머신러닝 프로그래밍 10주차 - Regression Gradient Descent
Regression Gradient Descent
선형 회귀(Linear Regression)
참고사이트 - https://wikidocs.net/21670
1) 단순 선형 회귀 분석(Simple Linear Regression Analysis)
2) 다중 선형 회귀 분석(Multiple Linear Regression Analysis)
비용 함수(Cost function) : 평균 제곱 오차(MSE)
앞서 주어진 데이터에서 와 의 관계를 와 를 이용하여 식을 세우는 일을 가설이라고 언급했습니다. 그리고 이제 해야할 일은 문제에 대한 규칙을 가장 잘 표현하는 와 를 찾는 일입니다. 머신 러닝은 와 를 찾기 위해서 실제값과 가설로부터 얻은 예측값의 오차를 계산하는 식을 세우고, 이 식의 값을 최소화하는 최적의 와 를 찾아냅니다.
이 때 실제값과 예측값에 대한 오차에 대한 식을 목적 함수(Objective function) 또는 비용 함수(Cost function) 또는 손실 함수(Loss function)라고 합니다. 함수의 값을 최소화하거나, 최대화하거나 하는 목적을 가진 함수를 목적 함수(Objective function)라고 합니다. 그리고 값을 최소화하려고 하면 이를 비용 함수(Cost function) 또는 손실 함수(Loss function)라고 합니다. 이 책에서는 목적 함수, 비용 함수, 손실 함수란 용어를 같은 의미로 혼용해서 사용합니다.
비용 함수는 단순히 실제값과 예측값에 대한 오차를 표현하면 되는 것이 아니라, 예측값의 오차를 줄이는 일에 최적화 된 식이어야 합니다. 앞으로 배울 러닝, 딥 러닝에는 다양한 문제들이 있고, 각 문제들에는 적합한 비용 함수들이 있습니다. 회귀 문제의 경우에는 주로 평균 제곱 오차(Mean Squared Error, MSE)가 사용됩니다.
import numpy as np
import random
import matplotlib.pyplot as plt
import math
import time
a = 1.5
b = 1.6
c = 0.1
n = 1000
xmin, xmax = -10, 10
numpy.vectorize이란?
참고사이트 - https://numpy.org/doc/stable/reference/generated/numpy.vectorize.html
from IPython.display import Image # 주피터 노트북에 이미지 삽입
Image("C://Users/MyCom/jupyter-tutorial/수업자료/data/20211117_003551_1.png")
def f(x,a,b,c):
#return a*x*x + b*x + c #2차함수 형태
return a*np.sin(b*x+c)
# def f(x, a, b): #1차함수형태
# return a*x + b
#return math.sin(a*x+b)
# vf = np.vectorize(f)
-uniform() 함수
2개의 숫자 사이의 랜덤 실수를 리턴합니다.
random.uniform(1, 10) # Random float x, 1.0 <= x < 10.0
결과 값 : 1.1800146073117523
xs = np.random.uniform(xmin,xmax,n) #randint는 정수를 uniform은 소수를 반환한다
# ys = f(xs,a,b,c) + np.random.normal(0,10,n) # 1차함수
ys = f(xs,a,b,c) + np.random.normal(0,0.1,n) #noise 추가 / normal (평균, 표준편차,만들어질 갯수) # 참고사이트 - https://lngnat.tistory.com/entry/%EB%A8%B8%EC%8B%A0%EB%9F%AC%EB%8B%9D-%EC%A0%95%EA%B7%9C%EB%B6%84%ED%8F%AC-Normal-Distribution-NumPyrandomnormal%ED%8F%89%EA%B7%A0%ED%91%9C%EC%A4%80%ED%8E%B8%EC%B0%A8%EA%B0%AF%EC%88%98
#2차함수
xs
array([-8.82450096, 8.35626007, 8.48698725, 1.41962675, -1.06510406,
-5.07269139, -8.48833348, -2.11441152, 1.46876428, -2.93171198,
-5.78185912, 9.01150006, 1.9069546 , -4.04589237, -5.92454961,
0.21274725, 4.38478928, -5.42623489, -6.29912032, -6.63538446,
8.84752356, -1.88496897, 7.97902809, -3.57310765, -3.56124911,
4.1458015 , -6.13943846, -9.78998499, 9.45614955, 1.78961294,
-9.91266107, 9.37651054, -4.65389185, -5.15437226, 7.09064049,
-3.72317394, 4.19433237, 1.43072925, -7.1189374 , 8.99745117,
-9.88745586, 3.01156743, -3.31321318, -6.99529032, -4.04959163,
-6.75505026, -0.26651557, 1.52938598, -7.05729805, -2.15895518,
-8.32556604, 1.51520421, -7.25254632, -9.85233047, -5.65318472,
5.62698891, -5.51617032, -0.39112499, -0.33194447, 3.5642697 ,
3.76209268, -7.41973909, -2.83445195, -5.73555473, -2.63190555,
-0.52137738, -9.30054634, -8.10941359, -6.53975374, -0.20269328,
0.5145176 , 7.24360591, 5.99681504, 6.6239364 , 6.80770691,
-1.39463753, -5.52092595, -6.53239334, -0.12429043, -5.71684258,
