程序代写代做代考 python In [1]:

In [1]:
import pandas as pd
import numpy as np
import numpy as np
import matplotlib.pyplot as plt

1.1¶
In [2]:
data = pd.read_csv(‘./houses1.csv’)
In [3]:
data.describe()
Out[3]:

price (grands)
bedrooms
bathrooms
sqft_living
sqft_lot
floors
waterfront
view
condition
grade
sqft_above
sqft_basement
age
renovated_age
sqft_living15
sqft_lot15
count
21613.000000
21613.000000
21613.000000
21613.000000
2.161300e+04
21613.000000
21613.000000
21613.000000
21613.000000
21613.000000
21613.000000
21613.000000
21613.000000
21613.000000
21613.000000
21613.000000
mean
540.088142
3.370842
2.114757
2079.899736
1.510697e+04
1.494309
0.007542
0.234303
3.409430
7.656873
1788.390691
291.509045
45.994864
2.380882
1986.552492
12768.455652
std
367.127196
0.930062
0.770163
918.440897
4.142051e+04
0.539989
0.086517
0.766318
0.650743
1.175459
828.090978
442.575043
29.373411
12.359528
685.391304
27304.179631
min
75.000000
0.000000
0.000000
290.000000
5.200000e+02
1.000000
0.000000
0.000000
1.000000
1.000000
290.000000
0.000000
2.000000
0.000000
399.000000
651.000000
25%
321.950000
3.000000
1.750000
1427.000000
5.040000e+03
1.000000
0.000000
0.000000
3.000000
7.000000
1190.000000
0.000000
20.000000
0.000000
1490.000000
5100.000000
50%
450.000000
3.000000
2.250000
1910.000000
7.618000e+03
1.500000
0.000000
0.000000
3.000000
7.000000
1560.000000
0.000000
42.000000
0.000000
1840.000000
7620.000000
75%
645.000000
4.000000
2.500000
2550.000000
1.068800e+04
2.000000
0.000000
0.000000
4.000000
8.000000
2210.000000
560.000000
66.000000
0.000000
2360.000000
10083.000000
max
7700.000000
33.000000
8.000000
13540.000000
1.651359e+06
3.500000
1.000000
4.000000
5.000000
13.000000
9410.000000
4820.000000
117.000000
114.000000
6210.000000
871200.000000
In [4]:
#split target and feature
y = data[‘price (grands)’]
X = data.drop(‘price (grands)’,axis=1)
In [5]:
#extract the sqft_living column into a feature vector name X_1
X[‘X_1’] = X[‘sqft_living’]
In [6]:
X.head(3)
Out[6]:

bedrooms
bathrooms
sqft_living
sqft_lot
floors
waterfront
view
condition
grade
sqft_above
sqft_basement
age
renovated_age
sqft_living15
sqft_lot15
X_1
0
3
1.00
1180
5650
1.0
0
0
3
7
1180
0
62
0
1340
5650
1180
1
3
2.25
2570
7242
2.0
0
0
3
7
2170
400
66
40
1690
7639
2570
2
2
1.00
770
10000
1.0
0
0
3
6
770
0
84
0
2720
8062
770
In [7]:
y.head(3)
Out[7]:
0 221.9
1 538.0
2 180.0
Name: price (grands), dtype: float64
In [ ]:

1.2 Linear Regression¶
In [8]:
y = y.values
y = (y-y.min())/(y.max()-y.min())
In [9]:
from sklearn.preprocessing import MinMaxScaler,StandardScaler,Imputer
scale = MinMaxScaler()
X = scale.fit_transform(X)

D:\Anaconda\anaconda\lib\site-packages\sklearn\preprocessing\data.py:334: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by MinMaxScaler.
return self.partial_fit(X, y)
In [ ]:

