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class_09_19

# class_09_19 - Statistical Data Mining ORIE 474 Fall 2006...

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Statistical Data Mining ORIE 474 Fall 2006 Tatiyana Apanasovich 09/25/06 Model Structures for Prediction & Curse of Dimensionality

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6.3 Model Structure for Prediction Main model classes used in DM: A Regression models w/ linear structure B Local piecewise model structures for regression C Nonparametric “memory-based” local models D Stochastic components of model structures E Predictive models for classification
A. Regression Models w/ Linear Structure Model Structure: Θ={a 0 ,..,a p } Geometric interpretation: p-dim. hyperplane embedded in a (p+1)-dim. space with slope parameters a 1 ,..,a p and intercept a 0 Features: Additive ( individual contributions ) = + = p j j j X a a Y 1 0 ˆ

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Linear Regression Models (cont’d) Generalized Additive Models f j ’s are smooth (e.g. log(x), sqrt(x), etc.) Functions are nonlinear in X, but still linear in the parameters = + = p j j j j X f a a Y 1 0 ) ( ˆ
Linear Regression Models: Ex y=0.001x 3 -0.05x 2 +x+N(0,3)

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Parametric Models assume a particular, relatively simple, functional form e.g., uniform distribution, normal distribution, exponential, Poisson typically relatively small number of parameters often closed form solutions for parameter estimates that require a single pass through the data important to test the assumptions made by the model: – using simple visualizations – using statistical goodness-of-fit tests
Nonparametric Models take a local data-driven weighted average of around the point of interest simplest version: histogram – estimate for density is just (scaled) number of points in bin – problems: not smooth

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