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Clojure

(ns examples.scratch
(:require [clojure.java.io :as io]
[clojure.string :as string]
[clojure.set]
[com.owoga.prhyme.data.dictionary :as dict]
[com.owoga.prhyme.nlp.core :as nlp]
[com.owoga.prhyme.generation.simple-good-turing :as sgt]
[com.owoga.prhyme.util.math :as math]))
(def re-word
"Regex for tokenizing a string into words
(including contractions and hyphenations),
commas, periods, and newlines."
#"(?s).*?([a-zA-Z\d]+(?:['\-]?[a-zA-Z]+)?|,|\.|\n)")
(defn tokenize
"Tokenizes for suffix trie. First token is end of document."
[text]
(->> text
(re-seq re-word)
(map second)
(map string/lower-case)
(cons :bol)
(reverse)
(cons :eol)))
(defn tokenize-line
[line]
(->> line
(string/trim)
(re-seq re-word)
(map second)
(map string/lower-case)))
(comment
(->> (slurp "dev/examples/sandman.txt")
(#(string/split % #"\n"))
(map tokenize-line))
)
(defn zero-to-n-seq
([coll]
(zero-to-n-seq coll 1))
([coll i]
(let [l (count coll)]
(if
(> i l) nil
(cons (take i coll)
(lazy-seq (zero-to-n-seq coll (inc i))))))))
(comment
(zero-to-n-seq '(1 2 3 4))
;; => ((1) (1 2) (1 2 3) (1 2 3 4))
)
(defn i-to-j-seq
([coll i j]
(zero-to-n-seq (->> coll (drop i) (take (- j i))))))
(defn n-to-zero-seq
([coll]
(n-to-zero-seq coll 0))
([coll i]
(if (= i (count coll)) nil
(cons (drop i coll)
(lazy-seq (n-to-zero-seq coll (inc i)))))))
(comment
(n-to-zero-seq '(1 2 3 4))
;; => ((1 2 3 4) (2 3 4) (3 4) (4))
)
(defn add-to-trie [trie coll]
(update-in trie (concat coll [:count]) (fnil inc 0)))
(defn add-multiple-to-trie [trie colls]
(loop [colls colls
trie trie]
(cond
(empty? colls) trie
:else (recur (rest colls)
(add-to-trie trie (first colls))))))
(defn n-gram-suffix-trie
"Creates a suffix trie of 1-gram to n-gram.
Useful for backoff language model (I think)."
[n tokens]
(let [trie {}
windows (partition (inc n) 1 tokens)]
(loop [trie trie
windows windows]
(cond
(= 1 (count windows))
(add-multiple-to-trie
trie
(concat (zero-to-n-seq (first windows))
(rest (n-to-zero-seq (first windows)))))
:else
(recur (add-multiple-to-trie
trie
(zero-to-n-seq (first windows)))
(rest windows))))))
(defn add-to-trie-1
[trie n tokens]
(let [pad-n n
tokens (concat (repeat pad-n :bol) tokens (repeat pad-n :eol))
partitions (partition n 1 tokens)]
(reduce
(fn [acc tokens]
(update-in acc (concat tokens [:count]) (fnil inc 0)))
trie
partitions)))
(defn flatmap
([m]
(flatmap m []))
([m prefix]
(mapcat
(fn [[k v]]
(if (map? v)
(flatmap v (conj prefix k))
[(conj prefix k) v]))
m)))
(defn filter-trie-to-ngrams [trie n]
(->> trie
(flatmap)
(partition 2)
;; Inc to account for :count
(filter #(= (inc n) (count (first %))))))
(comment
(let [trie {}]
(-> (add-to-trie-1 trie 2 '("of" "lives" "lost" "at" "sea"))
(add-to-trie-1 1 '("of" "lives" "lost" "at" "sea"))))
)
(defn wrand
"given a vector of slice sizes, returns the index of a slice given a
random spin of a roulette wheel with compartments proportional to
slices."
