Notebook

TensorFlow로 간단한 linear regression을 구현¶

https://www.youtube.com/watch?v=mQGwjrStQgg&feature=youtu.be

Hypothesis and cost function¶

\begin{equation} H(x) = Wx+b \end{equation}\begin{equation} Cost(W,b) = \frac{1}{m} \sum_{i=1}^{m}(H(x^{(i)})-y^{(i)})^{2} \end{equation}

학습: cost가 최소가 되는 W,b를 찾는것

1. Build Graph using TF operations¶

1. 텐서플로 연산을 사용하여 그래프를 생성¶

\begin{equation} H(x) = Wx+b \end{equation}

In [1]:

import tensorflow as tf

# X and Y data
x_train = [1, 2, 3]
y_train = [1, 2, 3]

# 텐서플로가 사용하는 변수. trainable
W = tf.Variable(tf.random_normal([1]), name='weight')
b = tf.Variable(tf.random_normal([1]), name='bias')
# Our hypothesis XW+b
hypothesis = x_train * W + b

\begin{equation} Cost(W,b) = \frac{1}{m} \sum_{i=1}^{m}(H(x^{(i)})-y^{(i)})^{2} \end{equation}

In [2]:

# cost/loss function
cost = tf.reduce_mean(tf.square(hypothesis - y_train))

In [3]:

t = [1., 2., 3., 4.]
with tf.Session() as sess:
    print(sess.run(tf.reduce_mean(t)))

2.5

tf.reduce_mean(t) ==> 2.5

t의 값들의 평균을 구함

GradientDescent¶

In [4]:

# Minimize
optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.01)
train = optimizer.minimize(cost)

GradientDescent 부분을 통해 cost를 minimize함.

2. 3. Run/update graph and get results¶

2. 3. 그래프를 갱신하고 결과를 얻음¶

In [5]:

# Launch the graph in a session.
sess = tf.Session()
# Initializes global variables in the graph.
sess.run(tf.global_variables_initializer())

# Fit the line
for step in range(2001):
    sess.run(train)
    if step % 20 == 0:
        print(step, sess.run(cost), sess.run(W), sess.run(b))

