Review • Training Set / Testing Set (60/40) – In sample – Out of sample • ValiDation Metrics (training anD testing & Different moDels) Machine Learning – Root Mean Square Error (RMSE) – Mean Absolute Error (MAE) (fixes large resiDuals) – Cross ValiDation Training & Testing – Correlation • Over-fitting, UnDer-fitting Conclusion – KNN (k small : over-fitting, k large : unDer-fitting) – Parametric MoDels (Linear à Polynomials of Degree) – Compare to In-Sample & Out-of-Sample anD over/unDer fitting) Review: Learning MoDels Review: Learning MoDels • Parametric MoDels (Linear to Polynomials) • RanDom Forest (Breiman, Cutler) • KNN – Ensemble of random decision trees grown using bagging. • Decision Tree – Idea: A single tree in the forest is weaker than a full decision tree, but – NoDe Splitting by putting them all together, we get better overall performance thanks • Which feature to split on? to Diversity. – Classification maximize: information gain [concepts ranDom, entropy, information gain, Gini impurity] – Regression : Variance reDuction, correlation, mean square error (rmse), mean absolute error (mae) – Motivation: overcome the over-fitting problem of single full Decision • Which value to split on? MeDian, average, ranDom trees. – Depth of tree • RanDomness comes in two (sometimes three). – Aggregating Leaves (to control complexity) return average preDiction. – Bagging creating training Data. • Ensemble Learners – Feature selection at noDe: – Same Class of Learners • Best features among a ranDom (smaller) subset of ranDom features – Different Class of Learners. – Value selection/thresholD • Bootstrap Aggregating • RanDomly select value to spit on – Manipulate training sample (generate it ranDomly) • Project a variation (simplifieD) of RanDom Forest. – ADa Boost – Example. Subset of features is just 1. Project 2. Highlights Overview (see “NEW”): • Thinking: Which moDel to use for what type of New: All of the the Decision tree learners you create shoulD be Data? implementeD using a matrix Data representation (numpy nDarray). • DT Learner – What Does the Data look like? – BuilDTree() – adDEviDence() à calls BuilDTree() • ADDing Time Series how Do the assumption – SelectSplitFeature() • Best feature to split on change? • Absolute value correlation with Y. • RTLearner – BuildTree() – addEvidence() – SelectSplitFeature() à only one Different from DT • RanDomly selects a feature http://quantsoftware.gatech.eDu/images/4/4e/How-to-learn-a-Decision-tree.pDf • BagLearner() • InsaneLearner() – Bag of “BagLearners” (LinearRegression) – 20 BagLearner instances where: • each instance is composeD of 20 LinRegLearner instances. .