In [10]:
class LinearRegression(object):
def __init__(self,learning_rate,epochs,is_print_loss=True):
self.lr = learning_rate
self.epochs = epochs
self.theta = None
self.baise = None
self.print_loss = is_print_loss

def cost(self,y,update):
loss = np.dot((y-update).T, y-update)/len(y)
return loss.mean()

def gradient(self,x,y,update):
dleta = -(2/x.shape[0])*np.dot((y-update).T,x)
return dleta

def fit(self,X,y):
self.theta = np.ones(shape=(1,X.shape[1]))
self.baise = np.asarray([1])
self.cost_arr = []

for epoch in range(self.epochs):
update = np.dot(X,self.theta.T)+self.baise
loss = self.cost(y,update)
theta_update= self.gradient(X,y,update)
biase_update = -2*np.dot((y-update).T,
np.ones(shape=[X.shape[0],1]))/X.shape[0]

self.theta=self.theta-self.lr*theta_update
self.baise=self.baise-self.lr*biase_update
self.cost_arr.append(loss)
if self.print_loss:
print(‘epoch: {}\tloss: {:.4f}’.format(epoch,loss))

def predict(self,X):
pred = np.dot(X, self.theta[0,:]) + self.baise[0]
return pred

In [11]:
def linear_regression(lr,X,target,iteration):
lr = LinearRegression(learning_rate=lr,epochs=iteration,is_print_loss=True)
lr.fit(X,target)

return lr

def predict(X,params):
pred = params.predict(X)
return pred
In [12]:
lr = linear_regression(lr=0.001,iteration=10000,X=X[:200,:],target=y[:200])

