pysmoother 0.0.7

Fit natural cubic polynomial splines, local regression and weighted smoothing splines to fit generalized additive models

##pysmoother allows you to -

1. Fit Univariate Natural Cubic Polynomial Splines. Allowing you to smooth a predictor and measure its effect on a target variable. Refer - Page 151, Equation 5.9 ,The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Second Edition February 2009. Trevor Hastie, Robert Tibshirani, Jerome Friedman

2. Fit Generalized Additive Models for p predictors with one target variable y. Refer - Page 298, Algorithm 9.1- The Backfitting Algorithm For Additive Model ,The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Second Edition February 2009. Trevor Hastie, Robert Tibshirani, Jerome Friedman

3. Fit the Local Scoring Algorithm for the Additive Logistic Regression Model. Refer - Page 300, Algorithm 9.2, The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Second Edition February 2009. Trevor Hastie, Robert Tibshirani, Jerome Friedman

4. Fit Local Regression Models to with p predictors. Allowing one to perform smoothing. Refer - Page 200, Local Regression in Rp, The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Second Edition February 2009. Trevor Hastie, Robert Tibshirani, Jerome Friedman

Code Demo -

1. Fit Univariate Natural Cubic Polynomial Splines

ss = SMOOTHING_SPLINES(X[:,i],Y,penalty = 10) ss.make_expanded_basis() ss.make_integral_matrix() ss.generate_coefficients(plot=True)

2. Fit Generalized Additive Models for p predictors with one target variable y.

smoothing_type = {0:'s',1:'1',2:'s'} ## l = Loess, s = Smoothing Splines gam = GAM(X,Y,penalty=4,smoothing_type=smoothing_type) print(gam.fit_additive_models(iterations=15)) print(gam.fitted_func) print(gam.alpha) print(gam.resid)

##Your Final Fitted Curve will be gam.alpha + gam.fitted_func plt.plot(Y) plt.plot(np.sum(gam.fitted_func,axis=1)) plt.show()

3a) Fit a Weighted Smoothing Spline wss = WEIGHTED_SMOOTHING_SPLINE(X[:,i],Y,penalty=10,weight=np.ones(len(X))) wss.make_expanded_basis() wss.make_integral_matrix() wss.generate_coefficients(plot=True)

3b) Fit the Local Scoring Algorithm for the Additive Logistic Regression Model. LGAM = ADDITIVE_LOGISTIC_REGRESSION_MODEL(X,Y,penalty=10) LGAM.model_fit(iterations=10)