;-------------------------------------------------------------------------------------------------
; Ch02.17, Naiive Bayesian Classifier 'Spam Filter' ---  ----
;          with Laplacian Correction
; 
; PCM 2015/01/25
;-------------------------------------------------------------------------------------------------

(define no_of_samples 20000)
(define no_of_vars 1)                ; Spam
(define math_expect 
 ;0.999995   ; P(spam | money, ...),                   Bess.&al, Bayes.Prog.,2014,p.33,Tab 2.3 row 1
 ;0.996073   ; P(spam | next, money, ...),             Bess.&al, Bayes.Prog.,2014,p.33,Tab 2.3 row 2
 ;0.996073   ; P(spam | next, money, you, ...),        Bess.&al, Bayes.Prog.,2014,p.33,Tab 2.3 row 3
  0.00134393 ; P(spam | next, programming, money, ...),Bess.&al, Bayes.Prog.,2014,p.33,Tab 2.3 row 4
 ;0.999984   ; P(spam | fortune, next, money, ...),    Bess.&al, Bayes.Prog.,2014,p.33,Tab 2.3 row 5
 ;0.502648976369882 ; P(Spam=true|programming, money)  Bess.&al, Bayes.Prog.,2014, assignment 7
  )
;-------------------------------------------------------------------------------------------------
; Bessiere et al. 2014, p. 33, Table 2.1
;
(define a_f 250) ; a_f  = a(f)   = #(Spam=false)
(define a_t 750) ; a_t  = a(t)   = #(Spam=true)
(define a_if_s '(0 125 150 0 125)) ; a_if_s = (..., a(i,f), ...) = (..., #(Word(i)=true|Spam=false), ...)
(define a_it_s '(375 0 0 750 375)) ; a_it_s = (..., a(i,t), ...) = (..., #(Word(i)=true|Spam=true) , ...)
;
; Laplacian Correction, Bess.& al, Bayes.Prog.,2014,p.27
;
(define (cond_freq->cond_p a_i a)
    (/ (+ 1 a_i) (+ 2 a)))          ; P(Leaf(i)=true | Root)      
;
;-------------------------------------------------------------------------------------------------
;

(define (expected_value nth samples no_of_samples)
  (mean (map (lambda (sample) (list-ref sample nth)) samples)))

(define (expected_values samples vars)
  (let ((no_of_samples (length samples)))
    (if (= vars 0) '()
        (cons (expected_value (- no_of_vars vars) samples no_of_samples)
              (expected_values samples (- vars 1)))))) 

(define (take-a-sample)
  (rejection-query
   (define Spam (if (flip 0.75) 1 0))                     ; generative model 
   (define Fortune      ; generative model, word 0
     (cond ;((= Spam 0) (if (flip 0.00396825) 1 0))
            ((= Spam 0) (if (flip (cond_freq->cond_p (list-ref a_if_s 0) a_f))   1 0))
           ;((= Spam 1) (if (flip 0.5)        1 0))))
            ((= Spam 1) (if (flip (cond_freq->cond_p (list-ref a_it_s 0) a_t))   1 0))))
   (define Next         ; generative model, word 1
     (cond ;((= Spam 0) (if (flip 0.5)        1 0))
            ((= Spam 0) (if (flip (cond_freq->cond_p (list-ref a_if_s 1) a_f))   1 0))
           ;((= Spam 1) (if (flip 0.00132979) 1 0))))
            ((= Spam 1) (if (flip (cond_freq->cond_p (list-ref a_it_s 1) a_t))   1 0))))
   (define Programming  ; generative model, word 2
     (cond ;((= Spam 0) (if (flip 0.996032)   1 0))
            ((= Spam 0) (if (flip (cond_freq->cond_p (list-ref a_if_s 2) a_f))   1 0))
           ;((= Spam 1) (if (flip 0.00132979) 1 0))))
            ((= Spam 1) (if (flip (cond_freq->cond_p (list-ref a_it_s 2) a_t))   1 0))))
   (define Money        ; generative model, word 3
     (cond ;((= Spam 0) (if (flip 0.00396825) 1 0))
            ((= Spam 0) (if (flip (cond_freq->cond_p (list-ref a_if_s 3) a_f))   1 0))
           ;((= Spam 1) (if (flip 0.99867)    1 0))))
            ((= Spam 1) (if (flip (cond_freq->cond_p (list-ref a_it_s 3) a_t))   1 0))))
   (define You          ; generative model, word 4
     (cond ;((= Spam 0) (if (flip 0.5)        1 0))
            ((= Spam 0) (if (flip (cond_freq->cond_p (list-ref a_if_s 4) a_f))   1 0))
           ;((= Spam 1) (if (flip 0.5)        1 0))))
            ((= Spam 1) (if (flip (cond_freq->cond_p (list-ref a_it_s 4) a_t))   1 0))))
   (list Spam)                      ; sampled value
   (and                             ; condition expression, observational evidence, constraint
    ;                                       Bessiere & al, Bayes.Prog.,2014,p.33,Tab 2.3 row 1
;   (= Money 1)
;   (= Fortune 0) (= Next 0) (= Programming 0) (= Money 1) (= You 0)
    ;                                       Bessiere & al, Bayes.Prog.,2014,p.33,Tab 2.3 row 2
;   (= Next 1) (= Money 1)
;   (= Fortune 0) (= Next 1) (= Programming 0) (= Money 1) (= You 0)
    ;                                       Bessiere & al, Bayes.Prog.,2014,p.33,Tab 2.3 row 3
;   (= Next 1) (= Money 1) (= You 1)
;   (= Fortune 0) (= Next 1) (= Programming 0) (= Money 1) (= You 1)
    ;                                       Bessiere & al, Bayes.Prog.,2014,p.33,Tab 2.3 row 4
;   (= Next 1) (= Programming 1) (= Money 1)
    (= Fortune 0) (= Next 1) (= Programming 1) (= Money 1) (= You 0)
    ;                                       Bessiere & al, Bayes.Prog.,2014,p.33,Tab 2.3 row 5
;   (= Fortune 1) (= Next 1) (= Money 1)
;   (= Fortune 1) (= Next 1) (= Programming 0) (= Money 1) (= You 0)
    ;
    ;                                       Bessiere & al, Bayes.Prog.,2014,p.33,assignment 7
;   (= Programming 1) (= Money 1)
;   (= Fortune 0) (= Next 0) (= Programming 1) (= Money 1) (= You 0)
    )             
   ))

(define (my_return)
  (let* ((time_start (get-time))
         (header1 
          (display "Ch02.17, Naiive Bayesian Classifier 'SpamFilter' *** CHURCH-code by PCM 2015/01/25 ***"))
         (header2 
          (display "         with Laplacian correction "))
         (line
          (display 
           "--------------------------------------------------------------------------------------"))
         (comment1 (display "sample size = " no_of_samples))
         (samples (repeat no_of_samples take-a-sample))
         (dummy_value (hist samples "smpl-b.est.of P(Spam=t | ... )"))
         (sample-based-estimator (first (expected_values samples no_of_vars)))
         (comment2 (display "by ...."
                            "parameter theta E[Spam | ... ] = " math_expect))
         (comment3 (display "by CHURCH's approximate rejection sampling:"
                            "sample-based estimator E[Spam | ... ] = " 
                            sample-based-estimator))
         (comment4(display "|deviation| = " (abs (- math_expect sample-based-estimator))))
         (time_stop (get-time)))
    (display "computation time in sec =" (/ (- time_stop time_start) 1000))))
  

(my_return) 

;-------------------------------------------------------------------------------------------------