epoch: 0 loss: 15.7763
epoch: 1 loss: 15.6447
epoch: 2 loss: 15.5142
epoch: 3 loss: 15.3848
epoch: 4 loss: 15.2565
epoch: 5 loss: 15.1293
epoch: 6 loss: 15.0032
epoch: 7 loss: 14.8781
epoch: 8 loss: 14.7541
epoch: 9 loss: 14.6312
epoch: 10 loss: 14.5092
epoch: 11 loss: 14.3884
epoch: 12 loss: 14.2685
epoch: 13 loss: 14.1496
epoch: 14 loss: 14.0318
epoch: 15 loss: 13.9149
epoch: 16 loss: 13.7990
epoch: 17 loss: 13.6842
epoch: 18 loss: 13.5702
epoch: 19 loss: 13.4573
epoch: 20 loss: 13.3453
epoch: 21 loss: 13.2342
epoch: 22 loss: 13.1241
epoch: 23 loss: 13.0149
epoch: 24 loss: 12.9067
epoch: 25 loss: 12.7993
epoch: 26 loss: 12.6929
epoch: 27 loss: 12.5873
epoch: 28 loss: 12.4827
epoch: 29 loss: 12.3789
epoch: 30 loss: 12.2760
epoch: 31 loss: 12.1740
epoch: 32 loss: 12.0728
epoch: 33 loss: 11.9725
epoch: 34 loss: 11.8731
epoch: 35 loss: 11.7744
epoch: 36 loss: 11.6767
epoch: 37 loss: 11.5797
epoch: 38 loss: 11.4836
epoch: 39 loss: 11.3882
epoch: 40 loss: 11.2937
epoch: 41 loss: 11.2000
epoch: 42 loss: 11.1071
epoch: 43 loss: 11.0149
epoch: 44 loss: 10.9236
epoch: 45 loss: 10.8330
epoch: 46 loss: 10.7431
epoch: 47 loss: 10.6541
epoch: 48 loss: 10.5658
epoch: 49 loss: 10.4782
epoch: 50 loss: 10.3914
epoch: 51 loss: 10.3053
epoch: 52 loss: 10.2199
epoch: 53 loss: 10.1353
epoch: 54 loss: 10.0513
epoch: 55 loss: 9.9681
epoch: 56 loss: 9.8856
epoch: 57 loss: 9.8038
epoch: 58 loss: 9.7226
epoch: 59 loss: 9.6422
epoch: 60 loss: 9.5624
epoch: 61 loss: 9.4833
epoch: 62 loss: 9.4049
epoch: 63 loss: 9.3271
epoch: 64 loss: 9.2500
epoch: 65 loss: 9.1736
epoch: 66 loss: 9.0978
epoch: 67 loss: 9.0226
epoch: 68 loss: 8.9481
epoch: 69 loss: 8.8742
epoch: 70 loss: 8.8009
epoch: 71 loss: 8.7282
epoch: 72 loss: 8.6562
epoch: 73 loss: 8.5848
epoch: 74 loss: 8.5139
epoch: 75 loss: 8.4437
epoch: 76 loss: 8.3741
epoch: 77 loss: 8.3050
epoch: 78 loss: 8.2366
epoch: 79 loss: 8.1687
epoch: 80 loss: 8.1013
epoch: 81 loss: 8.0346
epoch: 82 loss: 7.9684
epoch: 83 loss: 7.9028
epoch: 84 loss: 7.8377
epoch: 85 loss: 7.7732
epoch: 86 loss: 7.7092
epoch: 87 loss: 7.6458
epoch: 88 loss: 7.5829
epoch: 89 loss: 7.5205
epoch: 90 loss: 7.4587
epoch: 91 loss: 7.3974
epoch: 92 loss: 7.3366
epoch: 93 loss: 7.2763
epoch: 94 loss: 7.2165
epoch: 95 loss: 7.1573
epoch: 96 loss: 7.0985
epoch: 97 loss: 7.0402
epoch: 98 loss: 6.9824
epoch: 99 loss: 6.9251
epoch: 100 loss: 6.8683
epoch: 101 loss: 6.8120
epoch: 102 loss: 6.7562
epoch: 103 loss: 6.7008
epoch: 104 loss: 6.6459
epoch: 105 loss: 6.5914
epoch: 106 loss: 6.5374
epoch: 107 loss: 6.4839
epoch: 108 loss: 6.4308
epoch: 109 loss: 6.3782
epoch: 110 loss: 6.3260
epoch: 111 loss: 6.2743
epoch: 112 loss: 6.2230
epoch: 113 loss: 6.1721
epoch: 114 loss: 6.1216
epoch: 115 loss: 6.0716
epoch: 116 loss: 6.0220
epoch: 117 loss: 5.9728
epoch: 118 loss: 5.9241
epoch: 119 loss: 5.8757
epoch: 120 loss: 5.8278
epoch: 121 loss: 5.7803
