Experiments with simple good turing estimation

dev/examples/scratch.clj

@@ -327,51 +327,68 @@
   (let [n (count xs)
         sum-x (apply + xs)
         sum-y (apply + ys)
-        sum-xy (apply + (map #(apply * %) (map vector xs ys)))
+        mean-x (/ sum-x n)
-        sum-x-sqr (apply + (map #(* % %) xs))
+        mean-y (/ sum-y n)
-        m (/ (- (* n sum-xy) (* sum-x sum-y))
+        err-x (map #(- % mean-x) xs)
-             (- (* n sum-x-sqr) (* sum-x sum-x)))
+        err-y (map #(- % mean-y) ys)
+        err-x-sqr (map #(* % %) err-x)
+        m (/ (apply + (map #(apply * %) (map vector err-x err-y)))
+             (apply + err-x-sqr))
         b (/ (- sum-y (* m sum-x)) n)]
+    (println (format "intercept %f slope %f" b m))
     (fn [x]
-      (+ (* m x) b))))
+      (+ b (* m x)))))
+
+(comment
+  (float ((least-squares-linear-regression
+           [1 2 3 4]
+           [2 4 5 7])
+          5))
+  )
 
 (defn average-consecutives
   "Average all the non-zero counts using the equation
-  Zr = Nr / 0.5 (t - q)"
+  q, r, t
+  Zr = Nr / 0.5 (t - q)
+  or
+  Zr = 2 Nr / (t - q)"
   [freqs Nrs]
   (let [freqs (vec freqs)
         Nrs (vec Nrs)]
     (loop [i 0
            result []]
-      (let [q (nth freqs (max (dec i) 0))
+      (let [q (if (= i 0) 0 (nth freqs (dec i)))
-            Nr (nth Nrs (min (dec (count freqs)) i))
+            Nr (nth Nrs i)
-            r (nth freqs (min (dec (count freqs)) i))
+            r (nth freqs i)
-            t (nth freqs (min (dec (count freqs)) (inc i)))]
+            t (if (= (inc i) (count freqs))
+                (- (* 2 r) q)
+                (nth freqs (inc i)))]
+        (println q Nr r t)
         (cond
-          (= i (count freqs)) result
+          (= (inc i) (count freqs))
-
+          (conj result (/ (* 2 Nr) (- t q)))
-          (zero? i)
-          (recur (inc i)
-                 (conj result (/ (* 2 Nr) t)))
 
-          (= (dec i) (count freqs))
-          (recur (inc i)
-                 (conj result (/ (* 2 Nr (- t q)))))
           :else
-          (recur (inc i)
+          (recur
-                 (conj result (/ Nr (- r q)))))))))
+           (inc i)
+           (conj result (/ (* 2 Nr) (- t q)))))))))
 
 (comment
   (let [xs [1 2 3 4 5 6 7 8 9 10 12 26]
         ys [32 20 10 3 1 2 1 1 1 2 1 1]
-        smoothed (average-consecutives xs ys)
+        ys-avg-cons (average-consecutives xs ys)]
-        logged (map #(Math/log %) smoothed)
+    (map float ys-avg-cons))
-        lm (least-squares-linear-regression xs ys)
-        log-lm (map lm xs)
-        log-ys (map #(Math/pow % Math/E) log-lm)]
-    ;; => [32 20 10 3 1 2 1 1 1 2 1/2 1/14]
 
-    [log-lm log-ys])
+  ;; y = (r[j] + 1) * smoothed(r[j] + 1) / smoothed(r[j]);
+  (let [xs [1 2 3 4 5 6 7 8 9 10 12 26]
+        ys [32 20 10 3 1 2 1 1 1 2 1 1]
+        ys-avg-cons (average-consecutives xs ys)
+        log-xs (map #(Math/log %) xs)
+        log-ys (map #(Math/log %) ys-avg-cons)
+        lm (least-squares-linear-regression log-xs log-ys)
+        zs (map lm log-xs)]
+    ;; => [32 20 10 3 1 2 1 1 1 2 1/2 1/14]
+    [log-ys log-xs zs (map #(Math/pow Math/E %) zs)])
 