[slices]
(let [total (reduce + slices)
r (rand total)]
(loop [i 0 sum 0]
(if (< r (+ (slices i) sum))
i
(recur (inc i) (+ (slices i) sum))))))
(defn depth-of-map
[m]
(loop [d 0
m m]
(let [child-maps (filter map? (vals m))]
(if (empty? child-maps)
(dec d)
(recur (inc d) (first child-maps))))))
(defn completions [trie probs words]
(let [n (apply min (concat (keys probs) [(depth-of-map trie) (inc (count words))]))
possibilities (->> (get-in trie words)
(filter #(or (string? (first %))
(#{:eol :bol} (first %))))
(map (fn [[k v]]
[k (get-in probs [n (:count v)])]))
(into {}))
sum-probs (apply + (or (vals possibilities) '()))
possibilities (into {} (map (fn [[k v]] [k (/ v sum-probs)]) possibilities))]
possibilities))
(defn backoff-completions [trie probs words]
(if (empty? words)
'()
(let [c (completions trie probs words)]
(if (empty? c)
(backoff-completions trie probs (rest words))
c))))
(defn generate-lines
[trie n]
(let [probs (->> (range 1 (inc n))
(map #(vector % (filter-trie-to-ngrams trie %)))
(map (fn [[n v]] [n (map #(second %) v)]))
(map (fn [[n v]] [n (into (sorted-map) (frequencies v))]))
(map (fn [[n v]] [n (math/sgt (keys v) (vals v))]))
(map (fn [[n [rs probs]]]
[n (into {} (map vector rs probs))]))
(into {}))]
(loop [words [:bol]
freqs []]
(if (= :eol (last words))
[words freqs]
(let [cs (backoff-completions trie probs words)]
(if (empty? cs)
[words freqs]
(let [word (->> (reverse (sort-by second cs))
(math/weighted-selection second))]
(recur
(conj words (first word))
(conj freqs (second word))))))))))
(defn normalize [coll]
(let [s (apply + coll)]
(map #(/ % s) coll)))
(comment
(def trie
(let [documents (->> "dark-corpus"
io/file
file-seq
(remove #(.isDirectory %)))]
(->> documents
(take 10000)
(map slurp)
(mapcat #(string/split % #"\n"))
(map tokenize-line)
(filter #(> (count %) 1))
(reduce
(fn [acc tokens]
(-> (add-to-trie-1 acc 1 tokens)
(add-to-trie-1 2 tokens)
(add-to-trie-1 3 tokens)))
{})
((fn [trie]
(assoc
trie
:count
(->> trie
(map second)
(map :count)
(apply +))))))))
(->> (get-in trie ["you're" "my"])
(remove (fn [[k _]] (= :count k))))
(def r*s (sgt/trie->r*s trie))
(get-in r*s [1 :N])
(get-in trie ["you're" "my"])
(get-in r*s [1 :r*s 2616])
(get-in r*s [1 :r0])
(get-in trie ["you're" :count])
(get-in trie [1 :r0])
(get-in {:a 1} '())
(sgt/katz-alpha
trie
r*s
["you're" "my" "lady"]
(sgt/katz-beta trie r*s ["you're" "my" "lady"]))
(sgt/alpha trie r*s ["eat" "my"] 2)
(get-in trie ["you're" "my" "lady"])
(sgt/katz-estimator trie r*s 0 ["you're" "my" "head"])
;; => 0.1067916992217116
(sgt/katz-estimator trie r*s 0 ["you're" "my" "lady"])
;; => 0.016222893164898698
(sgt/katz-estimator trie r*s 0 ["you're" "my" "baz"])
(get-in trie ["you're" ])
(get-in r*s [1 :N])
(sgt/katz-beta-alpha trie r*s 0 ["you're" "not"])
;; => 0.14643662138043667
;; => 0.014190462313655283
(/ 0.14 0.014)
(/ 0.27 0.14)
(sgt/P-sub-s trie r*s 0 ["you're" "tearing" "foo"])