epoch: 122 loss: 5.7331
epoch: 123 loss: 5.6864
epoch: 124 loss: 5.6400
epoch: 125 loss: 5.5941
epoch: 126 loss: 5.5485
epoch: 127 loss: 5.5034
epoch: 128 loss: 5.4586
epoch: 129 loss: 5.4141
epoch: 130 loss: 5.3701
epoch: 131 loss: 5.3264
epoch: 132 loss: 5.2831
epoch: 133 loss: 5.2402
epoch: 134 loss: 5.1976
epoch: 135 loss: 5.1554
epoch: 136 loss: 5.1136
epoch: 137 loss: 5.0721
epoch: 138 loss: 5.0309
epoch: 139 loss: 4.9901
epoch: 140 loss: 4.9496
epoch: 141 loss: 4.9095
epoch: 142 loss: 4.8697
epoch: 143 loss: 4.8303
epoch: 144 loss: 4.7912
epoch: 145 loss: 4.7524
epoch: 146 loss: 4.7140
epoch: 147 loss: 4.6758
epoch: 148 loss: 4.6380
epoch: 149 loss: 4.6006
epoch: 150 loss: 4.5634
epoch: 151 loss: 4.5265
epoch: 152 loss: 4.4900
epoch: 153 loss: 4.4538
epoch: 154 loss: 4.4178
epoch: 155 loss: 4.3822
epoch: 156 loss: 4.3469
epoch: 157 loss: 4.3119
epoch: 158 loss: 4.2771
epoch: 159 loss: 4.2427
epoch: 160 loss: 4.2086
epoch: 161 loss: 4.1747
epoch: 162 loss: 4.1411
epoch: 163 loss: 4.1078
epoch: 164 loss: 4.0748
epoch: 165 loss: 4.0421
epoch: 166 loss: 4.0097
epoch: 167 loss: 3.9775
epoch: 168 loss: 3.9456
epoch: 169 loss: 3.9139
epoch: 170 loss: 3.8826
epoch: 171 loss: 3.8515
epoch: 172 loss: 3.8206
epoch: 173 loss: 3.7901
epoch: 174 loss: 3.7597
epoch: 175 loss: 3.7297
epoch: 176 loss: 3.6999
epoch: 177 loss: 3.6703
epoch: 178 loss: 3.6410
epoch: 179 loss: 3.6119
epoch: 180 loss: 3.5831
epoch: 181 loss: 3.5545
epoch: 182 loss: 3.5262
epoch: 183 loss: 3.4981
epoch: 184 loss: 3.4703
epoch: 185 loss: 3.4426
epoch: 186 loss: 3.4153
epoch: 187 loss: 3.3881
epoch: 188 loss: 3.3612
epoch: 189 loss: 3.3345
epoch: 190 loss: 3.3080
epoch: 191 loss: 3.2818
epoch: 192 loss: 3.2557
epoch: 193 loss: 3.2299
epoch: 194 loss: 3.2043
epoch: 195 loss: 3.1790
epoch: 196 loss: 3.1538
epoch: 197 loss: 3.1289
epoch: 198 loss: 3.1041
epoch: 199 loss: 3.0796
epoch: 200 loss: 3.0553
epoch: 201 loss: 3.0312
epoch: 202 loss: 3.0073
epoch: 203 loss: 2.9836
epoch: 204 loss: 2.9600
epoch: 205 loss: 2.9367
epoch: 206 loss: 2.9136
epoch: 207 loss: 2.8907
epoch: 208 loss: 2.8680
epoch: 209 loss: 2.8454
epoch: 210 loss: 2.8231
epoch: 211 loss: 2.8010
epoch: 212 loss: 2.7790
epoch: 213 loss: 2.7572
epoch: 214 loss: 2.7356
epoch: 215 loss: 2.7142
epoch: 216 loss: 2.6930
epoch: 217 loss: 2.6719
epoch: 218 loss: 2.6510
epoch: 219 loss: 2.6303
epoch: 220 loss: 2.6098
epoch: 221 loss: 2.5895
epoch: 222 loss: 2.5693
epoch: 223 loss: 2.5493
epoch: 224 loss: 2.5294
epoch: 225 loss: 2.5098
epoch: 226 loss: 2.4903
epoch: 227 loss: 2.4709
epoch: 228 loss: 2.4517
epoch: 229 loss: 2.4327
epoch: 230 loss: 2.4139
epoch: 231 loss: 2.3952
epoch: 232 loss: 2.3766
epoch: 233 loss: 2.3582
epoch: 234 loss: 2.3400
epoch: 235 loss: 2.3219
epoch: 236 loss: 2.3040
epoch: 237 loss: 2.2863
epoch: 238 loss: 2.2686
epoch: 239 loss: 2.2512
epoch: 240 loss: 2.2338
