1. Over fitting
&
Transformation Based Learning
CS 371: Spring 2012

2. Machine Learning
• Machines can learn from examples
– Learning modifies the agent's decision mechanisms to improve
performance
• Given training data, machines analyze the data, and learn
rules which generalize to new examples
– Can be sub-symbolic (rule may be a mathematical function)
– Or it can be symbolic (rules are in a representation that is similar
to representation used for hand-coded rules)
• In general, machine learning approaches allow for more tuning
to the needs of a corpus, and can be reused across corpora

3. Training data example
• Inductive learning
Empirical error function:
E(h) = x distance[h(x; ) , f]
Empirical learning = finding h(x), or h(x; ) that minimizes E(h)
• Note an implicit assumption:
– For any set of attribute values there is a unique target value
– This in effect assumes a “no-noise” mapping from inputs to targets
• This is often not true in practice (e.g., in medicine).

4. Learning Boolean Functions
• Given examples of the function, can we learn the function?
• 2 to the power of 2d different Boolean functions can be defined on d
attributes
– This is the size of our hypothesis space
• Observations:
– Huge hypothesis spaces –> directly searching over all functions is impossible
– Given a small data (n pairs) our learning problem may be underconstrained
• Ockham’s razor: if multiple candidate functions all explain the data
equally well, pick the simplest explanation (least complex function)
• Constrain our search to classes of Boolean functions, e.g.,
– decision trees

5. Decision Tree Learning
• Constrain h(..) to be a decision tree

6. Pseudocode for Decision tree learning

7. Major issues
Q1: Choosing best attribute: what quality measure to use?
Q2: Handling training data with missing attribute values
Q3: Handling training data with noise, irrelevant attributes
- Determining when to stop splitting: avoid overfitting

8. Major issues
Q1: Choosing best attribute: different quality measures.
Information gain, gain ratio …
Q2: Handling training data with missing attribute values: blank
value, most common value, or fractional count
Q3: Handling training data with noise, irrelevant attributes:
- Determining when to stop splitting: ????

9. Assessing Performance
Training data performance is typically optimistic
e.g., error rate on training data
Reasons?
- classifier may not have enough data to fully learn the concept (but
on training data we don’t know this)
- for noisy data, the classifier may overfit the training data
In practice we want to assess performance “out of sample”
how well will the classifier do on new unseen data? This is the
true test of what we have learned (just like a classroom)
With large data sets we can partition our data into 2 subsets, train and test
- build a model on the training data
- assess performance on the test data

10. Example of Test Performance
Restaurant problem
- simulate 100 data sets of different sizes
- train on this data, and assess performance on an independent test set
- learning curve = plotting accuracy as a function of training set size
- typical “diminishing returns” effect

11. Example

12. Example

13. Example

14. Example

15. Example

16. How Overfitting affects Prediction
Predictive
Error
Error on Training Data
Model Complexity

17. How Overfitting affects Prediction
Predictive
Error
Error on Test Data
Error on Training Data
Model Complexity

18. How Overfitting affects Prediction
Underfitting Overfitting
Predictive
Error
Error on Test Data
Error on Training Data
Model Complexity
Ideal Range
for Model Complexity

19. Training and Validation Data
Full Data Set
Idea: train each
Training Data model on the
“training data”
and then test
each model’s
Validation Data accuracy on
the validation data

20. The v-fold Cross-Validation Method
• Why just choose one particular 90/10 “split” of the data?
– In principle we could do this multiple times
• “v-fold Cross-Validation” (e.g., v=10)
– randomly partition our full data set into v disjoint subsets (each
roughly of size n/v, n = total number of training data points)
• for i = 1:10 (here v = 10)
– train on 90% of data,
– Acc(i) = accuracy on other 10%
• end
• Cross-Validation-Accuracy = 1/v i Acc(i)
– choose the method with the highest cross-validation accuracy
– common values for v are 5 and 10
– Can also do “leave-one-out” where v = n

21. Disjoint Validation Data Sets
Full Data Set
Validation Data
Training Data
1st partition

22. Disjoint Validation Data Sets
Full Data Set
Validation Data
Validation
Data
Training Data
1st partition 2nd partition

23. More on Cross-Validation
• Notes
– cross-validation generates an approximate estimate of how well
the learned model will do on “unseen” data
– by averaging over different partitions it is more robust than just a
single train/validate partition of the data
– “v-fold” cross-validation is a generalization
• partition data into disjoint validation subsets of size n/v
• train, validate, and average over the v partitions
• e.g., v=10 is commonly used
– v-fold cross-validation is approximately v times computationally
more expensive than just fitting a model to all of the data

24. Lets look at an other symbolic learner …

25. Problem Domain: POS Tagging
What is text tagging?
– Some sort of markup, enabling understanding of
language.
– Can be word tags:
He will race/VERB the car.
He will not race/VERB the truck.
When will the race/NOUN end?

