Computational Learning An intuitive approach Human Learning Objects
Computational Learning An intuitive approach Human Learning Objects in world Learning by exploration and who knows? Language
informal training, inputs may be incorrect Programming A couple of examples of loops or recursions Medicine See one, do one, teach one
People: few complex examples, informal, complex behavioral output Computational Learning Representation provided Simple inputs: vectors of values Simple outputs: e.g. yes or no, a number, a disease
Many examples (thousands to millions) Quantifiable + Useful, e.g. automatic generation of expert systems Concerns Generalization accuracy Performance on unseen data
Evaluation Noise and overfitting Biases of representation You only find what you look for. Three Learning Problems Classification: from known examples
create decision procedure to guess class Patient data -> guess disease Regression: from known examples create decision procedure to guess real numbers Stock data -> guess price Clustering: putting data into meaningful
groups Patient Data -> new diseases Simple data attribute-value representation = 1 example
Sex, age, smoker, etc are the attributes Values are male, 50, true etc Only data of this form allowed. The Data: squares and circles ? ?
? ? Linear Decision Boundaries Perceptron Learning a (hyper)-line Given data
Construct line the decision boundary Usually defined by a normal n data is on one side if dot product data * n >0 Recall * is x1*y1+x2*y2. What a neuron does SVM: Optimization approach
middle line Decision Trees: rectangular boundaries 1-Nearest Neighbor Piecewise Linear boundaries
1-Nearest Neighbor classification If x is a example, find the nearest neighbor NN in the data using euclidean distance. Guess the class of c is the class of NN K-nearest neighbor: let the k-nearest neighbors vote Renamed as IB-k in Weka
Neural Nets Smooth boundaries Neural Net A single perceptron cant learn some simple concepts, like XOR A multilayered network of perceptrons can learn any boolean function
Learning is not biological but follows from multivariable calculus Gedanken experiments
Try ML algorithms on imagined data Ex. Concept: x>y, ie. Data looks like 3,1,+. 2,4,-. etc Which algorithms do best? And how well?
Consider the boundaries. My guesses: SMO> Perceptron>NearestN>DT. Check Guesses with Weka
199 examples. DT= 92.9 (called J48 in weka) NN= 97.5 (called IB1 in weka) SVM = 99.0 (called SMO in weka)
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Keep the same denominator Simplify. Adding Fractions To add fractions with different denominators: 1. Write each fraction as an equivalent fraction with the LCD. 2. Add the numerators and keep the LCD. 3. Simplify.
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