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linear-regression.cl
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linear-regression.cl
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(defpackage :linear-regression
(:use :cl
:hjs.learn.read-data
:hjs.util.matrix
:hjs.util.meta)
(:import-from :hc
#:i-thvector
#:square-sum
#:product-sum
#:vector-shift
#:vector-mean)
(:export #:mlr
#:residual-vector
#:residual-quantile-vector
#:residual-std-err
#:std-err-vector
#:t-value-vector
#:d.f
#:pt
#:pt-value-vector
#:r^2
#:adjusted-r^2
#:f-value
#:pf
#:pf-value))
(in-package :linear-regression)
(defun aux-quantile (x n)
(if (= n (floor n))
(aref x (floor n))
(+ (* (- (ceiling n) n) (aux-quantile x (floor n)))
(* (- n (floor n)) (aux-quantile x (ceiling n))))))
(defun quantile (vector q)
(let ((x (sort vector #'<=)))
(aux-quantile x (* q (- (length vector) 1)))))
(defun s-i-j (x-i x-j)
(product-sum (vector-shift x-i (vector-mean x-i))
(vector-shift x-j (vector-mean x-j))))
(defun make-matrix-s (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(assert (<= 2 (length range) (length (aref (dataset-numeric-points numeric-dataset) 0))))
(let* ((n (- (length range) 1))
(s (make-array (list n n) :element-type 'double-float)))
(dotimes (i n s)
(dotimes (j n)
(setf (aref s i j)
(s-i-j (i-thvector numeric-dataset (nth i range))
(i-thvector numeric-dataset (nth j range))))))))
(defun solve-system-of-equations (matrix vector)
(m-times-v (m^-1 matrix) vector))
(defun m-times-v (matrix vector)
(let* ((n (array-dimension vector 0))
(a (make-array n)))
(dotimes (i n a)
(setf (aref a i)
(loop for k below n
sum (* (aref matrix i k) (aref vector k)))))))
(defun make-vector-c (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(let* ((n (- (length range) 1))
(c (make-array n :element-type 'double-float)))
(dotimes (i n c)
(setf (aref c i)
(s-i-j (i-thvector numeric-dataset (nth i range))
(i-thvector numeric-dataset (first (last range))))))))
(defun mlr-intercept (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(let* ((s (make-matrix-s numeric-dataset range))
(c (make-vector-c numeric-dataset range))
(coefficients (solve-system-of-equations s c))
(n (first (array-dimensions coefficients)))
(intercept (vector-mean (i-thvector numeric-dataset (first (last range))))))
(dotimes (i n intercept)
(setf intercept
(- intercept
(* (aref coefficients i) (vector-mean (i-thvector numeric-dataset (nth i range)))))))))
(defun mlr (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(let* ((s (make-matrix-s numeric-dataset range))
(c (make-vector-c numeric-dataset range))
(coefficients (solve-system-of-equations s c))
(n (first (array-dimensions coefficients)))
(intercept (mlr-intercept numeric-dataset range))
(answer (make-array (+ n 1) :element-type 'double-float)))
(dotimes (i (+ n 1) answer)
(setf (aref answer i)
(if (= i 0)
intercept
(aref coefficients (- i 1)))))))
(defun fitted (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(let* ((n (length (dataset-numeric-points numeric-dataset)))
(coef (mlr numeric-dataset range))
(y-hat (make-array n)))
(dotimes (i n y-hat)
(setf (aref y-hat i)
(+ (aref coef 0)
(loop
for k below (1- (length range))
sum (* (aref coef (+ k 1))
(aref (i-thvector numeric-dataset (nth k range)) i))))))))
(defun residual-vector (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(let* ((n (length (dataset-numeric-points numeric-dataset)))
