core.clj

;; This is proof-of-concept, it's not idiomatic and needs a lot of refactoring, take it with a block of salt.

(ns gradient-descent.core)


;; Thetas with starting values
(def theta0 (atom 1))
(def theta1 (atom 1))
(def theta2 (atom 1))

;; learning step rate
(def alpha 1e-9)


;; Dataoints gathered as example data
;; points = x0, x1, x2, y
;; x0 - constant, always 1
;; x1 - square footage of house
;; x2 - # of bedrooms
;; y  - price of the house
(def points [
             [1 2104 3 400000]
             [1 1416 2 232000]
             [1 1534 3 315000]
             [1 852  2 178000]
             [1 1940 4 240000]
             ])


(defn h
  "Given a datapoint, return the suspected price of the house"
  [[x0 x1 x2 y]]
  (+
   (* @theta0 x0)
   (* @theta1 x1)
   (* @theta2 x2)))


(defn h?
  "Attempt to calculate a price for a house using arbitrary x0, x1 and x2 values"
  [x0 x1 x2]
  (+
   (* @theta0 x0)
   (* @theta1 x1)
   (* @theta2 x2)))


(defn single-j-theta
  "Calculate a single J(theta) (without the summing)"
  [i theta-index]
  (*
   (- (h (butlast i))
      (last i))
   (get i theta-index)))


(defn J-theta
  "Given a theta-index to resolve, calculate J(theta)"
  [theta-index]
  (reduce + (map (fn [p] (single-j-theta p theta-index)) points)))


(defn new-theta
  "Given a theta and the theta-index, return a new theta value"
  [theta theta-index]
  (- theta (* alpha (J-theta theta-index))))


(defn set-thetas
  "Update all thetas to new values"
  []
  (let [newt0 (new-theta @theta0 0)
        newt1 (new-theta @theta1 1)
        newt2 (new-theta @theta2 2)]
    #_(println "New thetas are:")
    #_(println "t0:" newt0)
    #_(println "t1:" newt1)
    #_(println "t2:" newt2)
    (reset! theta0 newt0)
    (reset! theta1 newt1)
    (reset! theta2 newt2)))


;;; Using this:

; user=> (use 'gradient-descent.core)
; nil
; user=> (dotimes [_ 100000] (set-thetas))
; nil

;; A 1400 sq. foot house with 2 bedrooms should be priced what?

; user=> (h? 1 1400 2)
; 239468.77647838247

Someone is taking CS229 Machine Learning with Andrew Ng! Recognize the example from years ago when I took it.

@aria42: I am! Aspiring to be able to understand your blog posts :)

Awesome best of luck! Make sure to also take CS228 with Daphne, that class taught me all I know.