0 13.1854 [-1.33570743] [ 1.58136511]
20 0.735851 [-0.04721653] [ 2.02556849]
40 0.566408 [ 0.11423562] [ 1.97974777]
60 0.513496 [ 0.16655035] [ 1.89140821]
80 0.466357 [ 0.20673704] [ 1.80296659]
100 0.423553 [ 0.24411441] [ 1.71827638]
120 0.384678 [ 0.27964747] [ 1.63752782]
140 0.34937 [ 0.31350225] [ 1.56057036]
160 0.317304 [ 0.3457652] [ 1.48722947]
180 0.28818 [ 0.37651184] [ 1.41733515]
200 0.26173 [ 0.40581352] [ 1.35072541]
220 0.237707 [ 0.43373808] [ 1.28724647]
240 0.21589 [ 0.46035028] [ 1.22675061]
260 0.196075 [ 0.48571181] [ 1.16909802]
280 0.178078 [ 0.50988138] [ 1.1141547]
300 0.161733 [ 0.53291523] [ 1.06179345]
320 0.146889 [ 0.55486649] [ 1.01189291]
340 0.133407 [ 0.57578617] [ 0.96433771]
360 0.121162 [ 0.59572256] [ 0.91901743]
380 0.110041 [ 0.61472219] [ 0.87582701]
400 0.0999414 [ 0.63282883] [ 0.83466631]
420 0.0907683 [ 0.65008456] [ 0.79544002]
440 0.0824372 [ 0.66652936] [ 0.7580573]
460 0.0748708 [ 0.68220115] [ 0.72243142]
480 0.0679988 [ 0.69713652] [ 0.68847978]
500 0.0617577 [ 0.71137005] [ 0.65612382]
520 0.0560893 [ 0.72493458] [ 0.62528843]
540 0.0509412 [ 0.73786157] [ 0.5959022]
560 0.0462656 [ 0.75018114] [ 0.56789696]
580 0.0420192 [ 0.7619217] [ 0.54120791]
600 0.0381625 [ 0.77311057] [ 0.51577306]
620 0.0346598 [ 0.7837736] [ 0.49153358]
640 0.0314786 [ 0.79393542] [ 0.46843323]
660 0.0285893 [ 0.80361968] [ 0.44641864]
680 0.0259653 [ 0.81284875] [ 0.42543861]
700 0.0235821 [ 0.82164425] [ 0.40544456]
720 0.0214176 [ 0.83002627] [ 0.38639015]
740 0.0194518 [ 0.83801442] [ 0.36823127]
760 0.0176665 [ 0.84562713] [ 0.35092577]
780 0.016045 [ 0.85288209] [ 0.33443353]
800 0.0145723 [ 0.85979611] [ 0.31871641]
820 0.0132348 [ 0.86638516] [ 0.30373788]
840 0.0120201 [ 0.87266451] [ 0.28946337]
860 0.0109168 [ 0.87864894] [ 0.27585965]
880 0.00991482 [ 0.88435191] [ 0.26289526]
900 0.0090048 [ 0.88978696] [ 0.25054011]
920 0.0081783 [ 0.89496654] [ 0.23876567]
940 0.00742766 [ 0.89990282] [ 0.22754458]
960 0.00674593 [ 0.904607] [ 0.21685077]
980 0.00612676 [ 0.9090901] [ 0.20665959]
1000 0.00556442 [ 0.91336256] [ 0.19694737]
1020 0.0050537 [ 0.91743416] [ 0.18769155]
1040 0.00458985 [ 0.92131442] [ 0.17887077]
1060 0.00416857 [ 0.92501235] [ 0.17046453]
1080 0.00378597 [ 0.92853642] [ 0.16245335]
1100 0.00343848 [ 0.93189502] [ 0.15481864]
1120 0.00312288 [ 0.93509567] [ 0.14754273]
1140 0.00283625 [ 0.938146] [ 0.1406088]
1160 0.00257592 [ 0.94105291] [ 0.13400066]
1180 0.0023395 [ 0.94382322] [ 0.12770312]
1200 0.00212477 [ 0.94646329] [ 0.12170152]
1220 0.00192974 [ 0.94897938] [ 0.11598199]
1240 0.00175263 [ 0.95137715] [ 0.11053121]
1260 0.00159176 [ 0.95366216] [ 0.10533665]
1280 0.00144566 [ 0.95583993] [ 0.10038622]
1300 0.00131298 [ 0.95791525] [ 0.09566843]
1320 0.00119246 [ 0.95989305] [ 0.09117243]
1340 0.00108302 [ 0.96177793] [ 0.08688767]
1360 0.000983619 [ 0.96357429] [ 0.08280428]
1380 0.000893336 [ 0.96528614] [ 0.07891276]
1400 0.000811341 [ 0.96691757] [ 0.07520416]
1420 0.000736873 [ 0.96847236] [ 0.07166984]
1440 0.00066924 [ 0.96995401] [ 0.06830166]
1460 0.000607814 [ 0.97136605] [ 0.06509172]
1480 0.000552024 [ 0.9727118] [ 0.06203262]
1500 0.000501358 [ 0.9739942] [ 0.0591173]
1520 0.000455342 [ 0.97521639] [ 0.05633902]
1540 0.000413548 [ 0.97638112] [ 0.05369127]
1560 0.000375591 [ 0.97749114] [ 0.05116797]
1580 0.000341117 [ 0.97854894] [ 0.04876323]
1600 0.00030981 [ 0.97955704] [ 0.04647155]
1620 0.000281374 [ 0.98051786] [ 0.04428752]
1640 0.000255547 [ 0.98143345] [ 0.04220613]
1660 0.000232092 [ 0.982306] [ 0.04022259]
1680 0.000210791 [ 0.98313755] [ 0.03833229]
1700 0.000191443 [ 0.98393005] [ 0.03653081]
1720 0.000173872 [ 0.9846853] [ 0.034814]
1740 0.000157911 [ 0.98540503] [ 0.03317784]
1760 0.000143417 [ 0.98609096] [ 0.03161858]
1780 0.000130254 [ 0.98674464] [ 0.03013258]
1800 0.000118299 [ 0.98736757] [ 0.02871647]
1820 0.000107442 [ 0.98796123] [ 0.02736692]
1840 9.75799e-05 [ 0.988527] [ 0.02608078]
1860 8.8623e-05 [ 0.98906618] [ 0.02485507]
1880 8.04903e-05 [ 0.98957992] [ 0.02368699]
1900 7.31019e-05 [ 0.99006969] [ 0.02257388]
1920 6.63927e-05 [ 0.99053645] [ 0.02151295]
1940 6.02978e-05 [ 0.99098122] [ 0.02050187]
1960 5.47633e-05 [ 0.99140507] [ 0.01953833]
1980 4.97365e-05 [ 0.99180901] [ 0.01862007]
2000 4.51714e-05 [ 0.992194] [ 0.01774498]

Placeholders¶

Placeholder: 세션을 실행할 때 필요한 값을 넘길 때 사용.