26. Why do we care?
Sometimes, meaning changes a lot
– Transcribed speech lacks clear punctuation:
“I called, John and Mary are there.”
→ I called John and Mary are there.
(I called John) and (Mary are there.) ??
I called ((John and Mary) are there.)
– We can tell, but can a computer?
Here, needs to know about verb forms and collections
– Can be important!
Quick! Wrap the bandage on the table around her leg!
Imagine a robotic medical assistant with this one . . .

27. Where is this used?
• Any natural language task!
– Translators: word-by-word translation does not always work,
sentences need re-arranging.
– It can help with OCR or voice transcription
“I need to writer. I'm a good write her.”
“to writer”?? “a good write”?
→ “I need to write her. I'm a good writer.

28. Some terms
Corpus
– Big body of text, annotated (expert-tagged) or not
Dictionary
– List of known words, and all possible parts of speech
Lexical/Morphological vs. Contextual
– Is it a word property (spelling) or surroundings (neighboring
parts of speech)?
Semantics vs Syntax
– Meaning (definition) vs. Structure (phrases, parsing)
Tokenizer
– Separates text into words or other sized blocks (idioms,
phrases . . . )
Disambiguator
– Extra pass to reduce possible tags to a single one.

29. Some problems we face
Classification challenges:
– Large number of classes:
English POS: varying tagsets, 48 to 195 tags
– Often ambiguous, varying with use/context
POS: There must be a way to go there; I know a
person from there – see that guy there?
(pron., adv., n.)
– Varying number of relevant features
Spelling, position, surrounding words, paragraph
position, article topic . . .

30. TBL: A Symbolic Learning Method
• A method called error-driven Transformation-Based Learning
(TBL) (Brill algorithm) can be used for symbolic learning
– The rules (actually, a sequence of rules) are learned from an
annotated corpus
– Performs about as accurately as other statistical approaches
• Can have better treatment of context compared to HMMs (as
we’ll see)
– rules which use the next (or previous) POS
• HMMs just use P(Ti| Ti-1) or P(Ti| Ti-2 Ti-1)
– rules which use the previous (next) word
• HMMs just use P(Wi|Ti)

31. What does it do?
Transformation-Based Error-Driven Learning:
– First, a dictionary tags every word with its most
common POS. So, “run” is tagged as a verb in both:
“The run lasted 30 minutes” and “We run 3 miles every day”
– Unknown capitalized words are assumed to be proper
nouns, and remaining unknown words are assigned the most
common tag for their three-letter ending.
→ “blahblahous” is probably an adjective.
– Finally, the tags are updated by a set of “patches,” with the
form “Change tag a to b if:”
– The word is in context C (eg, the pattern of surrounding tags)
– The word or one in a region R has lexical property P (eg,
capitalization)

32. Rule Templates
• Brill’s method learns transformations which fit different
templates
– Template: Change tag X to tag Y when previous word is W
• Transformation: NN  VB when previous word = to
– Change tag X to tag Y when previous tag is Z
Ex:
– The can rusted.
→ The (determiner) can (modal verb) rusted (verb) . (.)
– Transformation: Modal  Noun when previous tag = DET
→ The (determiner) can (noun) rusted (verb) . (.)
– Change tag X to tag Y when previous 1st, 2nd, or 3rd word is W
• VBP  VB when one of previous 3 words = has
• The learning process is guided by a small number of templates
(e.g., 26) to learn specific rules from the corpus
• Note how these rules sort of match linguistic intuition

33. Brill Algorithm (Overview)
• Assume you are given a 1. Initial-state annotator:
training corpus G (for gold Label every word token
standard) in V with most likely tag
for that word type from
• First, create a tag-free G.
version V of it … then do
2. Consider every possible
steps 1-4 transformational rule:
• Notes: select the one that leads
to the most
– As the algorithm improvement in V using
proceeds, each G to measure the error
successive rule covers
3. Retag V based on this
fewer examples, but rule
potentially more
4. Go back to 2, until there
accurately
is no significant
– Some later rules may improvement in accuracy
change tags changed over previous iteration
by earlier rules

