On the Optimality of Probability Estimation by Random Decision Trees Wei Fan IBM T.J.Watson.
Is Random Model Better? - On its accuracy and efficiency - Wei Fan IBM T.J.Watson Joint work with...
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Transcript of Is Random Model Better? - On its accuracy and efficiency - Wei Fan IBM T.J.Watson Joint work with...
Is Random Model Better? -On its accuracy and efficiency-
Wei FanIBM T.J.Watson
Joint work withHaixun Wang, Philip S. Yu, and Sheng Ma
Optimal Model Loss function L(t,y) to evaluate performance.
t is true label and y is prediction Optimal decision decision y* is the label that
minimizes expected loss when x is sampled repeatedly: 0-1 loss: y* is the label that appears the most
often, i.e., if P(fraud|x) > 0.5, predict fraud cost-sensitive loss: the label that minimizes the
“empirical risk”.• If P(fraud|x) * $1000 > $90 or p(fraud|x) > 0.09, predict
fraud
How we look for optimal model? NP-hard for most “model representation” We think that simplest hypothesis that fits
the data is the best. We employ all kinds of heuristics to look
for it. info gain, gini index, Kearns-Mansour, etc pruning: MDL pruning, reduced error-pruning,
cost-based pruning. Reality: tractable, but still pretty
expensive
On the other hand Occam’s Razor’s interpretation: two
hypotheses with the same loss, we should prefer the simpler one.
Very complicated hypotheses that are highly accurate: Meta-learning Boosting (weighted voting) Bagging (sampling without replacement)
Where are we? The above are very complicated to compute.
Question: do we have to?
Do we have to be “perfect”? 0-1 loss binary problem:
P(positive|x) > 0.5, we predict x to be positive. P(positive|x) = 0.6, P(positive|x) = 0.9 makes
no difference in final prediction! Cost-sensitive problems:
P(fraud|x) * $1000 > $90, we predict x to be fraud.
Re-write it P(fraud|x) > 0.09 P(fraud|x) = 1.0 and P(fraud|x) = 0.091 makes
no difference.
Random Decision Tree Building several empty iso-depth tree structures
without even looking at the data. Example is sorted through a unique path from
the root the the leaf. Each tree node records the number of instances belonging to each class.
Update each empty node by scanning the data set only once. It is like “classifying” the data. When an example reaches a node, the number of
examples belonging to a particular class label increments
Classification Each tree outputs membership probability
p(fraud|x) = n_fraud/(n_fraud + n_normal) The membership probability from multiple
random trees are averaged to approximate the true probability
Loss function is required to make a decision 0-1 loss: p(fraud|x) > 0.5, predict fraud cost-sensitive loss: p(fraud|x) $1000 > $90
Tree depth To create diversity Half of the number of features Combinations peak at half the size
of population Such as, combine 2 out 4 gives 6
choices.
Number of trees Sampling theory:
30 gives pretty good estimate with reasonably small variance
10 is usually already in the range. Worst scenario
Only one feature is relevant. All the rest are noise.
Probability:
Simple Feature Info Gain Limitation:
At least one feature with info gain by itself
Same limitation as C4.5 and dti Example
Training Efficiency One complete scan of the training
data. Memory Requirement:
Hold one tree (or better multiple trees) One example read at a time.
Donation Dataset Decide whom to send charity
solicitation letter. It costs $0.68 to send a letter. Loss function
Result
Result
Credit Card Fraud Detect if a transaction is a fraud There is an overhead to detect a
fraud, {$60, $70, $80, $90} Loss Function
Result
Extreme situation
Tree Depth
Compare with Boosting
Compare with Bagging
Conclusion Point out the reality that
conventional inductive learning (single best and multiple complicated) are probably way too complicated beyond necessity
Propose a very efficient and accurate random tree algorithm