;; => 1.739617874207705E-4
(let [k 0
words ["not"]]
(->> (get-in trie (butlast words))
(remove #(= :count (first %)))
(filter (fn [[_ v]] (> (:count v) k)))
(map first)
(map #(concat (butlast words) [%]))
(map #(sgt/P-bar trie r*s %))
(apply +)))
(let [words ["you're" "my"]]
(->> (get-in trie (butlast words))
(remove #(= :count (first %)))
(filter (fn [[_ v]] (> (:count v) 0)))
(map first)
(map #(concat (butlast words) [%]))
(map #(sgt/katz-estimator trie r*s 0 %))
(apply +)))
(sgt/P-bar trie r*s ["foo"])
(let [words ["my"]]
(->> (get-in trie (butlast words))
(remove #(= :count (first %)))
(filter (fn [[_ v]] (> (:count v) 0)))
(map first)
(map #(concat (butlast words) [%]))
(map #(sgt/katz-estimator trie r*s 0 %))
(apply +)))
;; => 9.223367982725652E-6
(float (/ 1 27))
(get-in trie ["eat" "my"])
(sgt/sum-of-betas trie r*s ["you're" "my"])
(sgt/katz-beta trie r*s ["you're" "my" "lady"])
(get-in trie ["eat" "my" "heart"])
(get-in trie ["my" "heart"])
(sgt/katz-smoothing trie r*s ["eat" "my" "heart"] 5)
(sgt/prob-observed-ngram trie r*s ["eat"])
(->> ["pathe" "way"] (get trie) (map :count))
(sgt/mle trie ["you're"])
(let [words ["eat" "my"]
r (get-in trie (concat words [:count]) 0)
flattened (sgt/filter-trie-to-ngrams trie 2)]
(count flattened))
(get-in r*s [2])
(def probs
(->> (range 1 4)
(map #(vector % (filter-trie-to-ngrams trie %)))
(map (fn [[n v]] [n (map #(second %) v)]))
(map (fn [[n v]] [n (into (sorted-map) (frequencies v))]))
(map (fn [[n v]] [n (sgt/simple-good-turing (keys v) (vals v))]))
(map (fn [[n [rs probs]]]
[n (into {} (map vector rs probs))]))
(into {})))
(sgt/katz-backoff trie probs r*s)
;; probability of 3-grams
(let [bigram ["eat" "my"]
trigrams (map #(conj bigram %) dict/popular)]
(->> trigrams
(map #(vector % (sgt/stupid-backoff trie probs %)))
(map #(apply vec %))
(sort-by second)
(reverse)
(take 20)))
(repeatedly
10
(fn []
(let [bigram ["eat" "my"]
trigrams (map #(conj bigram %) dict/popular)]
(->> trigrams
(map #(vector % (sgt/stupid-backoff trie probs %)))
(take 10)))))
(let [documents (->> "dark-corpus"
io/file
file-seq
(remove #(.isDirectory %))
(drop 500)
(take 50000))
t (->> documents
(map slurp)
(mapcat #(string/split % #"\n"))
(map tokenize-line)
(filter #(> (count %) 1)))
trie (->> documents
(map slurp)
(mapcat #(string/split % #"\n"))
(map tokenize-line)
(filter #(> (count %) 1))
(take 5000)
(reduce
(fn [acc tokens]
(-> (add-to-trie-1 acc 1 tokens)
(add-to-trie-1 2 tokens)
(add-to-trie-1 3 tokens)))
{}))
probs (->> (range 1 4)
(map #(vector % (filter-trie-to-ngrams trie %)))
(map (fn [[n v]] [n (map #(second %) v)]))
(map (fn [[n v]] [n (into (sorted-map) (frequencies v))]))
(map (fn [[n v]] [n (math/sgt (keys v) (vals v))]))
(map (fn [[n [rs probs]]]
[n (into {} (map vector rs probs))]))
(into {}))]
(sgt/stupid-backoff trie probs [:bol "you" "must" "not"])
(count t))
;; Turning corpus into a trie.