epoch: 241 loss: 2.2167
epoch: 242 loss: 2.1996
epoch: 243 loss: 2.1827
epoch: 244 loss: 2.1660
epoch: 245 loss: 2.1494
epoch: 246 loss: 2.1329
epoch: 247 loss: 2.1166
epoch: 248 loss: 2.1004
epoch: 249 loss: 2.0844
epoch: 250 loss: 2.0685
epoch: 251 loss: 2.0527
epoch: 252 loss: 2.0370
epoch: 253 loss: 2.0215
epoch: 254 loss: 2.0061
epoch: 255 loss: 1.9909
epoch: 256 loss: 1.9758
epoch: 257 loss: 1.9608
epoch: 258 loss: 1.9459
epoch: 259 loss: 1.9311
epoch: 260 loss: 1.9165
epoch: 261 loss: 1.9020
epoch: 262 loss: 1.8877
epoch: 263 loss: 1.8734
epoch: 264 loss: 1.8593
epoch: 265 loss: 1.8453
epoch: 266 loss: 1.8314
epoch: 267 loss: 1.8176
epoch: 268 loss: 1.8039
epoch: 269 loss: 1.7904
epoch: 270 loss: 1.7769
epoch: 271 loss: 1.7636
epoch: 272 loss: 1.7504
epoch: 273 loss: 1.7373
epoch: 274 loss: 1.7243
epoch: 275 loss: 1.7115
epoch: 276 loss: 1.6987
epoch: 277 loss: 1.6860
epoch: 278 loss: 1.6735
epoch: 279 loss: 1.6610
epoch: 280 loss: 1.6487
epoch: 281 loss: 1.6365
epoch: 282 loss: 1.6243
epoch: 283 loss: 1.6123
epoch: 284 loss: 1.6004
epoch: 285 loss: 1.5885
epoch: 286 loss: 1.5768
epoch: 287 loss: 1.5652
epoch: 288 loss: 1.5537
epoch: 289 loss: 1.5422
epoch: 290 loss: 1.5309
epoch: 291 loss: 1.5196
epoch: 292 loss: 1.5085
epoch: 293 loss: 1.4974
epoch: 294 loss: 1.4865
epoch: 295 loss: 1.4756
epoch: 296 loss: 1.4648
epoch: 297 loss: 1.4542
epoch: 298 loss: 1.4436
epoch: 299 loss: 1.4331
epoch: 300 loss: 1.4226
epoch: 301 loss: 1.4123
epoch: 302 loss: 1.4021
epoch: 303 loss: 1.3919
epoch: 304 loss: 1.3819
epoch: 305 loss: 1.3719
epoch: 306 loss: 1.3620
epoch: 307 loss: 1.3522
epoch: 308 loss: 1.3424
epoch: 309 loss: 1.3328
epoch: 310 loss: 1.3232
epoch: 311 loss: 1.3137
epoch: 312 loss: 1.3043
epoch: 313 loss: 1.2950
epoch: 314 loss: 1.2857
epoch: 315 loss: 1.2765
epoch: 316 loss: 1.2675
epoch: 317 loss: 1.2584
epoch: 318 loss: 1.2495
epoch: 319 loss: 1.2406
epoch: 320 loss: 1.2318
epoch: 321 loss: 1.2231
epoch: 322 loss: 1.2145
epoch: 323 loss: 1.2059
epoch: 324 loss: 1.1974
epoch: 325 loss: 1.1890
epoch: 326 loss: 1.1806
epoch: 327 loss: 1.1723
epoch: 328 loss: 1.1641
epoch: 329 loss: 1.1560
epoch: 330 loss: 1.1479
epoch: 331 loss: 1.1399
epoch: 332 loss: 1.1319
epoch: 333 loss: 1.1241
epoch: 334 loss: 1.1162
epoch: 335 loss: 1.1085
epoch: 336 loss: 1.1008
epoch: 337 loss: 1.0932
epoch: 338 loss: 1.0857
epoch: 339 loss: 1.0782
epoch: 340 loss: 1.0708
epoch: 341 loss: 1.0634
epoch: 342 loss: 1.0561
epoch: 343 loss: 1.0489
epoch: 344 loss: 1.0417
epoch: 345 loss: 1.0346
epoch: 346 loss: 1.0275
epoch: 347 loss: 1.0205
epoch: 348 loss: 1.0136
epoch: 349 loss: 1.0067
epoch: 350 loss: 0.9999
epoch: 351 loss: 0.9931
epoch: 352 loss: 0.9864
epoch: 353 loss: 0.9798
epoch: 354 loss: 0.9732
epoch: 355 loss: 0.9667
epoch: 356 loss: 0.9602
epoch: 357 loss: 0.9537
epoch: 358 loss: 0.9474
epoch: 359 loss: 0.9410
epoch: 360 loss: 0.9348
