By Wu, James; Coggeshall, Stephen
Drawing at the authors’ 20 years of expertise in utilized modeling and information mining, Foundations of Predictive Analytics provides the elemental historical past required for reading information and construction types for lots of sensible functions, akin to shopper habit modeling, possibility and advertising analytics, and different parts. It additionally discusses various sensible themes which are often lacking from related texts.
The e-book starts with the statistical and linear algebra/matrix beginning of modeling tools, from distributions to cumulant and copula features to Cornish–Fisher growth and different precious yet hard-to-find statistical concepts. It then describes universal and strange linear equipment in addition to well known nonlinear modeling ways, together with additive versions, bushes, help vector desktop, fuzzy platforms, clustering, naïve Bayes, and neural nets. The authors move directly to disguise methodologies utilized in time sequence and forecasting, equivalent to ARIMA, GARCH, and survival research. in addition they current a number of optimization suggestions and discover a number of distinctive themes, akin to Dempster–Shafer theory.
An in-depth selection of an important primary fabric on predictive analytics, this self-contained booklet offers the mandatory details for realizing a number of strategies for exploratory info research and modeling. It explains the algorithmic info in the back of each one procedure (including underlying assumptions and mathematical formulations) and indicates the way to organize and encode facts, decide on variables, use version goodness measures, normalize odds, and practice reject inference.
The book’s web site at www.DataMinerXL.com bargains the DataMinerXL software program for construction predictive versions. the positioning additionally contains extra examples and data on modeling.
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Extra info for Foundations of predictive analytics
199) 2 − λ 2π t3 e = λ(t−µ) 2µ2 t ∼ IG(µ, λ). 200) the characteristic function is √ 2 E eiux = eλ/µ(1− 1−iu2µ /λ) . 201) If x ∼ IG(µ, λ), we have √ √ 2 2 E eiucx = eλ/µ(1− 1−iuc2µ /λ) = ecλ/(cµ)(1− 1−iu2(cµ) /(cλ)) . 202) Thus cx ∼ IG(cµ, cλ). By direct integration we can verify that ∞ f (x)dx = 0 λ µλ 2e 2π ∞ e 2 λ −λ 2 t − 2µ2 changing variable y = √ ax − √ dt. 203) 0 By using the integration shown above, we have 1 By 1 t2 ∞ 0 f (x)dx = 1. b/x, we can easily carry out this integration. 36 Foundations of Predictive Analytics The first moment is ∞ ∞ λ µλ 2e 2π xf (x)dx = 0 e 2 λ λ − 2µ 2t −2 1 t2 dt = µ.
18) Another useful related integral that is not easy to find is ∞ 2 dx xn e−ax , In (a) = a > 0. 19) 0 This branches depending on whether or not n is even or odd: √ 1 (2n − 1)! π −(n+1/2) a and I2n+1 (a) = n! a−(n+1) . I2n (a) = 2n 2 (n − 1)! 20) The generalization to p-dimensional integration is straightforward. 21) 1/2 (A−1 )ij . 22) Distributions can easily be extended into higher dimensions. 23) p/2 1/2 (2π) (det Σ) where the mean µ now is a vector and the standard deviation now is the covariance matrix Σ.
204) 0 Here we have used the same integration shown above. 205) we have ∞ ∞ λ µλ 2e 2π x2 f (x)dx = 0 t2 e 2 λ λ − 2µ 2t −2 1 t2 dt = µ2 + µ3 /λ. 17 Var[x] = µ3 /λ. 207) Normal Inverse Gaussian (NIG) Distribution If a random variable conditional to another random variable with an inverse Gaussian distribution is a normal distribution, then it is distributed as a normal inverse Gaussian distribution. 208) y ∼ IG(a, b). We will choose a and b such that the distribution function of x has a simple form.