-1.41836688, -8.2535425 , 3.175049 , -4.05423072, -0.10799905,
-4.25134831, 8.85242881, 9.96253069, -3.3367241 , -1.4493517 ,
1.55906117, -8.46887337, -8.93214856, -0.45819726, -8.39542314,
7.1332123 , 3.88324879, -4.22276731, -8.38518956, -4.86069379,
3.62265617, 8.95106384, 9.66874208, 0.16319792, -7.81746697,
-7.99780849, -8.66880192, -7.88604183, -6.20942053, -7.16168191,
4.76628932, -0.08604518, -7.52072956, -7.61414723, 8.91029293,
-4.26513484, 0.3837306 , -6.79427942, 9.49125564, 5.56347336,
-5.43190082, -0.15607811, 2.99897718, -3.50404086, -6.02506022,
-6.08771578, 2.01412929, -4.8760307 , 3.77947048, -4.25593801,
6.18855131, 3.37448288, 8.1712301 , 7.38822221, 3.78341934,
2.07014865, 9.46500589, -2.97791217, -2.56721005, -0.0656148 ,
-3.77247349, -4.9111143 , -2.13403781, 6.57597064, 1.67505357,
3.69998754, -7.51783802, -6.04484207, 0.84290602, 9.72284651,
-2.51509898, -6.6551389 , -4.58099345, -7.5797443 , 4.17838948,
-3.12111814, -7.76455697, 9.59514807, 6.85949525, -4.15070149,
-6.10254394, 7.21138513, -4.76004024, -1.74162444, -3.14739487,
-2.92748158, -4.70850376, -3.64457411, 4.246319 , 7.72470543,
4.59270536, -3.8285139 , -5.63776405, 7.32020783, -9.02382367,
2.94915453, -1.0634599 , 6.35224358, 1.11102993, 9.15862349,
5.78833701, -6.02209631, 8.35548943, -2.15594363, 1.52398245,
0.84672962, -1.62643178, 1.1787552 , -3.1653484 , -9.95581726,
-8.4148917 , 7.8145782 , -9.0598313 , 5.24677638, -1.31823573,
-1.89289641, 1.94626889, 2.44795796, 8.58059276, -7.12080131,
-9.32126322, 5.03403923, 3.71904243, 7.11219699, 7.87645983,
-5.68800647, -1.50584184, -9.20346735, -8.25003537, 7.67051917,
-3.36181384, -3.93995486, 1.91927534, 0.7850455 , 2.10639639,
4.98924884, -4.94013614, -3.90117475, 0.94380741, 0.10395165,
0.4626688 , 1.10594747, -8.38912759, 8.792229 , -3.88434184,
-3.25004609, -1.92264504, -2.27935075, 3.58199062, 3.6592385 ,
0.8257611 , 7.2106722 , -5.8673145 , -7.3294766 , -7.13812962,
0.47443151, -8.45667227, 7.62723939, 3.16300657, -7.39776645,
2.90154736, 0.11259181, 8.05883445, 3.68919492, 4.4235687 ,
7.97156418, -0.85523058, -5.84223877, -8.74297601, -5.30229967,
5.12037168, 9.02946969, -2.49330399, 5.14949742, -8.26703426,
7.0148967 , -8.41439233, 7.11268464, 1.97820582, -5.91192613,
8.57509742, -7.40607138, 3.47231959, 7.85263074, -0.16774354,
-8.94299044, 4.44842666, 5.24395354, 2.42608216, -0.42221399,
3.79364468, 3.20839214, 2.83929874, 7.33981982, -6.03290378,
-4.80721672, -1.3173894 , -5.10360516, -4.09208608, 9.04309994,
-5.6648452 , -9.91521075, 4.52944444, 7.77701095, -6.35827256,
-8.38051222, 3.24720986, -3.91040484, 5.00749974, -9.78900477,
3.52590552, -1.03270246, -4.14761154, -0.10066622, -9.01996868,
-6.19235415, -2.41134607, 5.41132572, -1.53208389, 0.74226056,
-4.84605165, -3.27412518, 3.12167179, -4.84657059, 5.15630954,
5.06465315, 4.95009655, 5.43626962, -6.57196957, -8.19316819,
-3.01753242, 0.40885492, -5.99804447, 4.93059836, -0.95912138,
-9.35977347, -8.23316225, -0.28397579, 8.43844063, -4.3135255 ,