(let [documents (->> "dark-corpus"
io/file
file-seq
(remove #(.isDirectory %))
(drop 500)
(take 5))
trie (->> documents
(map slurp)
(mapcat #(string/split % #"\n"))
(map tokenize-line)
(filter #(> (count %) 1))
(take 5000)
(reduce
(fn [acc tokens]
(-> (add-to-trie-1 acc 1 tokens)
(add-to-trie-1 2 tokens)
(add-to-trie-1 3 tokens)))
{}))
probs (->> (range 1 4)
(map #(vector % (filter-trie-to-ngrams trie %)))
(map (fn [[n v]] [n (map #(second %) v)]))
(map (fn [[n v]] [n (into (sorted-map) (frequencies v))]))
(map (fn [[n v]] [n (math/sgt (keys v) (vals v))]))
(map (fn [[n [rs probs]]]
[n (into {} (map vector rs probs))]))
(into {}))
poss (->> (get-in trie ["the" "dungeons"])
(filter #(or (string? (first %))
(#{:eol :bol} (first %))))
(map (fn [[k v]]
[k (get-in probs [3 (:count v)])]))
(into {}))]
poss)
(into {} (map vector [1 2 3] [4 5 6]))
;;
;; => ([1 (1 2 8 7 3 6 4 23) (85 18 2 2 6 3 1 1)]
;; [2 (1 2 5 3 4 7) (170 25 2 4 2 2)]
;; [3 (1 2 3 4 7 5) (213 30 5 1 1 3)])
(let [last-window '("in" "the" "frat")]
(concat (zero-to-n-seq last-window)
(rest (n-to-zero-seq last-window))))
;; => (("in") ("in" "the") ("in" "the" "frat") ("the" "frat") ("frat"))
(n-gram-suffix-trie
2
(string/split
"the cat in the hat is the rat in the frat"
#" "))
;; => {"the"
;; {:count 3,
;; "cat" {:count 1, "in" {:count 1}},
;; "hat" {:count 1, "is" {:count 1}},
;; "rat" {:count 1, "in" {:count 1}},
;; "frat" {:count 1}},
;; "cat" {:count 1, "in" {:count 1, "the" {:count 1}}},
;; "in" {:count 2, "the" {:count 2, "hat" {:count 1}, "frat" {:count 1}}},
;; "hat" {:count 1, "is" {:count 1, "the" {:count 1}}},
;; "is" {:count 1, "the" {:count 1, "rat" {:count 1}}},
;; "rat" {:count 1, "in" {:count 1, "the" {:count 1}}},
;; "frat" {:count 1}}
)
(comment
(def unigram
(n-gram-suffix-trie
1
(tokenize (slurp "dev/examples/sandman.txt"))))
unigram
(->> unigram
(map (fn [[k v]] (vector k (:count v))))
(map second)
(apply +))
(def bigram
(n-gram-suffix-trie
2
(tokenize (slurp "dev/examples/sandman.txt"))))
(->> bigram
(map (fn [[k v]] (vector k (:count v))))
(map second)
(apply +))
(count bigram)
(->> bigram
(take 4)
(into {}))
;; => {"cutest" {:count 2, "the" {:count 2, "him" {:count 2}}},
;; "us" {:count 3, "bring" {:count 3, "," {:count 2}, "yeesss" {:count 1}}},
;; "his" {:count 2, "that" {:count 2, "him" {:count 2}}},
;; "him"
;; {:count 8,
;; "give" {:count 4, "\n" {:count 4}},
;; "tell" {:count 2, "then" {:count 2}},
;; "make" {:count 2, "\n" {:count 2}}}}
(->> bigram
vals
(map :count)
frequencies
(into [])
sort
(map #(apply * %))
(apply +))
(count (tokenize (slurp "dev/examples/sandman.txt")))
;; => ([1 32] [2 20] [3 10] [4 3] [5 1] [6 2] [7 1] [8 2] [9 1] [10 1] [12 1] [26 1])
)
(defn P [trie w]
(let [ws (trie w)
c (get-in trie [w :count])]
(->> ws
(#(dissoc % :count))
(map
(fn [[k v]]
[k (/ (:count v) c)])))))
(defn vals-or-seconds [m]
(cond
(empty? m) m
(map? m) (apply concat (vals m))
:else (apply concat (map second m))))
(defn flat-at-depth
"Convenience way of getting frequencies of n-grams.
Given a trie with a depth of 0, it will return all 1-grams key/value pairs.
That collection can be filtered for keys that hold the freqs."
