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Instance Based Learning Ata Kaban The University of Birmingham 1 Instance Based Learning Ata Kaban The University of Birmingham 1

Today we learn: n K-Nearest Neighbours n Case-based reasoning n Lazy and eager learning Today we learn: n K-Nearest Neighbours n Case-based reasoning n Lazy and eager learning 2

Instance-based learning n n n One way of solving tasks of approximating discrete or Instance-based learning n n n One way of solving tasks of approximating discrete or real valued target functions Have training examples: (xn, f(xn)), n=1. . N. Key idea: – just store the training examples – when a test example is given then find the closest matches 3

n 1 -Nearest neighbour: Given a query instance xq, • first locate the nearest n 1 -Nearest neighbour: Given a query instance xq, • first locate the nearest training example xn • then f(xq): = f(xn) n K-Nearest neighbour: Given a query instance xq, • first locate the k nearest training examples • if discrete values target function then take vote among its k nearest nbrs else if real valued target fct then take the mean of the f values of the k nearest nbrs 4

The distance between examples n n n We need a measure of distance in The distance between examples n n n We need a measure of distance in order to know who are the neighbours Assume that we have T attributes for the learning problem. Then one example point x has elements xt , t=1, …T. The distance between two points xi xj is often defined as the Euclidean distance: 5

Voronoi Diagram 6 Voronoi Diagram 6

Characteristics of Inst-b-Learning n n An instance-based learner is a lazy-learner and does all Characteristics of Inst-b-Learning n n An instance-based learner is a lazy-learner and does all the work when the test example is presented. This is opposed to so-called eager-learners, which build a parameterised compact model of the target. It produces local approximation to the target function (different with each test instance) 7

When to consider Nearest Neighbour algorithms? n n Instances map to points in Not When to consider Nearest Neighbour algorithms? n n Instances map to points in Not more then say 20 attributes per instance Lots of training data Advantages: – Training is very fast – Can learn complex target functions – Don’t lose information n Disadvantages: – ? (will see them shortly…) 8

one two three four five six seven Eight ? 9 one two three four five six seven Eight ? 9

Training data Test instance 10 Training data Test instance 10

Keep data in normalised form One way to normalise the data ar(x) to a´r(x) Keep data in normalised form One way to normalise the data ar(x) to a´r(x) is 11

Normalised training data Test instance 12 Normalised training data Test instance 12

Distances of test instance from training data Classification 1 -NN Yes 3 -NN Yes Distances of test instance from training data Classification 1 -NN Yes 3 -NN Yes 5 -NN No 7 -NN No 13

What if the target function is real valued? n The k-nearest neighbour algorithm would What if the target function is real valued? n The k-nearest neighbour algorithm would just calculate the mean of the k nearest neighbours 14

Variant of k. NN: Distance-Weighted k. NN n We might want to weight nearer Variant of k. NN: Distance-Weighted k. NN n We might want to weight nearer neighbors more heavily n Then it makes sense to use all training examples instead of just k (Stepard’s method) 15

Difficulties with k-nearest neighbour algorithms n n Have to calculate the distance of the Difficulties with k-nearest neighbour algorithms n n Have to calculate the distance of the test case from all training cases There may be irrelevant attributes amongst the attributes – curse of dimensionality 16

Case-based reasoning (CBR) n n CBR is an advanced instance based learning applied to Case-based reasoning (CBR) n n CBR is an advanced instance based learning applied to more complex instance objects Objects may include complex structural descriptions of cases & adaptation rules 17

n n n CBR cannot use Euclidean distance measures Must define distance measures for n n n CBR cannot use Euclidean distance measures Must define distance measures for those complex objects instead (e. g. semantic nets) CBR tries to model human problem-solving – uses past experience (cases) to solve new problems – retains solutions to new problems n CBR is an ongoing area of machine learning research with many applications 18

Applications of CBR n Design – landscape, building, mechanical, conceptual design of aircraft sub-systems Applications of CBR n Design – landscape, building, mechanical, conceptual design of aircraft sub-systems n Planning – repair schedules n Diagnosis – medical n Adversarial reasoning – legal 19

CBR process New Case Retrieve matching Learn Retain Matched Cases Case Base Knowledge and CBR process New Case Retrieve matching Learn Retain Matched Cases Case Base Knowledge and Adaptation rules Closest Case Suggest solution No Adapt? Yes Reuse Revise 20

CBR example: Property pricing Test instance 21 CBR example: Property pricing Test instance 21

How rules are generated n n There is no unique way of doing it. How rules are generated n n There is no unique way of doing it. Here is one possibility: Examine cases and look for ones that are almost identical – case 1 and case 2 • R 1: If recep-rooms changes from 2 to 1 then reduce price by £ 5, 000 – case 3 and case 4 • R 2: If Type changes from semi to terraced then reduce price by £ 7, 000 22

Matching n Comparing test instance – matches(5, 1) = 3 – matches(5, 2) = Matching n Comparing test instance – matches(5, 1) = 3 – matches(5, 2) = 3 – matches(5, 3) = 2 – matches(5, 4) = 1 n Estimate price of case 5 is £ 25, 000 23

Adapting n Reverse rule 2 – if type changes from terraced to semi then Adapting n Reverse rule 2 – if type changes from terraced to semi then increase price by £ 7, 000 n Apply reversed rule 2 – new estimate of price of property 5 is £ 32, 000 24

Learning n So far we have a new case and an estimated price – Learning n So far we have a new case and an estimated price – nothing is added yet to the case base n If later we find house sold for £ 35, 000 then the case would be added – could add a new rule • if location changes from 8 to 7 increase price by £ 3, 000 25

Problems with CBR n n How should cases be represented? How should cases be Problems with CBR n n How should cases be represented? How should cases be indexed for fast retrieval? How can good adaptation heuristics be developed? When should old cases be removed? 26

Advantages n n n A local approximation is found for each test case Knowledge Advantages n n n A local approximation is found for each test case Knowledge is in a form understandable to human beings Fast to train 27

Summary n n n K-Nearest Neighbours Case-based reasoning Lazy and eager learning 28 Summary n n n K-Nearest Neighbours Case-based reasoning Lazy and eager learning 28

Lazy and Eager Learning n Lazy: wait for query before generalizing – k-Nearest Neighbour, Lazy and Eager Learning n Lazy: wait for query before generalizing – k-Nearest Neighbour, Case based reasoning n Eager: generalize before seeing query – Radial Basis Function Networks, ID 3, … n Does it matter? – Eager learner must create global approximation – Lazy learner can create many local approximations 29