-2.80746955, 4.02984491, -2.02261723, -7.93024724, 0.58573894,
9.17642626, 3.52120209, -6.51846145, -3.52389109, 8.46796388,
-7.92618622, -5.88917369, 7.36445309, -2.09083814, -0.28082232,
4.77284202, -8.46202707, -4.31872913, -6.3175906 , -7.68735731,
-3.17718596, -3.80407262, -0.24137666, 7.3121785 , -3.05038644,
9.62804267, 9.56800596, 8.78322082, 9.56006026, -1.96892445,
3.99579167, 2.95438539, -5.47989802, -5.68473639, 5.64156555,
-1.75920524, 6.26321723, 0.26425384, -1.49778286, 9.92540513,
-7.34110554, 2.23725519, -2.82310168, -3.8648367 , 8.42501897,
-2.70664492, -4.91193181, 0.25625718, -1.16848806, 1.22443867,
-9.98343735, -5.59774943, -9.37867496, 4.031186 , -3.47216747,
-0.56448791, -3.54534904, -0.23240101, -4.8725857 , -9.14379381,
-2.50783462, -8.28429973, -7.49165875, 8.36193742, 7.82438516,
-6.62141959, -0.6348411 , -0.34349315, 0.20840962, 9.39210552,
-9.32018427, -6.44820774, 2.43508308, 5.88763925, 5.33959252,
-0.98341209, 8.0840926 , -1.70980916, -4.2074682 , 0.45220001,
-1.15785262, 9.85293816, -7.52516425, 8.94382877, 0.20500227,
-4.03812843, -8.94069514, 5.56622595, -0.4814476 , -8.43441478,
1.0231455 , -6.72941568, 0.92474421, -5.92929824, 5.66423663,
1.20764531, 0.40371695, 6.21224496, 4.88388099, -3.97300848,
9.56332116, 3.15629847, 5.74061535, -7.43781357, 2.56937527,
-5.12127996, 2.14308116, 7.38264169, -7.16603693, -2.67634218,
6.6890594 , 1.63603528, -2.31545244, 3.59738852, -7.8381993 ,
-6.03438108, 3.19760919, 0.13117816, 8.35526352, 0.06192172,
-1.67858187, -4.89934542, -2.19386041, 3.15934698, 3.05127875,
-5.52766433, -2.44789547, 6.19323293, -1.29220432, 2.55410193,
3.41950739, 9.12552716, 4.58089419, 9.5162472 , -3.97705633,
-0.60644106, -2.4946234 , -6.46175527, 6.69733804, 4.58749378,
9.0302445 , -2.15743602, -2.1320435 , 6.4270277 , 5.68214905,
-6.81073651, 8.36368183, 7.34810634, -7.07907175, 8.62042131,
-2.43769107, 5.87279417, -7.45361783, 5.06985699, 9.54927133,
-8.99883367, 9.01543793, 2.04475522, 8.72202199, 5.46322901,
-5.12836184, 8.65831771, -4.48646683, 6.01237451, -3.30848378,
-8.41683157, -5.4760174 , 8.39289351, -1.88054622, 1.68404438,
1.4287122 , 2.0535045 , -6.39740138, -0.6576019 , 7.19749769,
-0.14512938, 3.28160302, 2.20698896, 0.89480673, 3.85779572,
-2.09392987, 2.80888012, 6.10379094, 8.115145 , 2.97472402,
7.75592919, -9.57135587, 0.28060373, -7.94443901, 6.39706711,
-0.44983579, 4.3833689 , 9.21618502, -8.63969568, 2.625887 ,
-5.07757567, -5.74116246, -9.25337365, -7.65799007, 7.16584356,
-1.45678855, -9.64055305, 2.28386869, -0.60004658, -9.98861755,
-9.75868336, 1.19202758, 5.10853877, 3.90426036, -2.91400426,
-8.34639662, -2.74549632, -8.28052859, -1.67928943, -9.32057149,
-1.99378113, -1.6782252 , 0.05269223, 8.48519948, -0.97993055,
2.3409084 , -4.32805102, -2.01456102, -6.81020437, -8.81674496,
4.55189956, -1.17573182, 6.57244644, 7.60402957, 8.02918828,
2.62678018, -2.84726538, -4.2237969 , -0.85356231, 2.55835208,
0.88620787, 8.45645521, 9.72099652, 2.26884486, -0.0982231 ,
4.68467616, -5.87891132, -2.23202573, -4.54597516, -3.63166501,