[m depth]
(let [m (if (map? m) (into [] m) m)]
(cond
(<= depth 0) m
:else (flat-at-depth (->> m (mapcat second) (remove #(= :count (first %))))
(dec depth)))))
(defn flatmap
([m]
(flatmap m []))
([m prefix]
(mapcat
(fn [[k v]]
(if (map? v)
(flatmap v (conj prefix k))
[(conj prefix k) v]))
m)))
(defn filter-trie-to-ngrams [trie n]
(->> trie
(flatmap)
(partition 2)
;; Inc to account for :count
(filter #(= (inc n) (count (first %))))))
(comment
(apply hash-map (flatmap {1 {2 {3 4} 5 {6 7}} 8 {9 10}} []))
(let [trie {"d" {:count 3
"o" {:count 3
"g" {:count 2}
"t" {:count 1}}
"a" {:count 1
"y" {:count 1}}}
"f" {:count 2
"o" {:count 1
"g" {:count 1}}
"i" {:count 1
"g" {:count 1}}}}]
(filter-trie-to-ngrams trie 3)
(sgt/trie->r*s trie))
)
;; Let Nc be the number of N-grams that occur c times.
;; Good-turing discounting:
;; c* = (c + 1) * Nc+1 / Nc
(defn n-gram-frequencies [trie n]
(if (< n 0)
{}
(->> trie
(#(flat-at-depth % (dec n)))
(map second)
(map :count)
frequencies
(into (sorted-map)))))
(defn n-gram->occurence-count-frequencies [trie n]
(n-gram-frequencies trie n))
(comment
(def tokens ["d" "o" "g" "\n" "d" "a" "y" "\n" "d" "o" "g" "\n" "d" "o" "t"])
(def trie (n-gram-suffix-trie 2 tokens))
trie
;; => {"d"
;; {:count 4,
;; "o" {:count 3, "g" {:count 2}, "t" {:count 1}},
;; "a" {:count 1, "y" {:count 1}}},
;; "o" {:count 2, "g" {:count 2, "\n" {:count 2}}},
;; "g" {:count 2, "\n" {:count 2, "d" {:count 2}}},
;; "\n" {:count 3, "d" {:count 3, "a" {:count 1}, "o" {:count 2}}},
;; "a" {:count 1, "y" {:count 1, "\n" {:count 1}}},
;; "y" {:count 1, "\n" {:count 1, "d" {:count 1}}}}
(count bigram)
(count (flat-at-depth bigram 0))
(->> bigram
(#(flat-at-depth % 0))
(filter #(= :count (first %)))
(map second)
frequencies
(into (sorted-map))
(map #(apply * %))
(apply +))
(n-gram-frequencies trie 2)
;; => {3 2, 1 3, 2 2}
;; for bigrams
;; of frequency 3 occurs 2 times
;; of frequency 2 occurs 2 times
;; of frequency 1 occurs 3 times
(n-gram-frequencies trie 1)
;; => {4 1, 2 2, 3 1, 1 2}
)
(defn num-seen-n-grams [trie n]
(->> trie
(#(flat-at-depth % (dec n)))
(remove #(= :count (first %)))
count))
(defn n-gram-frequency-map
"Map of n-gram to frequency of frequencies."
[trie n]
(into
{}
(map
#(vector % (n-gram-frequencies trie %))
(range 1 (inc n)))))
(comment
(n-gram-frequencies bigram 1)
(n-gram-frequency-map bigram 2)
)
(defn number-of-n-grams [trie n]
(->> trie
(#(flat-at-depth % (dec n)))
(remove #(= :count (first %)))
count))
(defn number-of-possible-n-grams [dict n]
(int (Math/pow (count dict) n)))
(defn number-of-n-grams-that-occur-c-times [trie n c]
(if (zero? c)
(- (number-of-possible-n-grams trie n)
(count (flat-at-depth trie (dec n))))
(let [frequencies-map (->> (n-gram-frequency-map trie n)
(#(get % n)))]
(get frequencies-map c 0))))
(comment
(number-of-possible-n-grams bigram 2)
(count (flat-at-depth bigram 1))
(count bigram)
(->> (number-of-n-grams-that-occur-c-times bigram 1 1))
(->> (number-of-n-grams-that-occur-c-times bigram 0 3)
(filter #(= :count (first %)))
(map second)
frequencies
sort)
)
(defn mle [trie c]
(let [N (->> trie vals (map :count) (apply +))]
(/ c N)))
;; Good-Turing Smoothing
;;
;; There are 4 steps to perform the GT smoothing, which are:
;; 1. Count the frequency of frequency Nr
;; 2. Average all the non-zero counts using Zr = Nr / 0.5 (t - q)
;; 3. Fit a linear regression model log(Zr) = a + b log(r)
;; 4. Update r with r* using Katz equation and constant k, with
;; updated Zr corresponding to specific r read out from the linear
;; regression model.