epoch: 361 loss: 0.9286
epoch: 362 loss: 0.9224
epoch: 363 loss: 0.9163
epoch: 364 loss: 0.9102
epoch: 365 loss: 0.9042
epoch: 366 loss: 0.8983
epoch: 367 loss: 0.8924
epoch: 368 loss: 0.8865
epoch: 369 loss: 0.8807
epoch: 370 loss: 0.8750
epoch: 371 loss: 0.8692
epoch: 372 loss: 0.8636
epoch: 373 loss: 0.8580
epoch: 374 loss: 0.8524
epoch: 375 loss: 0.8469
epoch: 376 loss: 0.8414
epoch: 377 loss: 0.8360
epoch: 378 loss: 0.8306
epoch: 379 loss: 0.8253
epoch: 380 loss: 0.8200
epoch: 381 loss: 0.8147
epoch: 382 loss: 0.8095
epoch: 383 loss: 0.8044
epoch: 384 loss: 0.7993
epoch: 385 loss: 0.7942
epoch: 386 loss: 0.7892
epoch: 387 loss: 0.7842
epoch: 388 loss: 0.7792
epoch: 389 loss: 0.7743
epoch: 390 loss: 0.7695
epoch: 391 loss: 0.7647
epoch: 392 loss: 0.7599
epoch: 393 loss: 0.7551
epoch: 394 loss: 0.7504
epoch: 395 loss: 0.7458
epoch: 396 loss: 0.7412
epoch: 397 loss: 0.7366
epoch: 398 loss: 0.7320
epoch: 399 loss: 0.7275
epoch: 400 loss: 0.7231
epoch: 401 loss: 0.7186
epoch: 402 loss: 0.7142
epoch: 403 loss: 0.7099
epoch: 404 loss: 0.7056
epoch: 405 loss: 0.7013
epoch: 406 loss: 0.6970
epoch: 407 loss: 0.6928
epoch: 408 loss: 0.6886
epoch: 409 loss: 0.6845
epoch: 410 loss: 0.6804
epoch: 411 loss: 0.6763
epoch: 412 loss: 0.6723
epoch: 413 loss: 0.6683
epoch: 414 loss: 0.6643
epoch: 415 loss: 0.6604
epoch: 416 loss: 0.6565
epoch: 417 loss: 0.6526
epoch: 418 loss: 0.6488
epoch: 419 loss: 0.6450
epoch: 420 loss: 0.6412
epoch: 421 loss: 0.6375
epoch: 422 loss: 0.6338
epoch: 423 loss: 0.6301
epoch: 424 loss: 0.6264
epoch: 425 loss: 0.6228
epoch: 426 loss: 0.6192
epoch: 427 loss: 0.6157
epoch: 428 loss: 0.6121
epoch: 429 loss: 0.6087
epoch: 430 loss: 0.6052
epoch: 431 loss: 0.6017
epoch: 432 loss: 0.5983
epoch: 433 loss: 0.5950
epoch: 434 loss: 0.5916
epoch: 435 loss: 0.5883
epoch: 436 loss: 0.5850
epoch: 437 loss: 0.5817
epoch: 438 loss: 0.5785
epoch: 439 loss: 0.5753
epoch: 440 loss: 0.5721
epoch: 441 loss: 0.5689
epoch: 442 loss: 0.5658
epoch: 443 loss: 0.5627
epoch: 444 loss: 0.5596
epoch: 445 loss: 0.5565
epoch: 446 loss: 0.5535
epoch: 447 loss: 0.5505
epoch: 448 loss: 0.5475
epoch: 449 loss: 0.5446
epoch: 450 loss: 0.5417
epoch: 451 loss: 0.5388
epoch: 452 loss: 0.5359
epoch: 453 loss: 0.5330
epoch: 454 loss: 0.5302
epoch: 455 loss: 0.5274
epoch: 456 loss: 0.5246
epoch: 457 loss: 0.5218
epoch: 458 loss: 0.5191
epoch: 459 loss: 0.5164
epoch: 460 loss: 0.5137
epoch: 461 loss: 0.5110
epoch: 462 loss: 0.5084
epoch: 463 loss: 0.5058
epoch: 464 loss: 0.5031
epoch: 465 loss: 0.5006
epoch: 466 loss: 0.4980
epoch: 467 loss: 0.4955
epoch: 468 loss: 0.4930
epoch: 469 loss: 0.4905
epoch: 470 loss: 0.4880
epoch: 471 loss: 0.4855
epoch: 472 loss: 0.4831
epoch: 473 loss: 0.4807
epoch: 474 loss: 0.4783
epoch: 475 loss: 0.4759
epoch: 476 loss: 0.4736
epoch: 477 loss: 0.4712
epoch: 478 loss: 0.4689
epoch: 479 loss: 0.4666