-6.47260448, -0.25494149, -9.34894223, -8.18096018, 4.67172684,
-8.53862097, -5.52045076, 5.20051333, 6.43593356, 4.62656807,
-0.78407774, 6.01525013, -9.8470548 , 7.26315861, -0.81187932,
0.90287167, 9.91582383, -9.68414692, 9.22632792, -7.74027283,
-6.98351939, -9.39248254, -2.40637618, 1.88386073, -3.49959818,
-8.92086711, 7.95984206, -4.01164455, -4.12007986, 1.88949362,
-1.23832451, 9.94042174, -6.82585697, 9.79088727, -2.22454134,
-8.31042533, 9.73358223, -9.42715423, -1.54921157, 3.00850872,
-0.42704372, 9.00754799, -8.35957297, 4.20130084, -3.22674587,
-9.59795248, 7.48184945, -5.61396974, -8.72022444, -4.26686049,
-7.16399655, -9.60725157, -3.55253645, -0.37204589, -6.65636015,
-7.16280586, 7.50258432, -8.96109707, 9.28642911, -0.29788887,
-9.73481531, -3.56345775, 9.43754118, 5.10305566, 5.31997424,
1.02299777, -3.85717717, -4.85692981, 5.00369753, 5.66379488,
3.49247411, 7.18543683, 1.51945616, 1.95212321, -4.78848353,
-0.59976358, 7.75857548, -6.37251227, -9.49685289, -4.98691331,
9.03410806, 6.06671711, -0.98902141, 2.27512478, 6.27816686,
8.7714181 , -4.61080951, -0.05131483, -5.73585186, 2.03347027,
7.07593177, -2.06363223, -5.54346859, 1.23224762, -9.16235296,
-7.41316765, -9.18017826, 4.385383 , 9.89648275, 1.97327256,
-8.25725171, 2.61605802, 3.48777179, -8.77723651, -0.48742548,
1.11047202, 3.71478794, 2.85155998, 7.77424114, -2.39454872,
-5.8348042 , -3.26596297, -1.07160637, 6.03360473, 9.93737948,
4.52967536, 1.2594118 , 1.12623349, -5.23668859, 3.13273613,
0.62716865, -8.88213693, -7.75189218, 3.97271066, -5.72325941,
7.41189405, -9.688778 , 1.43220238, 7.99778626, 1.16323832,
6.70096975, -4.98809668, -3.96875764, 4.52763073, -2.19692082,
-6.51315927, 0.47575634, 8.80728611, 9.53243149, -6.35564752,
-3.70782232, -5.77102195, -8.94275399, 4.69241809, 9.59563031,
4.62906527, -4.13372871, 4.39579834, -8.37964476, 6.12633561,
3.44571203, -8.54000157, -9.07268842, 8.51683636, -8.3009988 ,
1.40433244, -4.02079645, 7.38670715, 2.01014087, 8.0853672 ,
-9.70807032, -6.20103038, 0.98709881, 0.22348996, -6.542874 ,
7.15010407, 5.2098732 , 0.62136102, 6.65297283, 7.22624023,
-5.14404408, -1.27071169, -9.98193563, -5.02051074, -8.77846353,
-9.87617207, -2.39882994, 4.25520725, 2.16942571, -9.976912 ,
2.39362798, 5.56113025, 2.63238948, 0.82817681, 9.31784216,
-5.63404241, 1.79536128, 7.09970921, -5.27104842, 0.01695788,
-3.78974731, 8.68848185, -2.50550906, -1.6524935 , 5.25003909,
-6.6015042 , -8.95915767, 8.68997782, 1.25577181, -5.21506271,
7.58362148, 6.1168738 , 2.93946819, 5.54235226, 0.78601974,
-1.6169377 , -1.56918951, -8.01141256, -5.70559227, -9.96447934,
-1.15385332, -6.14971336, -0.77118078, -5.27148622, -8.42865193,
5.42357309, -3.26648765, 3.66936431, -1.8711219 , -1.7541717 ,
4.16565588, -1.24497552, -3.58080512, -5.40819661, 4.91980434,
4.72247028, 8.07507777, 9.34911837, 0.26280899, 6.18848424,
0.81375428, -1.65969104, -7.90945737, 8.08444385, -5.86687503,
3.61177173, 7.26484781, -6.69086842, 2.85614699, 7.75808275,