34. Error-driven method
• How does one learn the rules?
• The TBL method is error-driven
– The rule which is learned on a given iteration is the one which
reduces the error rate of the corpus the most, e.g.:
– Rule 1 fixes 50 errors but introduces 25 more  net decrease is 25
– Rule 2 fixes 45 errors but introduces 15 more  net decrease is 30
 Choose rule 2 in this case
• We set a stopping criterion, or threshold  once we stop
reducing the error rate by a big enough margin, learning is
stopped

35. Example of Error Reduction
From Eric Brill (1995):
Computational Linguistics, 21, 4, p. 7

36. Rule ordering
• One rule is learned with every pass through the corpus.
– The set of final rules is what the final output is
– Unlike HMMs, such a representation allows a linguist to look
through and make more sense of the rules
• Thus, the rules are learned iteratively and must be applied in
an iterative fashion.
– At one stage, it may make sense to change NN to VB after to
– But at a later stage, it may make sense to change VB back to NN
in the same context, e.g., if the current word is school

37. Example of Learned Rule Sequence
• 1. NN VB PREVTAG TO
– to/TO race/NN->VB
• 2. VBP VB PREV1OR20R3TAG MD
– might/MD vanish/VBP-> VB
• 3. NN VB PREV1OR2TAG MD
– might/MD not/RB reply/NN -> VB
• 4. VB NN PREV1OR2TAG DT
– the/DT great/JJ feast/VB->NN
• 5. VBD VBN PREV1OR20R3TAG VBZ
– He/PP was/VBZ killed/VBD->VBN by/IN Chapman/NNP

38. Insights on TBL
• TBL takes a long time to train, but is relatively fast at tagging
once the rules are learned
• The rules in the sequence may be decomposed into non-
interacting subsets, i.e., only focus on VB tagging (need to
only look at rules which affect it)
• In cases where the data is sparse, the initial guess needs to be
weak enough to allow for learning
• Rules become increasingly specific as you go down the
sequence.
– However, the more specific rules generally don’t overfit because
they cover just a few cases

39. Relation between DT and TBL

40. DT and TBL
DT is a subset of TBL
1. Label with S
2. If X then S  A
3. S  B

41. DT is a proper subset of TBL
• There exists a problem that can be solved by TBL but not a DT,
for a fixed set of primitive queries.
• Ex: Given a sequence of characters
– Classify a char based on its position
• If pos % 4 == 0 then “yes” else “no”
– Input attributes available: previous two chars

42. • Transformation list:
– Label with S: A/S A/S A/S A/S A/S A/S A/S
– If there is no previous character, then S F
A/F A/S A/S A/S A/S A/S A/S
– If the char two to the left is labeled with F, then S F
A/F A/S A/F A/S A/F A/S A/F
– If the char two to the left is labeled with F, then FS
A/F A/S A/S A/S A/F A/S A/S
– F  yes
– S  no

43. DT and TBL
• TBL is more powerful than DT
• Extra power of TBL comes from
– Transformations are applied in sequence
– Results of previous transformations are visible to following
transformations.

45. Brill Algorithm (More Detailed)
• 1. Label every word token with its most
likely tag (based on lexical generation
Most likely tag:
probabilities).
P(NN|race) = .98
• 2. List the positions of tagging errors and
their counts, by comparing with “truth” (T) P(VB|race) = .02
• 3. For each error position, consider each Is/VBZ expected/VBN to/TO
instantiation I of X, Y, and Z in Rule
race/NN tomorrow/NN
template.
– If Y=T, increment improvements[I], Rule template: Change a word from
else increment errors[I]. tag X to tag Y when previous tag is
• 4. Pick the I which results in the greatest Z
error reduction, and add to output
Rule Instantiation for above example:
– VB NN PREV1OR2TAG DT improves
NN VB PREV1OR2TAG TO
on 98 errors, but produces 18 new
errors, so net decrease of 80 errors Applying this rule yields:
• 5. Apply that I to corpus
Is/VBZ expected/VBN to/TO
• 6. Go to 2, unless stopping criterion is
race/VB tomorrow/NN
reached

46. Handling Unknown Words
• Can also use the Brill
Example Learned Rule Sequence
method to learn how to tag
for Unknown Words
unknown words
• Instead of using surrounding
words and tags, use affix
info, capitalization, etc.
– Guess NNP if capitalized,
NN otherwise.
– Or use the tag most
common for words
ending in the last 3
letters.
– etc.
• TBL has also been applied to
some parsing tasks