In [6]:

X = tf.placeholder(tf.float32, shape=[None]) ###
Y = tf.placeholder(tf.float32, shape=[None]) ###

# 텐서플로가 사용하는 변수. trainable
W = tf.Variable(tf.random_normal([1]), name='weight')
b = tf.Variable(tf.random_normal([1]), name='bias')
# Our hypothesis XW+b
hypothesis = X * W + b ##

# cost/loss function
cost = tf.reduce_mean(tf.square(hypothesis - Y))

# Minimize
optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.01)
train = optimizer.minimize(cost)

# Launch the graph in a session.
sess = tf.Session()
# Initializes global variables in the graph.
sess.run(tf.global_variables_initializer())

# Fit the line
for step in range(2001):
    cost_val, W_val, b_val, _ = sess.run([cost, W, b, train],
        feed_dict={X:[1,2,3,4,5],Y:[2.1,3.1,4.1,5.1,6.1]})
    if step % 20 == 0:
        print(step, cost_val, W_val, b_val)

0 23.297 [ 1.96590233] [ 1.62496638]
20 0.00962304 [ 0.94277626] [ 1.32471764]
40 0.00798899 [ 0.94218838] [ 1.30879986]
60 0.00697683 [ 0.94595498] [ 1.29511988]
80 0.0060929 [ 0.94949448] [ 1.282341]
100 0.00532099 [ 0.95280206] [ 1.27039945]
120 0.00464685 [ 0.9558931] [ 1.25923967]
140 0.00405813 [ 0.95878166] [ 1.24881101]
160 0.00354399 [ 0.96148115] [ 1.23906517]
180 0.00309499 [ 0.96400386] [ 1.22995758]
200 0.00270288 [ 0.96636122] [ 1.22144663]
220 0.00236043 [ 0.96856421] [ 1.21349287]
240 0.00206139 [ 0.97062302] [ 1.20606029]
260 0.00180021 [ 0.97254694] [ 1.19911397]
280 0.00157214 [ 0.97434491] [ 1.19262278]
300 0.00137297 [ 0.9760251] [ 1.18655694]
320 0.00119902 [ 0.97759521] [ 1.1808883]
340 0.00104712 [ 0.9790625] [ 1.17559099]
360 0.000914452 [ 0.98043376] [ 1.17064023]
380 0.0007986 [ 0.9817152] [ 1.16601384]
400 0.000697417 [ 0.98291272] [ 1.16169024]
420 0.000609056 [ 0.9840318] [ 1.15764999]
440 0.000531887 [ 0.98507762] [ 1.1538744]
460 0.000464507 [ 0.98605484] [ 1.1503464]
480 0.000405663 [ 0.9869681] [ 1.14704931]
500 0.000354267 [ 0.98782152] [ 1.14396811]
520 0.000309387 [ 0.98861903] [ 1.14108884]
540 0.00027019 [ 0.98936439] [ 1.13839781]
560 0.000235956 [ 0.99006093] [ 1.13588309]
580 0.000206065 [ 0.99071187] [ 1.133533]
600 0.000179956 [ 0.99132019] [ 1.13133681]
620 0.000157154 [ 0.99188864] [ 1.1292845]
640 0.000137247 [ 0.99241984] [ 1.12736666]
660 0.000119859 [ 0.99291629] [ 1.12557435]
680 0.000104673 [ 0.99338013] [ 1.12389958]
700 9.14121e-05 [ 0.99381369] [ 1.12233436]
720 7.98333e-05 [ 0.99421877] [ 1.1208719]
740 6.97188e-05 [ 0.99459738] [ 1.11950505]
760 6.08877e-05 [ 0.99495119] [ 1.11822772]
780 5.31733e-05 [ 0.99528182] [ 1.11703408]
800 4.6437e-05 [ 0.99559087] [ 1.1159184]
820 4.0554e-05 [ 0.99587953] [ 1.11487603]
840 3.54157e-05 [ 0.99614942] [ 1.11390185]
860 3.09304e-05 [ 0.99640155] [ 1.11299145]
880 2.70114e-05 [ 0.99663723] [ 1.11214054]
900 2.35899e-05 [ 0.99685746] [ 1.11134553]
