Transcription of Logistic Regression
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Logistic Regression
Logistic RegressionInstructor: Ping LiDepartment of Statistics and BiostatiticsDepartment of Computer ScienceRutgers University20151 Calculus Review: DerivativesSimple derivatives:[logx] =1x,[xn] =nxn 1,[ex] =ex,[ax] =axlogaChain rule:[f(h(x))] =f (h(x))h (x) log ax2+e2x =1(ax2+e2x) ax2+e2x =2ax+ 2e2x(ax2+ex)Multivariate derivatives:f(x, y) =ax+xny+cy2, f(x, y) x=axloga+nxn 1y, f(x, y) y=xn+ 2cy2 Quick Review of Numerical OptimizationSlides 4 - 15 are for reviewing some basic stuff about numerical optimization, which isessential in modern Likelihood Estimation (MLE)Observationsxi,i= 1ton, are samples from a distribution with probability densityfunctionfX(x; 1, 2.)
Multinomial Distribution The multinomial is a natural extension to the binomial distribution. Consider c cells and denote the observations by (n 1,n 2,...,nc), which follow a c-cell multinomial distribution with the underlying probabilities (π 1,π 2,...,πc) (with Pc i=1πi = …
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