Learning CPSC 386 Artificial Intelligence Ellen Walker Hiram College

What is learning? Process which changes a system to enable it to do the same task or tasks drawn from the same population more efficiently next time (improving performance). Examples (increasing abstraction) –Rote learning –Performance enhancement (problem solving) –Classification –Knowledge acquisition

Designing a Learning Agent Which components of the performance element are to be learned? What feedback is available to learn this? What representation is used?

Symbolic vs. Non-Symbolic learning If you “open the system up” after it has learned, can the knowledge be easily expressed? Symbolic uses accessible internal representations Non-symbolic uses inaccessible internal representations

Learning Examples Classified

Inductive learning Given a set of examples (x, y) where x is input, y is output Learn a function y=f(x) that –Returns correct results for all (x,y) pairs in the training set of examples –Generalizes well -- returns correct results for x values not in the training set

Ockham’s Razor If two functions fit, pick the simplest There is an inevitable tradeoff between the complexity of the hypothesis function and the degree of fit to the data.

Decision Trees Each node is a question Each leaf is a decision hair? legs? snakefrog Pet? Cat Lion

Learning Decision Trees from Examples Silly example: should I buy this car? 1. red VW (foreign, small, red) YES 2.green Cadillac (domestic, large, green) NO 3.blue Subaru (foreign, small, blue) YES 4. blue Mercedes (foreign, large, blue) NO 5. red Saturn (domestic, small, red) YES

Three types of learning Supervised –The system learns a function from examples of inputs and outputs –Correct outputs must be available during training Unsupervised –The system learns without feedback, based on global optimization criterion Reinforcement –System is rewarded (or punished) for decisions –This is the most general, models most human learning (except school).

Recursive Splitting Start with one big class –If there are some yes, some no, choose an attribute to split them (we now have 2 recursive problems) –Otherwise, we are done When all recursive problems are solved, the remaining classes will have all YES or all NO Each decision used for a split is a branch on the tree.

Recursive splitting example Initial class { (foreign,small,red,yes), (domestic, large, green, no), (foreign, small, blue, yes), (foreign,large,blue,no), (domestic,small,red,yes) } Split on size: { (foreign,small,red,yes), (foreign, small, blue, yes), (domestic,small,red,yes) } {(domestic, large, green, no), (foreign,large,blue,no)}

Choosing an attribute to split on We want to split on an attribute that gives us information –If an attribute splits the class into all pos/all neg that’s best! –Otherwise: if an attribute splits the class roughly evenly, and one subclass is mostly pos, one mostly neg, that’s pretty good

A formal notation of “best” Goal is to maximize information gain –Number of “bits” of information still needed after the split – number of bits needed before the split –Information I(p,n) = –( (p/p+n)lg(p/p+n) + (n/p+n)lg(n/p+n) ) –We need to subtract the sum of the informations for the split, weighted by the number of items in each Example: (4,2) -> (3, 0) and (1,2) Value is I(4,2) - 1/2 * I(3,0) - 1/2*I(1,2)

Updating our recursive algorithm Defun tree(examples) –If all examples are positive (or negative) return examples –Else Choose best attribute using Information gain Divide examples into sublists based on examples Return (cons attribute (mapcar #’Tree (list of sublists))) Result will be tree with each element being an attribute and a list of branches.

Assessing a Learning System Collect a large set of examples Divide into test and training sets (disjoint) Apply learning algorithm to training set (only) Measure its performance on test set (only) Repeat for different sizes of training sets Repeat for different randomly selected test sets of each training set

Learning Curve Training set size (% of total) % correct

Learning Depends on Training If the test set is not a random subset of the training set, strange results can occur! –What if test set contains only small cars, training set only large cars? If the overall set of examples doesn’t “cover the space” the wrong concept will be learned –Tank and weather example

Overfitting is Bad An algorithm is fully trained if it classifies every test case perfectly But what if every leaf is a set with only one element? –Training set is perfectly classified –Each element of test set creates a new category-- we have no experience! –Avoid by requiring minimum information gain value in order to split a set

One example at a time At any given point we have a current hypothesis that explains the examples Positive examples (that were incorrectly classified as negative) extend the hypothesis until it includes the new example Negative examples (that were incorrectly classified as positive) restrict the hypothesis until it does not include the new example

Extending and Restricting To extend a hypothesis, “add in” the new information –Extended hypothesis = hypothesis | pos. example To restrict a hypothesis “subtract out” the new information –Extended hypothesis = hypothesis & not(neg. ex.)

Candidate elimination (car example) 1. red VW (foreign, small, red) YES Min hypothesis: all foreign, small red things are good cars Max hypothesis: everything is a good car 2. green Cadillac (domestic, large, green) NO Min hypothesis: all foreign, small red things are good cars Max hypothesis: everything foreign or small or not green is a good car 3. blue Subaru (foreign, small, blue) YES Min hypothesis: all foreign, small (red or blue) things are good cars Max hypothesis: everything foreign or small or not green is a good car

Candidate elimination (car example) cont. 4. blue Mercedes (foreign, large, blue) NO Min hypothesis: all foreign, small, (red or blue) things are good cars Max hypothesis: everything small or (domestic and not green) or (foreign and not blue) or red is a good car 5. red Saturn (domestic, small, red) YES Min hypothesis: all small, (red or blue) things are good cars Max hypothesis: everything small or (domestic and not green) or (foreign and not blue) or red is a good car

Version Space Learning Consider the set of all hypotheses consistent with the examples –This will be the “range” from min to max in the prior examples –This is called a version space, and is updated after each example Least-commitment algorithm –We take no great leaps, but only make the minimal changes required for the concept to fit the examples.

Evaluating these algorithms Decision Tree learning is faster... But you need to have all examples in advance Decision trees make disjunctions easier to express Both are highly dependent on having the right attributes available Both are highly susceptible to noise (incorrect training examples)