epoch: 480 loss: 0.4644
epoch: 481 loss: 0.4621
epoch: 482 loss: 0.4599
epoch: 483 loss: 0.4577
epoch: 484 loss: 0.4555
epoch: 485 loss: 0.4533
epoch: 486 loss: 0.4511
epoch: 487 loss: 0.4490
epoch: 488 loss: 0.4468
epoch: 489 loss: 0.4447
epoch: 490 loss: 0.4426
epoch: 491 loss: 0.4406
epoch: 492 loss: 0.4385
epoch: 493 loss: 0.4365
epoch: 494 loss: 0.4345
epoch: 495 loss: 0.4324
epoch: 496 loss: 0.4305
epoch: 497 loss: 0.4285
epoch: 498 loss: 0.4265
epoch: 499 loss: 0.4246
epoch: 500 loss: 0.4227
epoch: 501 loss: 0.4208
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epoch: 9965 loss: 0.0701
epoch: 9966 loss: 0.0701
epoch: 9967 loss: 0.0701
epoch: 9968 loss: 0.0701
epoch: 9969 loss: 0.0701
epoch: 9970 loss: 0.0701
epoch: 9971 loss: 0.0701
epoch: 9972 loss: 0.0701
epoch: 9973 loss: 0.0701
epoch: 9974 loss: 0.0701
epoch: 9975 loss: 0.0701
epoch: 9976 loss: 0.0700
epoch: 9977 loss: 0.0700
epoch: 9978 loss: 0.0700
epoch: 9979 loss: 0.0700
epoch: 9980 loss: 0.0700
epoch: 9981 loss: 0.0700
epoch: 9982 loss: 0.0700
epoch: 9983 loss: 0.0700
epoch: 9984 loss: 0.0700
epoch: 9985 loss: 0.0700
epoch: 9986 loss: 0.0700
epoch: 9987 loss: 0.0700
epoch: 9988 loss: 0.0700
epoch: 9989 loss: 0.0700
epoch: 9990 loss: 0.0700
epoch: 9991 loss: 0.0700
epoch: 9992 loss: 0.0699
epoch: 9993 loss: 0.0699
epoch: 9994 loss: 0.0699
epoch: 9995 loss: 0.0699
epoch: 9996 loss: 0.0699
epoch: 9997 loss: 0.0699
epoch: 9998 loss: 0.0699
epoch: 9999 loss: 0.0699
In [13]:
pred = predict(X=X[:100,:],params=lr)
In [14]:
pred
Out[14]:
array([-0.26267712, 0.28741347, -0.22449469, -0.05273037, -0.27898006,
0.4322239 , -0.16445701, -0.27367997, -0.14995299, -0.15796809,
0.12728885, -0.22342187, -0.075625 , -0.26820486, 0.08232522,
0.33903086, -0.14243474, -0.02361523, -0.18416298, -0.28126949,
-0.08966817, 0.38857146, -0.06887447, -0.36541789, -0.06743128,
-0.0607618 , 0.14186539, -0.05860239, -0.13264656, -0.08149538,
-0.13169208, -0.2123847 , 0.09477783, -0.15853722, -0.10173075,
0.44312473, -0.01739514, 0.15489076, -0.25603743, -0.04461774,
-0.09013906, 0.19333471, 0.03179943, -0.02702913, -0.20599131,
-0.02066112, -0.292163 , -0.0438706 , -0.22860079, 1.11521997,
-0.2579039 , 0.11736883, -0.16983077, -0.17825749, 0.1607796 ,
-0.05683942, -0.11553365, -0.11768413, 0.50406229, -0.11028128,
0.19208374, -0.22767898, -0.02273964, -0.18344133, -0.2067084 ,
0.17462233, -0.04835153, -0.10859874, -0.30486269, 0.15788333,
0.33228821, -0.26393373, 0.17485023, -0.10806767, -0.05706815,
0.20300501, -0.09038381, -0.24721482, -0.20175579, 0.05262402,
-0.12988421, -0.11268906, -0.09729955, -0.22533587, -0.25399354,
0.02927436, 0.03741259, -0.0416057 , -0.15961721, -0.31704614,
-0.08896874, 0.03243099, -0.27177735, -0.1581307 , -0.1581307 ,
0.37511732, -0.16798312, -0.27804849, -0.02235951, 0.10341066])
In [15]:
plt.plot(list(range(999)),lr.cost_arr[1:])
plt.show()