-6.96379838, -7.43913489, 8.46173607, 7.57401974, -5.16354199,
-0.21978289, -7.51698223, 5.78612437, 1.6520984 , 3.55194789,
-9.29715517, 4.08967743, -8.46740488, -1.52140939, -8.79444499,
6.97370131, 0.93341097, 8.66684832, 0.75845129, -2.45499999,
7.95850145, 6.82967864, 9.80521605, 7.57527447, 3.3588022 ,
7.65485747, -7.88194897, 5.26679499, 3.270491 , 3.34412497,
5.76988346, -2.06374413, 2.41119655, -9.24282266, 4.66896653,
-7.25497653, 2.78291688, -8.56363261, -5.14720543, 2.86286347,
3.29993429, 2.78374563, 1.59095638, -0.24517971, 1.71379722,
-4.79988753, 4.67744209, 9.80795379, -4.24250067, -3.08291519,
-4.21998488, 9.64510694, 9.50623212, -4.38753524, 9.91233487,
0.24335963, -2.25035282, -4.65012 , -9.24754227, 2.55731572,
6.89521571, -9.05571189, -0.04509244, 1.12375144, -0.32428442,
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9.07759211e-01, 4.22511666e-01, 1.35387231e+00, -1.43362973e+00,
-1.48958954e+00, 9.60499826e-02, 1.27375302e+00, 5.39154415e-01,
1.12166737e+00, 1.13327547e+00, 1.44425590e+00, 5.60747121e-01,
9.85572496e-01, 7.33229154e-01, -4.88995306e-01, -1.38273161e+00,
1.44065916e+00, 4.00612567e-01, 1.51023909e+00, -4.05057901e-01,
1.16206673e+00, -9.42158861e-01, -6.41457955e-01, -1.12877691e+00,
-1.31448701e+00, -1.65975164e+00, 1.28958766e+00, -7.65840853e-01,
1.07813505e+00, -1.53382908e-01, -7.62744008e-01, -2.43457581e-01,
8.42334238e-01, -2.61501035e-01, 4.70483034e-01, 1.45127053e+00,
6.97037213e-01, 1.36419209e+00, -9.92495361e-01, 1.29165107e+00,
1.31065512e+00, -1.38574603e+00, -1.21370670e+00, -1.26135652e+00,
-1.25718836e+00, 3.25891372e-01, -1.54544429e+00, -1.38212359e+00,
1.44406977e-01, 8.18452247e-01, 9.29602795e-01, -6.54197165e-01,
1.90071583e-01, -1.12467703e+00, 4.56827337e-01, -1.39623605e+00,
1.39973173e+00, 1.00143407e+00, -7.90029483e-01, 6.67625543e-02,
-1.30513021e+00, -1.33370204e+00, 2.10806007e-02, 3.90566098e-01,
1.57098426e+00, 1.12788228e+00, -8.13403734e-01, 1.28125017e+00,
1.37592442e+00, -1.53164533e+00, 1.42658773e+00, 1.38008602e+00,
-1.48550911e+00, -5.90247877e-01, -7.90028714e-01, -1.49949698e+00,
9.15993137e-01, 1.47333288e+00, -9.26212547e-01, -1.00725226e+00,
-2.02449152e-01, -5.51116442e-01, 1.90594807e-01, -1.59392914e+00,
3.95058224e-01, -1.32553724e+00, -1.37149436e+00, -1.13796908e+00,
1.01544658e+00, 1.22063509e+00, -3.19198097e-01, -3.10978187e-01,
-7.16691002e-01, 6.45171498e-01, -1.53940967e+00, 9.62151551e-01,
-1.25321885e+00, 1.36299691e+00, 1.60060177e+00, 4.08259584e-01,
1.06776637e+00, 5.89430852e-01, -7.90386634e-01, 1.75077869e+00,
-8.00657422e-01, -1.84936920e-02, 5.32087414e-01, -2.87576895e-01,
-6.46022950e-01, -1.09647889e+00, 1.46930503e+00, -1.52935697e+00,
1.85075884e-01, 1.51185954e+00, 1.35973540e+00, 1.18854622e+00,
-5.22202515e-01, -1.39323304e+00, -4.15561015e-01, 8.77978340e-01,
3.86777533e-02, 4.96356650e-01, -8.63409883e-01, -1.16464390e+00,
6.19260064e-01, -1.17070036e+00, -1.03345004e+00, -1.38315205e+00,
-1.55683810e+00, 1.56236677e+00, 1.35882122e+00, 1.39106279e+00,
9.94120278e-01, 4.80540804e-01, -1.58657988e+00, -5.09433191e-02,
