value • Usually this is just the weighted sum of the activation on the links feeding into this node • The activation function transforms this input function into a final value • Typically this is a nonlinear function, often a sigmoid function corresponding to the “threshold” of that node

  12. Learning neural networks • Backpropagation • Cascade correlation: adding hidden units Take it away, Chih-Yun! Next up: Sohel

  13. B E A C Learning Bayesian networks • Given training set • Find B that best matches D • model selection • parameter estimation Inducer Data D

  14. Parameter estimation • Assume known structure • Goal: estimate BN parameters q • entries in local probability models, P(X | Parents(X)) • A parameterization q is good if it is likely to generate the observed data: • Maximum Likelihood Estimation (MLE) Principle: Choose q* so as to maximize L i.i.d. samples

  15. Parameter estimation in BNs • The likelihood decomposes according to the structure of the network → we get a separate estimation task for each parameter • The MLE (maximum likelihood estimate) solution: • for each value x of a node X • and each instantiation u of Parents(X) • Just need to collect the counts for every combination of parents and children observed in the data • MLE is equivalent to an assumption of a uniform prior over parameter values sufficient statistics

  16. Sufficient statistics: Example Moon-phase • Why are the counts sufficient? Light-level Earthquake Burglary Alarm

  17. Model selection Goal: Select the best network structure, given the data Input: • Training data • Scoring function Output: • A network that maximizes the score

  18. Same key property: Decomposability Score(structure) = Si Score(family of Xi) Structure selection: Scoring • Bayesian: prior over parameters and structure • get balance between model complexity and fit to data as a byproduct • Score (G:D) = log P(G|D)  log [P(D|G) P(G)] • Marginal likelihood just comes from our parameter estimates • Prior on structure can be any measure we want; typically a function of the network complexity Marginal likelihood Prior

  19. DeleteEA AddEC B E Δscore(C) Δscore(A) A B E C A C B E B E A A ReverseEA Δscore(A) C C Heuristic search

  20. DeleteEA DeleteEA AddEC B E Δscore(C) Δscore(A) Δscore(A) A B E B E C A A C C B E A To recompute scores, only need to re-score families that changed in the last move ReverseEA Δscore(A) C Exploiting decomposability

  21. Variations on a theme • Known structure, fully observable: only need to do parameter estimation • Unknown structure, fully observable: do heuristic search through structure space, then parameter estimation • Known structure, missing values: use expectation maximization (EM) to estimate parameters • Known structure, hidden variables: apply adaptive probabilistic network (APN) techniques • Unknown structure, hidden variables: too hard to solve!

  22. Handling missing data • Suppose that in some cases, we observe earthquake, alarm, light-level, and moon-phase, but not burglary • Should we throw that data away?? • Idea: Guess the missing valuesbased on the other data Moon-phase Light-level Earthquake Burglary Alarm

  23. EM (expectation maximization) • Guess probabilities for nodes with missing values (e.g., based on other observations) • Compute the probability distribution over the missing values, given our guess • Update the probabilities based on the guessed values • Repeat until convergence

  24. EM example • Suppose we have observed Earthquake and Alarm but not Burglary for an observation on November 27 • We estimate the CPTs based on the rest of the data • We then estimate P(Burglary) for November 27 from those CPTs • Now we recompute the CPTs as if that estimated value had been observed • Repeat until convergence! Earthquake Burglary Alarm

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