CMSC 671 Fall 2001

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CMSC 671Fall 2001

• Class 25-26 Tuesday, November 27 / Thursday,
  November 29

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Todays class

• Neural networks
• Bayesian learning

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Machine Learning Neural and Bayesian

• Chapter 19

Some material adapted from lecture notes by Lise
Getoor and Ron Parr
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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

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Biology of a neuron
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Brain structure

• Different areas of the brain have different
  functions
• Some areas seem to have the same function in all
  humans (e.g., Brocas 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 dont 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 dont 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

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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

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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

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Layered feed-forward network
Output units
Hidden units
Input units
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Neural unit
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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

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Learning neural networks

• Backpropagation
• Cascade correlation adding hidden units

Take it away, Chih-Yun!
Next up Sohel
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Learning Bayesian networks

• Given training set
• Find B that best matches D
• model selection
• parameter estimation

Inducer
Data D
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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
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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
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Sufficient statistics Example
Moon-phase

• Why are the counts sufficient?

Light-level
Earthquake
Burglary
Alarm
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Model selection

• Goal Select the best network structure, given
  the data
• Input
• Training data
• Scoring function
• Output
• A network that maximizes the score

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Structure selection Scoring

• Bayesian prior over parameters and structure
• get balance between model complexity and fit to
  data as a byproduct
• Score (GD) log P(GD) ? log P(DG) 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
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Heuristic search
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Exploiting decomposability
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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!

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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
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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

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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