-4.65879647e-01, -1.06430532e+00, -3.69378094e-01, 8.58977858e-02,
1.23675266e+00, -1.00420524e+00, -1.05963785e+00, 2.73923805e-02,
5.77930729e-02, -1.17563922e+00, -1.28080930e+00, 1.38324192e+00,
1.18402942e+00, -1.47649700e+00, -1.35207884e+00, -1.46525925e+00,
-1.65934302e+00, -1.36696475e+00, -1.41689267e+00, 6.78172505e-01,
-4.08910826e-01, 5.02397879e-01, -1.47774610e+00, 1.54521368e+00,
-2.27610001e-01, -6.61926321e-01, 1.53181784e+00, -5.73900179e-01,
2.22961875e-01, 5.82668977e-01, -7.61201973e-01, -2.70697154e-01,
7.39709568e-01, 5.65105411e-01, -1.19016320e+00, -1.30700887e+00,
-1.21736174e+00, -1.45540650e+00, -1.48089758e+00, 5.90130032e-02,
1.64295677e+00, -4.93535359e-01, 1.29504891e+00, -1.47996750e+00,
9.71700837e-01, 3.55853286e-01, 8.54289559e-01, 5.83698090e-01,
1.48399656e+00, 1.13499520e+00, -1.34573347e+00, -1.36455557e+00,
9.03683808e-02, 4.08107718e-01, 6.73343229e-01, 9.54460890e-01,
1.52004224e+00, 9.99216344e-01, -1.09167983e+00, 1.64607283e+00,
8.55647394e-01, -8.88999120e-01, 6.44329943e-01, -1.53505763e+00,
1.51779032e+00, -1.61602177e+00, 6.08086748e-01, -6.13249759e-01,
4.99110011e-01, -1.48032318e+00, -1.15738466e+00, -1.23262044e+00,
-1.60968788e+00, -9.31634706e-01, 6.17454154e-01, -2.75416475e-01,
8.50329049e-01, 9.36658851e-01, -4.70589170e-01, -1.47244457e-02,
9.03912763e-01, 7.13660971e-01, 8.77788145e-01, 3.27142108e-02,
-1.45477315e+00, 1.31824374e+00, 1.27905270e+00, -4.39586026e-01,
8.72543353e-01, 1.29555660e+00, -1.24439537e+00, -1.12764627e+00,
-9.00031712e-01, -1.32031899e+00, -1.61625759e+00, -1.60824063e+00,
-1.56662748e+00, -9.86476043e-01, -4.39632271e-01, 5.33628979e-01,
-1.03941085e+00, 1.33646372e+00, 1.78551259e-01, -2.88236286e-01,
4.21159676e-01, -6.30356841e-01, -1.42324926e+00, -4.12326911e-01,
-5.01855701e-01, -1.36744835e+00, 1.07692506e+00, -2.71953650e-01,
4.54802153e-01, -3.17370337e-01, -2.84135852e-02, 1.31788633e+00,
-1.11656924e+00, -1.28070769e+00, 9.28277261e-02, 2.79852824e-01,
-1.03884512e+00, -1.41930061e+00, -5.23565989e-01, 2.89077571e-01,
-1.23214031e+00, -1.39427070e+00, -1.33478868e+00, 9.62212130e-01,
-1.44592304e+00, -9.15339416e-01, 1.37308482e+00, 1.75274378e-02,
1.14844349e-01, 9.67386168e-01, -5.31589126e-02, 9.85463879e-01,
-1.39172371e+00, 7.53470963e-02, 1.37239085e+00, -4.88384559e-01,
9.60112843e-02, 4.53829855e-02, -1.58174481e-01, -3.72024869e-01,
-1.07065055e+00, 6.15513259e-01, 4.10037100e-01, 1.39420914e+00,
6.41816347e-01, 1.31629014e+00, 1.17558419e+00, 1.12364518e+00,
1.38924208e+00, -9.70789434e-01, 1.27950174e+00, 1.07016639e+00,
-1.43890290e+00, -1.19064169e+00, -1.28016341e+00, -1.50100222e+00,
-1.49054660e+00, -1.17517891e+00, 1.46251532e+00, 1.56273612e+00,
1.13611532e+00, -4.23621607e-01, -1.32334902e+00, -9.69125323e-02,
-1.39389209e+00, 1.17516626e+00, -9.83092310e-01, -1.10209384e+00])
# # 2번째 방법
# def f(x,a,b):
# return np.sin(a*x+b)
# xs = np.random.uniform(xmin,xmax,n)
# ys = f(xs,a,b) + np.random.normal(0,1) #노이즈 추가
# ys
plt.plot(xs,ys,'.')
