![Page 1: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/1.jpg)
Andrew Ng
Linear regression with one variable
Model representation
Machine Learning
![Page 2: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/2.jpg)
Andrew Ng
0
100
200
300
400
500
0 500 1000 1500 2000 2500 3000
0
100
200
300
400
500
0 500 1000 1500 2000 2500 3000
집가격(Portland, OR)
가격(in 1000s of dollars)
크기 (feet2)
감독학습(Supervised Learning)
자료의 “정확한답"이각예들에대해주어진
회귀문제(Regression Problem)
실수-값을갖는출력을예측
![Page 3: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/3.jpg)
Andrew Ng
기호:m = 훈련자료의갯수x’s = “입력” 변수 / 특징(features)y’s = “출력” 변수 / “목적(target)” 변수
Size in feet2 (x) Price ($) in 1000's (y)
2104 4601416 2321534 315852 178… …
집가격의훈련집합
(Portland, OR)
![Page 4: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/4.jpg)
Andrew Ng
훈련자료집합
학습알고리즘
h집크기 추정가격
우리는 h를어떻게표현하는가?
변수가하나인선형회귀.단변량선형회귀
(Univariate linear regression)
![Page 5: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/5.jpg)
Andrew Ng
Cost function
Machine Learning
Linear regression with one variable
![Page 6: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/6.jpg)
Andrew Ng
는어떻게선택하는가 ?
훈련자료
가설(Hypothesis):
‘s : 파라메타(Parameters)
Size in feet2 (x) Price ($) in 1000's (y)
2104 4601416 2321534 315852 178… …
![Page 7: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/7.jpg)
Andrew Ng
0
1
2
3
0 1 2 3
0
1
2
3
0 1 2 3
0
1
2
3
0 1 2 3
![Page 8: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/8.jpg)
Andrew Ng
y
x
생각: 이우리의훈련자료에대한 에
가깝도록 를선택한다.
![Page 9: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/9.jpg)
Andrew Ng
Cost functionintuition I
Machine Learning
Linear regression with one variable
![Page 10: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/10.jpg)
Andrew Ng
가설:
파라메타:
비용함수 :
목적:
간략화
![Page 11: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/11.jpg)
Andrew Ng
0
1
2
3
0 1 2 3
y
x
(고정된 에대하여, 이것은 x의함수) (파라메타 의함수 )
0
1
2
3
-0.5 0 0.5 1 1.5 2 2.5
![Page 12: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/12.jpg)
Andrew Ng
0
1
2
3
0 1 2 3
y
x
0
1
2
3
-0.5 0 0.5 1 1.5 2 2.5
(고정된 에대하여, 이것은 x의함수) (파라메타 의함수 )
![Page 13: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/13.jpg)
Andrew Ng
0
1
2
3
-0.5 0 0.5 1 1.5 2 2.5
y
x
0
1
2
3
0 1 2 3
(고정된 에대하여, 이것은 x의함수) (파라메타 의함수 )
![Page 14: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/14.jpg)
Andrew Ng
Cost functionintuition II
Machine Learning
Linear regression with one variable
![Page 15: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/15.jpg)
Andrew Ng
Hypothesis(가설):
파라메타:
비용함수:
목적:
![Page 16: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/16.jpg)
Andrew Ng
0
100
200
300
400
500
0 1000 2000 3000
Price ($) in 1000’s
Size in feet2 (x)
(고정된 에대하여, 이것은 x의함수) (파라메타 의함수 )
![Page 17: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/17.jpg)
Andrew Ng
![Page 18: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/18.jpg)
Andrew Ng
(파라메타 의함수 )(고정된 에대하여, 이것은 x의함수)
![Page 19: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/19.jpg)
Andrew Ng
(파라메타 의함수 )(고정된 에대하여, 이것은 x의함수)
![Page 20: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/20.jpg)
Andrew Ng
(파라메타 의함수 )(고정된 에대하여, 이것은 x의함수)
![Page 21: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/21.jpg)
Andrew Ng
(파라메타 의함수 )(고정된 에대하여, 이것은 x의함수)
![Page 22: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/22.jpg)
Andrew Ng
Gradient descent
Machine Learning
Linear regression with one variable
![Page 23: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/23.jpg)
Andrew Ng
어떤함수 를가지고
를원한다
Outline:
• 어떤 로시작한다.
• 최소값에도달할때까지, 가
감소하도록 를계속변화시킨다
![Page 24: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/24.jpg)
Andrew Ng
1
0
J(0,1)
![Page 25: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/25.jpg)
Andrew Ng
0
1
J(0,1)
![Page 26: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/26.jpg)
Andrew Ng
Gradient descent algorithm
Correct: Simultaneous update Incorrect:
![Page 27: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/27.jpg)
Andrew Ng
Gradient descentintuition
Machine Learning
Linear regression with one variable
![Page 28: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/28.jpg)
Andrew Ng
경사하강(Gradient descent) algorithm
![Page 29: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/29.jpg)
Andrew Ng
![Page 30: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/30.jpg)
Andrew Ng
α 가너무작으면, 경사하강이느릴수있다.
α 가너무크면, 경사하강은최소점을지나칠수있다. 수렴에실패하거나, 심지어는발산할수있다.
![Page 31: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/31.jpg)
Andrew Ng
at local optima
Current value of
![Page 32: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/32.jpg)
Andrew Ng
경사하강은학습률 α 가고정된상태로도, 국지적최소점으로수렴할수있다.
우리가국지적최소값에접근함에따라서, 경사하강은자동적으로더작은단계를취한다. 따라서, 시간에따라서 α 를줄일필요가없다.
![Page 33: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/33.jpg)
Andrew Ng
Gradient descent for linear regression
Machine Learning
Linear regression with one variable
![Page 34: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/34.jpg)
Andrew Ng
Gradient descent algorithm Linear Regression Model
![Page 35: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/35.jpg)
Andrew Ng
![Page 36: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/36.jpg)
Andrew Ng
Gradient descent algorithm
과 를동시에갱신
![Page 37: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/37.jpg)
Andrew Ng
1
0
J(0,1)
![Page 38: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/38.jpg)
Andrew Ng
![Page 39: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/39.jpg)
Andrew Ng
(for fixed , this is a function of x) (function of the parameters )
![Page 40: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/40.jpg)
Andrew Ng
(for fixed , this is a function of x) (function of the parameters )
![Page 41: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/41.jpg)
Andrew Ng
(for fixed , this is a function of x) (function of the parameters )
![Page 42: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/42.jpg)
Andrew Ng
(for fixed , this is a function of x) (function of the parameters )
![Page 43: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/43.jpg)
Andrew Ng
(for fixed , this is a function of x) (function of the parameters )
![Page 44: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/44.jpg)
Andrew Ng
(for fixed , this is a function of x) (function of the parameters )
![Page 45: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/45.jpg)
Andrew Ng
(for fixed , this is a function of x) (function of the parameters )
![Page 46: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/46.jpg)
Andrew Ng
(for fixed , this is a function of x) (function of the parameters )
![Page 47: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/47.jpg)
Andrew Ng
(for fixed , this is a function of x) (function of the parameters )
![Page 48: Introduction to Programming - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture2-kr.pdf · 2016-09-01 · Introduction to Programming Author: OpenClassroom Created Date: 9/1/2016 1:54:22](https://reader036.vdocuments.mx/reader036/viewer/2022062317/5edbb01fad6a402d66660817/html5/thumbnails/48.jpg)
Andrew Ng
“배치(Batch)” 경사강하
“Batch”: 경사강하의각단계마다모든훈련자료를
사용한다.