taming the learning zoo
DESCRIPTION
Taming the Learning Zoo. Supervised Learning Zoo. Bayesian learning (find parameters of a probabilistic model) Maximum likelihood Maximum a posteriori Classification Decision trees (discrete attributes, few relevant) Support vector machines (continuous attributes) Regression - PowerPoint PPT PresentationTRANSCRIPT
TAMING THE LEARNING ZOO
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SUPERVISED LEARNING ZOO Bayesian learning (find parameters of a
probabilistic model) Maximum likelihood Maximum a posteriori
Classification Decision trees (discrete attributes, few relevant) Support vector machines (continuous attributes)
Regression Least squares (known structure, easy to interpret) Neural nets (unknown structure, hard to interpret)
Nonparametric approaches k-Nearest-Neighbors Locally-weighted averaging / regression
AGENDA Quantifying learner performance
Cross validation Error vs. loss Confusion matrix Precision & recall
Computational learning theory
CROSS-VALIDATION
ASSESSING PERFORMANCE OF A LEARNING ALGORITHM Samples from X are typically unavailable Take out some of the training set
Train on the remaining training set Test on the excluded instances Cross-validation
CROSS-VALIDATION Split original set of examples, train
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-Hypothesis space H
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Examples D
CROSS-VALIDATION Evaluate hypothesis on testing set
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Hypothesis space H
Testing set
CROSS-VALIDATION Evaluate hypothesis on testing set
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Testing set
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Test
CROSS-VALIDATION Compare true concept against prediction
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9/13 correct
COMMON SPLITTING STRATEGIES k-fold cross-validation
Leave-one-out (n-fold cross validation)
Train TestDataset
COMPUTATIONAL COMPLEXITY k-fold cross validation requires
k training steps on n(k-1)/k datapoints k testing steps on n/k datapoints (There are efficient ways of computing L.O.O.
estimates for some nonparametric techniques, e.g. Nearest Neighbors)
Average results reported
BOOTSTRAPPING Similar technique for estimating the
confidence in the model parameters Procedure:1. Draw k hypothetical datasets from original
data. Either via cross validation or sampling with replacement.
2. Fit the model for each dataset with k parameters k
3. Return the standard deviation of 1,…,k (or a confidence interval)
Can also estimate confidence in a prediction y=f(x)
EXAMPLE: AVERAGE OF N NUMBERS Data D={x(1),…,x(N)}, model is constant Learning: minimize E() = i(x(i)-)2 => compute
average Repeat for j=1,…,k :
Randomly sample subset x(1)’,…,x(N)’ from D Learn j = 1/N i x(i)’
Return histogram of 1,…,j
10 100 1000 100000.44
0.46
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AverageLower rangeUpper range
|Data set|
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BEYOND ERROR RATES
BEYOND ERROR RATE Predicting security risk
Predicting “low risk” for a terrorist, is far worse than predicting “high risk” for an innocent bystander (but maybe not 5 million of them)
Searching for images Returning irrelevant images is
worse than omitting relevant ones
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BIASED SAMPLE SETS Often there are orders of magnitude more
negative examples than positive E.g., all images of Mark Wilson on Facebook If I classify all images as “not Mark” I’ll have
>99.99% accuracy
Examples of Mark should count much more than non-Mark!
FALSE POSITIVES
17x1
x2
True concept Learned concept
FALSE POSITIVES
18x1
x2
True concept Learned concept
New query
An example incorrectly predicted
to be positive
FALSE NEGATIVES
19x1
x2
True concept Learned concept
New query
An example incorrectly predicted
to be negative
PRECISION VS. RECALL Precision
# of relevant documents retrieved / # of total documents retrieved
Recall # of relevant documents retrieved / # of total
relevant documents Numbers between 0 and 1
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PRECISION VS. RECALL Precision
# of true positives / (# true positives + # false positives)
Recall # of true positives / (# true positives + # false
negatives) A precise classifier is selective A classifier with high recall is inclusive
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OPTION 1: CLASSIFICATION THRESHOLDS Many learning algorithms (e.g., linear
models, NNets, BNs, SVM) give real-valued output v(x) that needs thresholding for classification
v(x) > t => positive label given to xv(x) < t => negative label given to x
May want to tune threshold to get fewer false positives or false negatives
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REDUCING FALSE POSITIVE RATE
23x1
x2
True concept Learned concept
REDUCING FALSE NEGATIVE RATE
24x1
x2
True concept Learned concept
LOSS FUNCTIONS & WEIGHTED DATASETS General learning problem: “Given data D and
loss function L, find the best hypothesis from hypothesis class H”
Loss functions: L contains weights to favor accuracy on positive or negative examples E.g., L = 10 E+
+ 1 E-
Weighted datasets: attach a weight w to each example to indicate how important it is Or construct a resampled dataset D’ where each
example is duplicated proportionally to its w
PRECISION-RECALL CURVES
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Precision
Recall
Measure Precision vs Recall as tolerance (or weighting) is tuned
Perfect classifier
Actual performance
PRECISION-RECALL CURVES
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Precision
Recall
Measure Precision vs Recall as tolerance (or weighting) is tuned
Penalize false negatives
Penalize false positives
Equal weight
PRECISION-RECALL CURVES
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Precision
Recall
Measure Precision vs Recall as tolerance (or weighting) is tuned
PRECISION-RECALL CURVES
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Precision
Recall
Measure Precision vs Recall as tolerance (or weighting) is tuned
Better learningperformance
MODEL SELECTION
COMPLEXITY VS. GOODNESS OF FIT More complex models can fit the data better,
but can overfit Model selection: enumerate several possible
hypothesis classes of increasing complexity, stop when cross-validated error levels off
Regularization: explicitly define a metric of complexity and penalize it in addition to loss
MODEL SELECTION WITH K-FOLD CROSS-VALIDATION Parameterize learner by a complexity level C Model selection pseudocode:
For increasing levels of complexity C: errT[C],errV[C] = Cross-Validate(Learner,C,examples) If errT has converged,
Find value Cbest that minimizes errV[C] Return Learner(Cbest,examples)
REGULARIZATION Minimize:
Cost(h) = Loss(h) + Complexity(h) Example with linear models y = Tx:
L2 error: Loss() = i (y(i)-Tx(i))2
Lq regularization: Complexity(): j |j|q
L2 and L1 are most popular in linear regularization L2 regularization leads to simple computation
of optimal L1 is more complex to optimize, but produces
sparse models in which many coefficients are 0!
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OTHER TOPICS IN MACHINE LEARNING Unsupervised learning
Dimensionality reduction Clustering
Reinforcement learning Agent that acts and learns how to act in an
environment by observing rewards Learning from demonstration
Agent that acts and learns how to act in an environment by observing demonstrations from an expert
ISSUES IN PRACTICE The distinctions between learning algorithms
diminish when you have a lot of data The web has made it much easier to gather
large scale datasets than in early days of ML Understanding data with many more
attributes than examples is still a major challenge! Do humans just have really great priors?
PROJECT MIDTERM REPORT Due 11/10
~1 page description of current progress, challenges, changes in direction
NEXT LECTURES Intelligent agents (R&N 2) Decision-theoretic planning Reinforcement learning Applications of AI