[<matplotlib.lines.Line2D at 0x1dc0e1da940>]
# 1차함수
# bestA, bestB = None, None
# bestLoss = 1e9 # 10의 9승
# t0 = time.time()
# lossesBySearch = []
# #numpy 모듈의 arange 함수는 반열린구간 [start, stop) 에서 step 의 크기만큼 일정하게 떨어져 있는 숫자들을 array 형태로 반환해 주는 함수다.
# for aa in np.arange(-10,10,0.1):
# for bb in np.arange(-10,10,0.1):
# yys = f(xs, aa, bb)
# loss = ((yys - ys) ** 2).mean() #sum() 대신에 mean()으로 대체
# lossesBySearch.append(loss)
# if loss < bestLoss:
# bestA, bestB = aa, bb
# bestLoss = loss
# tf = time.time()
# print("Truth:",a,b)
# print("Fit results:", bestA,bestB)
# print("Elapsed time:", (tf-t0))
# 2차함수
bestA, bestB, bestC = None, None, None
bestLoss = 1e9 # 10의 9승
t0 = time.time()
lossesBySearch = []
#numpy 모듈의 arange 함수는 반열린구간 [start, stop) 에서 step 의 크기만큼 일정하게 떨어져 있는 숫자들을 array 형태로 반환해 주는 함수다.
for aa in np.arange(0,2,0.1):
for bb in np.arange(0,2,0.1):
for cc in np.arange(0,1,0.01):
yys = f(xs, aa, bb, cc)
loss = ((yys - ys) ** 2).mean() #sum() 대신에 mean()으로 대체
lossesBySearch.append(loss)
if loss < bestLoss:
bestA, bestB, bestC = aa, bb, cc
bestLoss = loss
tf = time.time()
print("Truth:",a,b,c)
print("Fit results:", bestA,bestB,bestC)
print("Elapsed time:", (tf-t0))
Truth: 1.5 1.6 0.1
Fit results: 1.9000000000000001 1.9000000000000001 0.72
Elapsed time: 0.8331818580627441
plt.plot(lossesBySearch)
[<matplotlib.lines.Line2D at 0x1dc0e3dc710>]
# #1방법
# plt.plot(xs,ys,'.')
# plt.plot([xmin,xmax], [f(xmin,a,b), f(xmax,a,b)])
# xxs = np.linspace(xmin,xmax,100)
# yys = f(xxs,bestA,bestB)
#2방법
plt.plot(xs,ys,'.')