   (Math/log 1)
   )

simple_good_turing_estimator.c

@@ -227,11 +227,15 @@
  void showEstimates(void)
         {
         int i;
-        
+
+        printf("intercept %f slope %f\n", intercept, slope);
         printf("0\t%.4g\n", PZero);
         for (i = 0; i < rows; ++i)
                 printf("%d\t%.4g\n", r[i], p[i]);
+        for (i = 0; i < rows; ++i)
+                printf("%d\t%.4g\n", r[i], smoothed(r[i]));
         }
+
         
  void analyseInput(void)
         {
@@ -260,6 +264,11 @@
                 log_r[j] = log(r[j]);
                 log_Z[j] = log(Z[j]);
                 }
+
+        for (i = 0; i < rows; ++i)
+                printf("%d\t%.4g\n", r[i], Z[i]);
+
+
         findBestFit();
         for (j = 0; j < rows; ++j)
                 {

src/com/owoga/prhyme/util/math.clj

@@ -147,9 +147,15 @@
         m (/ (apply + (map #(apply * %) (map vector err-x err-y)))
              (apply + err-x-sqr))
         b (/ (- sum-y (* m sum-x)) n)]
-    (assert (< m -1) "See Good-Turing Without Tears for why slope must be less than -1.")
+    (assert (< m -1)
+            (format
+             (str "See Good-Turing Without Tears"
+                  " for why slope must be less than -1."
+                  "\nSlope: %0.2f Intersect %0.2f")
+             (float m)
+             (float b)))
     (fn [x]
-      (+ b (* m x)))))
+      (Math/pow Math/E (+ b (* m (Math/log x)))))))
 
 (defn average-consecutives
   "Average all the non-zero frequency of observations (frequency of frequencies)
@@ -206,7 +212,6 @@
             t (if (= (inc i) (count freqs))
                 (- (* 2 r) q)
                 (nth freqs (inc i)))]
-        (println q Nr r t)
         (cond
           (= (inc i) (count freqs))
           (conj result (/ (* 2 Nr) (- t q)))
@@ -246,3 +251,67 @@
       (/ nr1 (Math/pow nr 2))
       (inc (/ nr1 nr)))))
 
+(defn estimator
+  ([lm rs nrs]
+   (estimator lm rs nrs false))
+  ([lm rs nrs take-lgt?]
+   (fn [x]
+     (let [i (.indexOf x rs)
+           turing-estimate (nth rs i)
+           stdv (stdv-for-turing-estimate (nth rs (inc i))
+                                          turing-estimate
+                                          (nth nrs (inc i)))
+           lgt-estimate (lm x)]
+       (assert (>= i 0) (str x " not found"))
+       (if (or (< (Math/abs (- lgt-estimate turing-estimate))
+                  (* 1.65 stdv))
+               take-lgt?)
+         [lgt-estimate (estimator lm rs nrs true)]
+         [turing-estimate (estimator lm rs nrs false)])))))
+
+(defn sgt [rs nrs]
+  (assert (and (not-empty nrs) (not-empty rs))
+          "frequencies and frequency-of-frequencies can't be empty")
+  (let [l (count rs)
+        N (apply + (map #(apply * %) (map vector rs nrs)))
+        p0 (/ (first nrs) N)
+        zrs (average-consecutives rs nrs)
+        log-rs (map #(Math/log %) rs)
+        log-zrs (map #(Math/log %) zrs)
+        lm (least-squares-linear-regression log-rs log-zrs)
+        lgts (map lm rs)
+        sgts (loop [i 0
+                    result []
+                    take-lgt? false]
+               (cond
+                 (= (inc i) l)
+                 (conj result (last lgts))
+
+                 :else
+                 (let [x (nth zrs i)
+                       y (nth lgts i)
+                       stdv (stdv-for-turing-estimate
+                             (nth rs (inc i))
+                             (nth zrs i)
+                             (nth zrs (inc i)))
+                       take-lgt? (or take-lgt?
+                                     (<= (Math/abs (- x y))
+                                         (* 1.65 stdv)))]
+                   (recur (inc i)
+                          (conj
+                           result
+                           (if take-lgt?
+                             (nth lgts i)
+                             (nth zrs i)))
+                          take-lgt?))))
+        N* (apply + (map #(apply * %) (map vector rs sgts)))]
+    ))
+
+(comment
+  (let [rs [1 2 3 4 5 6 7 8 9 10 12 26]
+        nrs [32 20 10 3 1 2 1 1 1 2 1 1]
+        sgts (sgt rs nrs)]
+    sgts
+    )
+
+  )