help.clj

(defn feature-vec
  [n]
  (map (partial cons 1)
       (for [x (range n)]
         (take 22 (repeatedly rand)))))

(defn label-vec
  [n]
  (for [x (range n)] (if (> (rand) 0.5) 1 0)))

(defn scaled-vector
  [scalar coll]
  (map #(* scalar %) coll))

(defn logistic-fn
  [x]
  (let [exp-x (Math/exp x)]
    (/ exp-x (inc exp-x))))

(defn dot-product
  [x y]
  (reduce + (map * x y)))

(defn logistic-prob
  [beta-seq x]
  (logistic-fn (dot-product beta-seq x)))

(defn log-likelihood
  [beta-seq label x]
  (let [prob (logistic-prob beta-seq x)]
    (+ (* label (Math/log prob))
       (* (- 1 label) (Math/log (- 1 prob))))))

(defn total-log-likelihood
  "returns the total log likelihood for a group of pixels; input
  labels and features for the group of pixels, aligned correctly so
  that the first label and feature correspond to the first pixel."
  [iterations batch-size beta-seq labels features]
  (loop [iter iterations ls labels fs features]
    (when (pos? iter)
      (time (dorun (map (partial log-likelihood beta-seq)
                        (take batch-size ls)
                        (take batch-size fs))))
      (recur (- iter batch-size)
             (drop batch-size ls)
             (drop batch-size fs)))))

(def X-rand (feature-vec 10000000))
(def y-rand (label-vec 10000000))
(def beta (repeat 22 0))

(total-log-likelihood 100000 25000 beta y-rand X-rand)
"Elapsed time: 343.759 msecs"
"Elapsed time: 408.516 msecs"
"Elapsed time: 333.686 msecs"
"Elapsed time: 371.483 msecs"


user> (total-log-likelihood 200000 25000 beta y-rand X-rand)
"Elapsed time: 372.326 msecs"
"Elapsed time: 356.37 msecs"
"Elapsed time: 362.232 msecs"
"Elapsed time: 342.627 msecs"
"Elapsed time: 1010.623 msecs"
"Elapsed time: 1181.387 msecs"
"Elapsed time: 1388.509 msecs"
"Elapsed time: 1322.818 msecs"

user> (total-log-likelihood 500000 25000 beta y-rand X-rand)
"Elapsed time: 370.097 msecs"
"Elapsed time: 389.351 msecs"
"Elapsed time: 422.98 msecs"
"Elapsed time: 429.956 msecs"
"Elapsed time: 453.33 msecs"
"Elapsed time: 419.977 msecs"
"Elapsed time: 374.716 msecs"
"Elapsed time: 416.268 msecs"
"Elapsed time: 1494.244 msecs"
"Elapsed time: 2634.889 msecs"
"Elapsed time: 4269.544 msecs"
"Elapsed time: 4088.356 msecs"
"Elapsed time: 8938.812 msecs"
"Elapsed time: 21680.063 msecs"