xxs = np.linspace(xmin,xmax,100)
yBest = f(xxs, bestA, bestB,bestC)
yTrue = f(xxs,a,b,c)
plt.plot(xxs, yTrue)
plt.plot(xxs, yBest)
[<matplotlib.lines.Line2D at 0x1dc0e4279b0>]
# 1차함수
# def gradF(x,a,b): #gradient 계산
# return (x,1)
# 2차함수
def gradF(x,a,b,c): #gradient 계산
## y = a*x*x + b*x +c
# return (x*x,x,1)
da = np.sin(b*x+c)
db = a*np.cos(b*x+c)*x
dc = a*np.cos(b*x+c)
return (da,db, dc)
# #1차함수
# t0 = time.time()
# fitA, fitB = -10,-10
# eta = 1e-4 #parameter 파라미터
# lossesByGrad = []
# for i in range(100000):
# yys = f(xs,fitA,fitB)
# gradA , gradB = gradF(xs, fitA, fitB)
# fitA = fitA - eta*((yys-ys)*gradA).mean() # sum()대신에 mean()으로 대체
# fitB = fitB - eta*((yys-ys)*gradB).mean()
# loss = ((yys-ys)**2).sum()
# lossesByGrad.append(loss)
# tf = time.time()
# print("Truth:",a,b)
# print("Fit results:",fitA,fitB)
# print("Elapsed time:",(tf-t0))
#2차함수
t0 = time.time()
fitA, fitB, fitC = 1.5,1.5,0
eta = 1e-4
lossesByGrad = []
for i in range(100000):
yys = f(xs,fitA,fitB,fitC)
gradA , gradB, gradC = gradF(xs, fitA, fitB, fitC)
fitA = fitA - eta*((yys-ys)*gradA).mean() # sum()대신에 mean()으로 대체
fitB = fitB - eta*((yys-ys)*gradB).mean()
fitC = fitC - eta*((yys-ys)*gradC).mean()
loss = ((yys-ys)**2).sum()
lossesByGrad.append(loss)
# if loss < 1e4: break #while true일 경우 사용함
tf = time.time()
print("Truth:",a,b,c)
print("Fit results:",fitA,fitB,fitC)
print("Elapsed time:",(tf-t0))
Truth: 1.5 1.6 0.1
Fit results: 1.5085357103949482 1.600510211957475 0.10446693264475382
Elapsed time: 8.28587293624878
lossesByGrad[:100]
[372.3115604303475,
370.29432286808674,
368.28559880905647,
366.28538025208843,
364.2936589734845,
362.31042652781593,
360.335674248745,
358.36939324987077,
356.4115744255973,
354.4622084520297,
352.5212857878871,
350.58879667544386,
348.6647311414897,
346.7490789983153,
344.84182984471715,
342.9429730670281,
341.0524978401672,
339.17039312870935,
337.2966476879816,
335.43125006517545,
333.57418860048375,
331.72545142825425,
329.8850264781673,
328.0529014764271,
326.22906394698293,
324.4135012127608,
322.6062003969188,
320.8071484241159,
319.01633202180915,
317.23373772155975,
315.4593518603597,
313.6931605819791,
311.93514983832813,
310.1853053908351,
308.4436128118438,
306.7100574860269,
304.98462461181134,
303.26729920282776,
301.5580660893662,
299.8569099198536,
298.16381516234196,
296.4787661060148,
294.80174686270294,
293.132741368419,
291.4717333849038,
289.81870650118356,
288.1736441351434,
286.53652953510976,
284.9073457814502,
283.28607578817923,
281.67270230457814,
280.0672079168302,
278.4695750496577,
276.87978596797745,
275.2978227785627,
273.7236674317156,
272.1573017229508,
270.5987072946839,
269.04786563793544,
267.5047580940356,
265.96936585634296,
264.44166997197016,
262.9216513435137,
261.4092907307962,
259.90456875260975,
258.40746588846866,
256.91796248037224,
255.43603873456397,
253.96167472330544,
252.49485038665102,
251.03554553422762,
249.58373984702,
248.13941287916003,
246.70254405972005,
245.2731126945073,
243.85109796786554,
242.43647894447813,
241.02923457117356,
239.62934367873243,
238.23678498369713,
236.85153709018388,
235.4735784916958,
234.10288757293807,
232.73944261163038,
231.3832217803249,
230.03420314822043,
228.69236468297726,
227.3576842525361,
226.03013962692899,
224.70970848009316,
223.39636839168793,
222.0900968488989,
220.790871248254,
219.49866889742643,
218.21346701704107,
216.93524274247676,
215.66397312566554,
214.39963513689008,
213.14220566657758,
211.89166152708708]
plt.yscale('log')
plt.plot(lossesByGrad, '.-')
[<matplotlib.lines.Line2D at 0x1dc0e4864a8>]
# 1차함수
# plt.plot(xs,ys,'.')
# xxs = np.linspace(xmin,xmax,100)
# yGrad = f(xxs,fitA, fitB)
# yScan = f(xxs, bestA, bestB)
# yTrue = f(xxs,a,b)
# plt.plot(xxs, yTrue)
# plt.plot(xxs, yScan)
# plt.plot(xxs, yGrad)
# 2차함수
plt.plot(xs,ys,'.')
xxs = np.linspace(xmin,xmax,100)
yGrad = f(xxs,fitA, fitB, fitC)
yScan = f(xxs, bestA, bestB, bestC)
yTrue = f(xxs,a,b,c)
plt.plot(xxs, yTrue)
plt.plot(xxs, yScan)
plt.plot(xxs, yGrad)
[<matplotlib.lines.Line2D at 0x1dc0e728f98>]