(y (i-thvector numeric-dataset (first (last range))))
(y-hat (fitted numeric-dataset range))
(e (make-array n)))
(dotimes (i n e)
(setf (aref e i) (- (aref y i) (aref y-hat i))))))
(defun residual-quantile-vector (numeric-dataset range)
(let ((v (sort (residual-vector numeric-dataset range) #'<=))
(w (make-array 5)))
(dotimes (i 5 w)
(setf (aref w i) (quantile v (* 0.25 i))))))
(defun capital-se (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(square-sum (residual-vector numeric-dataset range)))
(defun small-se (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(/ (capital-se numeric-dataset range)
(- (length (dataset-numeric-points numeric-dataset)) (- (length range) 1) 1)))
(defun residual-std-err (numeric-dataset range)
(sqrt (small-se numeric-dataset range)))
(defun std-err-intercept (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(let ((n (length (dataset-numeric-points numeric-dataset)))
(s^-1 (m^-1 (make-matrix-s numeric-dataset range))))
(sqrt (* (small-se numeric-dataset range)
(+ (/ 1 n)
(loop
for i below (1- (length range))
sum
(loop
for j below (1- (length range))
sum (* (vector-mean (i-thvector numeric-dataset (nth i range)))
(vector-mean (i-thvector numeric-dataset (nth j range)))
(aref s^-1 i j)))))))))
(defun std-err-of-ith-coef (numeric-dataset range i)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(sqrt (* (aref (m^-1 (make-matrix-s numeric-dataset range)) i i)
(small-se numeric-dataset range))))
(defun std-err-vector (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(let ((s (make-array (length range))))
(dotimes (i (length range) s)
(if (= i 0)
(setf (aref s i) (std-err-intercept numeric-dataset range))
(setf (aref s i) (std-err-of-ith-coef numeric-dataset range (- i 1)))))))
(defun t-value-of-intercept (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(/ (mlr-intercept numeric-dataset range)
(std-err-intercept numeric-dataset range)))
(defun t-value-of-ith-coef (numeric-dataset range i)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(/ (aref (mlr numeric-dataset range) (+ i 1))
(std-err-of-ith-coef numeric-dataset range i)))
(defun t-value-vector (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(let ((t-vector (make-array (length range))))
(dotimes (i (length range) t-vector)
(if (= i 0)
(setf (aref t-vector i) (t-value-of-intercept numeric-dataset range))
(setf (aref t-vector i) (t-value-of-ith-coef numeric-dataset range (- i 1)))))))
(defun r^2 (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(/ (square-sum (vector-shift (fitted numeric-dataset range)
(vector-mean (i-thvector numeric-dataset (first (last range))))))
(+ (square-sum (vector-shift (fitted numeric-dataset range)
(vector-mean (i-thvector numeric-dataset (first (last range))))))
(capital-se numeric-dataset range))))
(defun adjusted-r^2 (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(- 1
(/ (* (capital-se numeric-dataset range)
(- (length (dataset-numeric-points numeric-dataset)) 1))
(* (square-sum (vector-shift (i-thvector numeric-dataset (first (last range)))
(vector-mean (i-thvector numeric-dataset (first (last range))))))
(- (length (dataset-numeric-points numeric-dataset)) (- (length range) 1) 1)))))
(defun aic (numeric-dataset range)
(+ (* (length (dataset-numeric-points numeric-dataset))
(+ (log (/ (* 2 pi (capital-se numeric-dataset range))
(length (dataset-numeric-points numeric-dataset))))
1))
(* 2 (+ (length range) 1))))