(defn least-squares-linear-regression [xs ys]
(let [n (count xs)
sum-x (apply + xs)
sum-y (apply + ys)
mean-x (/ sum-x n)
mean-y (/ sum-y n)
err-x (map #(- % mean-x) xs)
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]
(+ 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
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 (if (= i 0) 0 (nth freqs (dec i)))
Nr (nth Nrs i)
r (nth freqs i)
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)))
:else
(recur
(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]
ys-avg-cons (average-consecutives xs ys)]
(map float ys-avg-cons))
;; y = (r[j] + 1) * smoothed(r[j] + 1) / smoothed(r[j]);
(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]
N (apply + (map #(apply * %) (map vector rs Nrs)))
P0 (float (/ (first Nrs) N))
sgt-estimator (sgt/simple-good-turing-estimator rs Nrs)
r*s (map sgt-estimator rs)
new-N (apply + (map #(apply * %) (map vector r*s Nrs)))
pr (fn [r]
(* (- 1 P0)
(/ r new-N)))
sum-pr-unnormalized (apply + (map pr r*s))
pr-normalized (map #(* (- 1 P0)
(/ (pr %) sum-pr-unnormalized))
r*s)]
(sgt/simple-good-turing-probability rs Nrs)
(apply + (map #(/ % N) (sgt/sgt-estimates rs Nrs))))
(Math/log 1)
)
(defn turings-estimate [trie n r]
(/ (* (inc r)
(number-of-n-grams-that-occur-c-times trie n (inc r)))
(number-of-n-grams-that-occur-c-times trie n r)))
(defn good-turing [trie n r]
(let [nr (number-of-n-grams-that-occur-c-times trie n r)
nr1 (number-of-n-grams-that-occur-c-times trie n (inc r))]
(println
(format "cx %d nc %d ncx1 %d - %f"
r nr nr1 (float (/ (* (inc r) nr1) nr))))
(/ (* (inc r) nr1) nr)))
(comment
(number-of-n-grams-that-occur-c-times bigram 1 1)
;; unigram counts
(def unigram-counts
(->> bigram
vals
(map :count)
frequencies
(into (sorted-map))))
;; => {1 32, 2 20, 3 10, 4 3, 5 1, 6 2, 7 1, 8 1, 9 1, 10 2, 12 1, 26 1}
;; revised good-turing counts
(->> unigram-counts
(map
(fn [[freq freq']]
[freq (good-turing bigram 1 freq)]))
(into (sorted-map)))
;; => {1 5/4, 2 3/2, 3 6/5, 4 5/3, 5 12, 6 7/2, 7 8, 8 9, 9 20, 10 0, 12 0, 26 0}
(map (fn [[r nr]]
(good-turing bigram 1 r))
unigram-counts)
;; => (5/4 3/2 6/5 5/3 12 7/2 8 9 20 0 0 0)
(turings-estimate bigram 1 7)
)
(defn revise-frequencies [frequencies N]
(let [m (reverse (sort (keys frequencies)))]
(loop [revised {}
m m]
(cond
(empty? m) revised
:else
(recur
(assoc
revised
(first m)
(good-turing (get frequencies (first m) 0)
(get frequencies (second m) 0)
N))
(rest m))))))
(comment
(get (n-gram-frequency-map trie 3) 1)
;; => {4 1, 2 2, 3 1, 1 2}
(revise-frequencies
(get (n-gram-frequency-map trie 3) 1)
(apply + (map :count (vals trie))))
;; => {4 2/13, 3 4/13, 2 3/13, 1 0}
(def n-gram-freq-map (n-gram-frequency-map trie 3))
(def unigram-frequencies (n-gram-freq-map 1))
unigram-frequencies
)
(defn number-of-n-grams-that-occur-with-count [trie n c]
)
(defn good-turing-discount [trie c]
)