Modified Baum-Welch to allow for both convergence and max-iteration t…

…ests

Unit tests now agree with hand-worked example to 3 decimal places

project.clj

@@ -1,4 +1,4 @@
-(defproject hidden-markov-music "0.1.3-SNAPSHOT"
+(defproject hidden-markov-music "0.1.3"
   :description "Generate original musical scores by means of a hidden Markov
                 model."
   :url "https://github.com/dwysocki/hidden-markov-music"

src/hidden_markov_music/hmm.clj

@@ -4,6 +4,7 @@
             [hidden-markov-music.stats :as  stats]
             [hidden-markov-music.random :refer [select-random-key]]
             [hidden-markov-music.util :refer [map-for map-vals
+                                              numbers-almost-equal?
                                               maps-almost-equal?]])
   (:use clojure.pprint))
 
@@ -744,8 +745,8 @@
                        observations))]
       (- numerator denominator))))
 
-(defn train-model-helper
-  [model observations threshold likelihood]
+(defn train-model-seq
+  [model observations]
   (let [alphas   (forward-probability-seq  model observations)
         betas    (reverse (backward-probability-seq model observations))
         gammas   (gamma-seq model alphas betas)
@@ -758,20 +759,43 @@
         new-model (assoc model
                     :initial-prob     new-initial-probs
                     :transition-prob  new-transition-probs
-                    :observation-prob new-observation-probs)
-        new-likelihood (likelihood-forward new-model observations)]
-    (if (> (- new-likelihood likelihood)
-           threshold)
-      (recur new-model observations threshold new-likelihood)
-      new-model)))
+                    :observation-prob new-observation-probs)]
+    (cons new-model
+          (lazy-seq (train-model-seq new-model observations)))))
 
 (defn train-model
   "Trains the model via the Baum-Welch algorithm."
-  ([model observations]
-     (train-model model observations 0.0))
-  ([model observations threshold]
-     (train-model-helper model observations threshold
-                         (likelihood-forward model observations))))
+  ([model observations & {:keys [decimal    max-iter]
+                          :or   {decimal 15 max-iter 100}}]
+     (let [;; generate the infinite lazy seq of trained models,
+           ;; and take the maximum number of them
+           trained-models
+           (take max-iter
+                 (cons model
+                       (train-model-seq model
+                                        observations)))
+           ;; associate with each trained model its likelihood
+           trained-model-likelihoods
+           (map (fn [model]
+                  [model (likelihood-forward model observations)])
+                trained-models)
+           ;; create a sliding window of pairs of trained-models
+           trained-model-likelihood-pairs
+           (partition 2 1 trained-model-likelihoods)]
+       (->> trained-model-likelihood-pairs
+            ;; take from the list until convergence to the given decimal place
+            ;; is reached
+            (take-while (fn [[[model-prev likelihood-prev]
+                              [model      likelihood     ]]]
+                          (not (numbers-almost-equal? likelihood-prev
+                                                      likelihood
+                                                      :decimal decimal))))
+            ;; the last element is where convergence happened
+            last
+            ;; extract the [model likelihood] pair later in the window
+            second
+            ;; extract the model itself from the [model likelihood] pair
+            first))))
 
 
 

test/hidden_markov_music/baum_welch_test.clj

@@ -10,10 +10,12 @@
      (is (hmm/valid-hmm?
            (hmm/train-model tm/ibe-ex-11-log-model
                             [:good :good :so-so :bad :bad :good :bad :so-so]
-                            0.00001))))
+                            :decimal 5))))
    (testing "with Emilio Frazzoli's Baum-Welch example"
-     (pprint
-      (hmm/LogHMM->HMM
-       (hmm/train-model tm/frazzoli-ex-log-model
-                        tm/frazzoli-ex-observations
-                        0.0001))))))
+     (is (hmm/hmms-almost-equal?
+           tm/frazzoli-ex-trained-model
+           (hmm/LogHMM->HMM
+             (hmm/train-model tm/frazzoli-ex-log-model
+                              tm/frazzoli-ex-observations
+                              :max-iter 20))
+           :decimal 3)))))