Taming the Learning Zoo

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

VERY APPROXIMATE “CHEAT-SHEET” FOR TECHNIQUES DISCUSSED IN CLASS

Task Attributes N scalability D scalability

Capacity

Bayes nets C D Good Good GoodNaïve Bayes C D Excellent Excellent LowDecision trees C D,C Excellent Excellent FairLinear least squares

R C Excellent Excellent Low

Nonlinear LS R C Poor Poor GoodNeural nets R C Poor Good GoodSVMs C C Good Good GoodNearest neighbors

C D,C L:E, E:P Poor Excellent*

Locally-weighted averaging

R C L:E, E:P Poor Excellent*

Boosting C D,C ? ? Excellent*

VERY APPROXIMATE “CHEAT-SHEET” FOR TECHNIQUES DISCUSSED IN CLASS

Task Attributes N scalability D scalability

Capacity

Bayes nets C D Good Good GoodNaïve Bayes C D Excellent Excellent LowDecision trees C D,C Excellent Excellent FairLinear least squares

R C Excellent Excellent Low

Nonlinear LS R C Poor Poor GoodNeural nets R C Poor Good GoodSVMs C C Good Good GoodNearest neighbors

C D,C L:E, E:P Poor Excellent*

Locally-weighted averaging

R C Good Poor Excellent*

Boosting C D,C ? ? Excellent*

Note: we have looked at a limited subset of existing techniques in this class (typically, the “classical” versions).

Most techniques extend to:• Both C/R tasks (e.g., support vector regression)• Both continuous and discrete attributes• Better scalability for certain types of problem

With “sufficiently large” data sets

With “sufficiently diverse” weak leaners

AGENDA Quantifying learner performance

Cross validation Error vs. loss Precision & recall

Model selection

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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CROSS-VALIDATION Evaluate hypothesis on testing set

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CROSS-VALIDATION Evaluate hypothesis on testing set

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CROSS-VALIDATION Compare true concept against prediction

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COMMON SPLITTING STRATEGIES k-fold cross-validation

Train TestDataset

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 to compute parameters k

3. Return the standard deviation of 1,…,k (or a confidence interval)

Can also estimate confidence in a prediction y=f(x)

SIMPLE 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

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AverageLower rangeUpper range

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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 Kris on Facebook If I classify all images as “not Kris” I’ll have

>99.99% accuracy

Examples of Kris should count much more than non-Kris!

FALSE POSITIVES

20x1

x2

True concept Learned concept

FALSE POSITIVES

21x1

x2


New query

An example incorrectly predicted

to be positive

FALSE NEGATIVES

22x1

x2


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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REDUCING FALSE POSITIVE RATE

25x1

x2


REDUCING FALSE NEGATIVE RATE

26x1

x2


PRECISION-RECALL CURVES

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Precision

Recall

Measure Precision vs Recall as the classification boundary is tuned

Perfect classifier

Actual performance


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Precision

Recall


Penalize false negatives

Penalize false positives

Equal weight


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Precision

Recall



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Precision

Recall


Better learningperformance

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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OPTION 2: LOSS FUNCTIONS & WEIGHTED DATASETS General learning problem: “Given data D and

loss function L, find the hypothesis from hypothesis class H that minimizes L”

Loss functions: L may contain 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

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!

DATA DREDGING As the number of attributes increases, the

likelihood of a learner to pick up on patterns that arise purely from chance increases

In the extreme case where there are more attributes than datapoints (e.g., pixels in a video), even very simple hypothesis classes can overfit E.g., linear classifiers

Many opportunities for charlatans in the big data age!

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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 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?

NEXT LECTURES Temporal sequence models (R&N 15) Decision-theoretic planning Reinforcement learning Applications of AI

Taming the Learning Zoo

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