(defun even-i (x v)
(if (= v 1)
(sqrt x)
(+ (even-i x (- v 1))
(/ (even-u x (- v 1)) (- v 1)))))
(defun even-u (x v)
(if (= v 1)
(* 0.5 (sqrt x) (- 1 x))
(* (even-u x (- v 1))
(* (- (* 2 v) 1)
(- 1 x)
(/ 1 (- (* 2 v) 2))))))
(defun odd-i (x v)
(if (= v 0.5)
(- 1 (* (/ 2 pi)
(atan (sqrt (/ (- 1 x) x)))))
(+ (odd-i x (- v 1))
(/ (odd-u x (- v 1)) (- v 1)))))
(defun odd-u (x v)
(if (= v 0.5)
(/ (sqrt (* x (- 1 x))) pi)
(* (odd-u x (- v 1))
(* (- (* 2 v) 1)
(- 1 x)
(/ 1 (- (* 2 v) 2))))))
(defun sign (x)
(if (>= x 0)
1
-1))
(defun pt (t-value phi)
(let ((x (/ (* t-value t-value) (+ phi (* t-value t-value))))
(v (/ phi 2)))
(if (evenp phi)
(+ 0.5 (* (sign t-value) (even-i x v) 0.5))
(+ 0.5 (* (sign t-value) (odd-i x v) 0.5)))))
(defun p-value (t-value phi)
(* 2 (- 1 (pt (abs t-value) phi))))
(defun d.f (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(- (length (dataset-numeric-points numeric-dataset)) (length range)))
(defun pt-value-vector (numeric-dataset range)
(assert (eq (type-of numeric-dataset) 'numeric-dataset))
(let ((p-vector (make-array (length range)))
(t-vector (t-value-vector numeric-dataset range)))
(dotimes (i (length range) p-vector)
(setf (aref p-vector i)
(p-value (aref t-vector i) (d.f numeric-dataset range))))))
(defun f-value (numeric-dataset range)
(/ (* (r^2 numeric-dataset range) (d.f numeric-dataset range))
(* (- 1 (r^2 numeric-dataset range)) (- (length range) 1))))
(defun i-11 (x m n)
(if (and (= m 0.5) (= n 0.5))
(- 1 (* (/ 2 pi)
(atan (sqrt (/ (- 1 x) x)))))
(if (= m 0.5)
(+ (i-11 x 0.5 (- n 1))
(/ (u-11 x 0.5 (- n 1))
(- n 1)))
(- (i-11 x (- m 1) n)
(/ (u-11 x (- m 1) n)
(- m 1))))))
(defun u-11 (x m n)
(if (and (= m 0.5) (= n 0.5))
(/ (sqrt (* x (- 1 x))) pi)
(if (= m 0.5)
(* (u-11 x 0.5 (- n 1))
(/ (- n 0.5)
(- n 1))
(- 1 x))
(* (u-11 x (- m 1) n)
(/ (+ m n -1) (- m 1))
x))))
(defun i-10 (x m n)
(if (and (= m 0.5) (= n 1.0))
(sqrt x)
(if (= m 0.5)
(+ (i-10 x 0.5 (- n 1))
(/ (u-10 x 0.5 (- n 1))
(- n 1)))
(- (i-10 x (- m 1) n)
(/ (u-10 x (- m 1) n)
(- m 1))))))
(defun u-10 (x m n)
(if (and (= m 0.5) (= n 1.0))
(* (- 1 x)
(sqrt x)
0.50)
(if (= m 0.5)
(* (u-10 x 0.5 (- n 1))
(/ (- n 0.5)
(- n 1))
(- 1 x))
(* (u-10 x (- m 1) n)
(/ (+ m n -1) (- m 1))
x))))
(defun i-01 (x m n)
(if (and (= m 1.0) (= n 0.5))
(- 1
(sqrt (- 1 x)))
(if (= m 1.0)
(+ (i-01 x 1.0 (- n 1))
(/ (u-01 x 1.0 (- n 1))
(- n 1)))
(- (i-01 x (- m 1) n)
(/ (u-01 x (- m 1) n)
(- m 1))))))
(defun u-01 (x m n)
(if (and (= m 1.0) (= n 0.5))
(* x
(sqrt (- 1 x))
0.50)
(if (= m 1.0)
(* (u-01 x 1.0 (- n 1))
(/ n
(- n 1))
(- 1 x))
(* (u-01 x (- m 1) n)
(/ (+ m n -1) (- m 1))
x))))
(defun i-00 (x m n)
(if (and (= m 1.0) (= n 1.0))
x
(if (= m 1.0)
(+ (i-00 x 1.0 (- n 1))
(/ (u-00 x 1.0 (- n 1))
(- n 1)))
(- (i-00 x (- m 1) n)
(/ (u-00 x (- m 1) n)
(- m 1))))))
(defun u-00 (x m n)
(if (and (= m 1.0) (= n 1.0))
(* x (- 1 x))
(if (= m 1.0)
(* (u-00 x 1.0 (- n 1))
(/ n
(- n 1))
(- 1 x))
(* (u-00 x (- m 1) n)
(/ (+ m n -1) (- m 1))
x))))
(defun pf (f phi-1 phi-2)
(let ((x (/ (* phi-1 f)
(+ phi-2 (* phi-1 f))))
(m (/ phi-1 2))
(n (/ phi-2 2)))
(cond ((and (oddp phi-1) (oddp phi-2))
(i-11 x m n))
((and (oddp phi-1) (evenp phi-2))
(i-10 x m n))
((and (evenp phi-1) (oddp phi-2))
(i-01 x m n))
((and (evenp phi-1) (evenp phi-2))
(i-00 x m n)))))
(defun pf-value (numeric-dataset range)
(- 1.0
(pf (f-value numeric-dataset range)
(- (length range) 1)
(d.f numeric-dataset range))))