Sequential Learning with Dependency Nets

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Sequential Learning with Dependency Nets

• William W. Cohen
• 2/22

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Announcements

• Critiques for the week due Tuesday
• Email to Vitor and me
• (Critiques showing evidence of classroom/classwork
  multiplexing are considered really really late)
• Confusion about number of student presentations
  for today (1,2?)
• Please dont make changes after I copy over the
  presentations to the web page
• Do we need a system?
• Office hours are no-appointment-necessary
• Appointments are via sharonw_at_cs
• Preferences on later topics?
• Relation extraction
• Semantic role labeling
• Semi-supervised IE IE on the web and large
  corpora bootstrapping

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CRFs the good, the bad, and the cumbersome

• Good points
• Global optimization of weight vector that guides
  decision making
• Trade off decisions made at different points in
  sequence
• Worries
• Cost (of training)
• Complexity (do we need all this math?)
• Amount of context
• Matrix for normalizer is Y Y, so high-order
  models for many classes get expensive fast.
• Strong commitment to maxent-style learning
• Loglinear models are nice, but nothing is always
  best.

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Dependency Nets
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• Proposed solution
• parents of node are the Markov blanket
• like undirected Markov net
• capture all correlational associations
• one conditional probability for each node X,
  namely P(Xparents of X)
• like directed Bayes netno messy clique
  potentials

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Example bidirectional chains


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DN chains


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• How do we do inference? Iteratively
• Pick values for Y1, Y2, at random
• Pick some j, and compute
• Set new value of Yj according to this
• Go back to (2)

Current values
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This an MCMC process
Transition probability
General case


Markov Chain Monte Carlo a randomized process
that doesnt depend on previous ys changes y(t)
to y(t1)
One particular run

• How do we do inference? Iteratively
• Pick values for Y1, Y2, at random y(0)
• Pick some j, and compute
• Set new value of Yj according to this y(1)
• Go back to (2) and repeat to get y(1) , y(2) , ,
  y(t) ,

Current values (t)
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This an MCMC process


Claim suppose Y(t) is drawn from some
distribution D such that
Then Y(t1) is also drawn from D (i.e., the
random flip doesnt move us away from D
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This an MCMC process


Burn-in
Claim if you wait long enough then for some t,
Y(t) will be drawn from some distribution D such
that
under certain reasonable conditions (e.g., graph
of potential edges is connected, ). So D is a
sink.
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This an MCMC process


averaged for prediction
burn-in - discarded

• An algorithm
• Run the MCMC chain for a long time t, and hope
  that Y(t) will be drawn from the target
  distribution D.
• Run the MCMC chain for a while longer and save
  sample S Y(t) , Y(t1) , , Y(tm)
• Use S to answer any probabilistic queries like
  Pr(YjX)

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More on MCMC

• This particular process is Gibbs sampling
• Transition probabilities are defined by sampling
  from the posterior of one variable Yj given the
  others.
• MCMC is very general-purpose inference scheme
  (and sometimes very slow)
• On the plus side, learning is relatively cheap,
  since theres no inference involved (!)
• A dependency net is closely related to a Markov
  random field learned by maximizing
  pseudo-likelihood
• Identical?
• Statistical relation learning community has some
  proponents of this approach
• Pedro Domingos, David Jensen,
• A big advantage is the generality of the approach
• Sparse learners (eg L1 regularized maxent,
  decision trees, ) can be used to infer Markov
  blanket (NIPS 2006)

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Examples


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Examples
POS?


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Examples


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Dependency nets

• The bad and the ugly
• Inference is less efficient MCMC sampling
• Cant reconstruct probability via chain rule
• Networks might be inconsistent
• ie local P(xpa(x))s dont define a pdf
• Exactly equal, representationally, to normal
  undirected Markov nets

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Dependency nets

• The good
• Learning is simple and elegant (if you know each
  nodes Markov blanket) just learn a
  probabilistic classifier for P(Xpa(X)) for each
  node X.
• (You might not learn a consistent model, but
  youll probably learn a reasonably good one.)
• Inference can be speeded up substantially over
  naïve Gibbs sampling.

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Dependency nets

• Learning is simple and elegant (if you know each
  nodes Markov blanket) just learn a
  probabilistic classifier for P(Xpa(X)) for each
  node X.

Pr(y1x,y2)
Pr(y2x,y1,y2)
Pr(y3x,y2,y4)
Pr(y4x,y3)
y1
y2
y3
y4
Learning is local, but inference is not, and need
not be unidirectional
x
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Toutanova, Klein, Manning, Singer

• Dependency nets for POS tagging vs CMMs.
• Maxent is used for local conditional model.
• Goals
• An easy-to-train bidirectional model
• A really good POS tagger

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Toutanova et al

• Dont use Gibbs sampling for inference instead
  use a Viterbi variant (which is not guaranteed to
  produce the ML sequence)

D 11, 11, 11, 12, 21, 33 ML state
11 P(a1b1)P(b1a1) lt 1 P(a3b3)P(b3a3)
1
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Results with model
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Results with model
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Results with model
Best model includes some special unknown-word
features, including a crude company-name
detector
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Results with model
Final test-set results
MXPost 47.6, 96.4, 86.2 CRF 95.7, 76.4
(Ratnaparki)
(Lafferty et al ICML2001)
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Other comments

• Smoothing (quadratic regularization, aka Gaussian
  prior) is importantit avoids overfitting effects
  reported elsewhere