920 2.06012e-05 [ 0.99706328] [ 1.11060238]
940 1.79884e-05 [ 0.99725574] [ 1.10990739]
960 1.57094e-05 [ 0.99743551] [ 1.10925865]
980 1.37192e-05 [ 0.99760342] [ 1.10865223]
1000 1.19814e-05 [ 0.99776036] [ 1.10808563]
1020 1.04639e-05 [ 0.99790704] [ 1.10755622]
1040 9.13835e-06 [ 0.99804407] [ 1.10706139]
1060 7.98016e-06 [ 0.99817216] [ 1.10659885]
1080 6.96877e-06 [ 0.99829185] [ 1.10616672]
1100 6.08597e-06 [ 0.99840379] [ 1.10576284]
1120 5.31547e-06 [ 0.99850827] [ 1.10538554]
1140 4.64177e-06 [ 0.99860597] [ 1.10503268]
1160 4.05328e-06 [ 0.99869728] [ 1.10470307]
1180 3.54009e-06 [ 0.99878258] [ 1.10439515]
1200 3.0916e-06 [ 0.99886233] [ 1.10410726]
1220 2.69998e-06 [ 0.99893683] [ 1.10383832]
1240 2.3579e-06 [ 0.99900645] [ 1.10358703]
1260 2.05914e-06 [ 0.99907148] [ 1.10335219]
1280 1.79858e-06 [ 0.99913228] [ 1.10313272]
1300 1.57044e-06 [ 0.99918902] [ 1.10292757]
1320 1.3717e-06 [ 0.99924219] [ 1.10273588]
1340 1.19803e-06 [ 0.99929178] [ 1.10255671]
1360 1.04596e-06 [ 0.99933821] [ 1.10238922]
1380 9.13619e-07 [ 0.99938154] [ 1.10223258]
1400 7.97728e-07 [ 0.99942201] [ 1.10208642]
1420 6.96617e-07 [ 0.99945992] [ 1.10194981]
1440 6.0862e-07 [ 0.99949527] [ 1.10182214]
1460 5.31349e-07 [ 0.99952829] [ 1.10170281]
1480 4.64173e-07 [ 0.9995591] [ 1.10159147]
1500 4.05457e-07 [ 0.99958801] [ 1.1014874]
1520 3.54099e-07 [ 0.99961495] [ 1.10138988]
1540 3.09269e-07 [ 0.99964017] [ 1.10129905]
1560 2.69982e-07 [ 0.99966371] [ 1.10121381]
1580 2.35905e-07 [ 0.9996857] [ 1.10113442]
1600 2.05917e-07 [ 0.99970639] [ 1.10106015]
1620 1.79893e-07 [ 0.99972558] [ 1.10099077]
1640 1.57064e-07 [ 0.99974358] [ 1.1009258]
1660 1.37143e-07 [ 0.99976033] [ 1.10086513]
1680 1.19873e-07 [ 0.99977601] [ 1.10080862]
1700 1.04663e-07 [ 0.99979061] [ 1.10075557]
1720 9.15154e-08 [ 0.99980432] [ 1.10070634]
1740 7.99159e-08 [ 0.99981713] [ 1.10066009]
1760 6.97393e-08 [ 0.99982917] [ 1.10061669]
1780 6.08945e-08 [ 0.99984032] [ 1.10057628]
1800 5.31413e-08 [ 0.99985081] [ 1.10053861]
1820 4.64375e-08 [ 0.99986058] [ 1.10050344]
1840 4.05344e-08 [ 0.9998697] [ 1.1004703]
1860 3.54076e-08 [ 0.99987817] [ 1.10043943]
1880 3.09444e-08 [ 0.99988616] [ 1.10041082]
1900 2.7042e-08 [ 0.99989355] [ 1.10038412]
1920 2.36139e-08 [ 0.99990052] [ 1.10035908]
1940 2.06039e-08 [ 0.99990708] [ 1.10033524]
1960 1.80461e-08 [ 0.9999131] [ 1.10031366]
1980 1.57384e-08 [ 0.99991882] [ 1.10029304]
2000 1.37607e-08 [ 0.999924] [ 1.10027397]

학습데이터를 feed_dict로 같이 전달할 수 있음.

tf.placeholder에는 인자로 shape=[None]을 줄 수 있고 원하는대로 값을 줄 수 있고 개수의 제한이 없다는 뜻임

In [7]:

# Testing our model, H(x) = 1.0 x + 1.1
print(sess.run(hypothesis, feed_dict={X: [5]}))   # [6.1]
print(sess.run(hypothesis, feed_dict={X: [2.5]})) # [3.6]
print(sess.run(hypothesis, feed_dict={X: [1.5, 3.5]})) # [2.6, 4.6]

[ 6.09989405]
[ 3.60008383]
[ 2.60016012  4.60000801]