—————————————————————————
ValueError Traceback (most recent call last)
in
—-> 1 plt.plot(list(range(999)),lr.cost_arr[1:])
2 plt.show()

D:\Anaconda\anaconda\lib\site-packages\matplotlib\pyplot.py in plot(scalex, scaley, data, *args, **kwargs)
2809 return gca().plot(
2810 *args, scalex=scalex, scaley=scaley, **({“data”: data} if data
-> 2811 is not None else {}), **kwargs)
2812
2813

D:\Anaconda\anaconda\lib\site-packages\matplotlib\__init__.py in inner(ax, data, *args, **kwargs)
1808 “the Matplotlib list!)” % (label_namer, func.__name__),
1809 RuntimeWarning, stacklevel=2)
-> 1810 return func(ax, *args, **kwargs)
1811
1812 inner.__doc__ = _add_data_doc(inner.__doc__,

D:\Anaconda\anaconda\lib\site-packages\matplotlib\axes\_axes.py in plot(self, scalex, scaley, *args, **kwargs)
1609 kwargs = cbook.normalize_kwargs(kwargs, mlines.Line2D._alias_map)
1610
-> 1611 for line in self._get_lines(*args, **kwargs):
1612 self.add_line(line)
1613 lines.append(line)

D:\Anaconda\anaconda\lib\site-packages\matplotlib\axes\_base.py in _grab_next_args(self, *args, **kwargs)
391 this += args[0],
392 args = args[1:]
–> 393 yield from self._plot_args(this, kwargs)
394
395

D:\Anaconda\anaconda\lib\site-packages\matplotlib\axes\_base.py in _plot_args(self, tup, kwargs)
368 x, y = index_of(tup[-1])
369
–> 370 x, y = self._xy_from_xy(x, y)
371
372 if self.command == ‘plot’:

D:\Anaconda\anaconda\lib\site-packages\matplotlib\axes\_base.py in _xy_from_xy(self, x, y)
229 if x.shape[0] != y.shape[0]:
230 raise ValueError(“x and y must have same first dimension, but ”
–> 231 “have shapes {} and {}”.format(x.shape, y.shape))
232 if x.ndim > 2 or y.ndim > 2:
233 raise ValueError(“x and y can be no greater than 2-D, but have ”

ValueError: x and y must have same first dimension, but have shapes (999,) and (9999,)

1.3¶
In [ ]:
import matplotlib.pyplot as plt
In [ ]:
plt.scatter(x=X[:200,-1],y=y[:200])
In [ ]:
plt.scatter(x=pred,y=y[:100])

1.4 Ridge Regression¶
In [ ]:
class LinearRegressionRidge(object):
def __init__(self,learning_rate,epochs,lamda,is_print_loss=True):
self.lr = learning_rate
self.epochs = epochs
self.lam = lamda
self.theta = None
self.baise = None
self.print_loss = is_print_loss

def cost(self,y,update):
loss = np.dot((y-update).T, y-update)/len(y)+self.lam*np.square(self.theta,self.theta).sum()
return loss.mean()

def gradient(self,x,y,update):
dleta = -(2/x.shape[0])*np.dot((y-update).T,x)
return dleta

def fit(self,X,y):
self.theta = np.ones(shape=(1,X.shape[1]))
self.baise = np.asarray([1])
self.cost_arr = []

for epoch in range(self.epochs):
update = np.dot(X,self.theta.T)+self.baise
loss = self.cost(y,update)
theta_update= self.gradient(X,y,update)
biase_update = -2*np.dot((y-update).T,
np.ones(shape=[X.shape[0],1]))/X.shape[0]

self.theta=self.theta-self.lr*theta_update
self.baise=self.baise-self.lr*biase_update
self.cost_arr.append(loss)

if self.print_loss:
print(‘epoch: {}\tloss: {:.4f}’.format(epoch,loss))

def predict(self,X):
pred = np.dot(X, self.theta[0,:]) + self.baise[0]
return pred

In [ ]:
def linear_regression_Ridge(lr,X,target,iteration,alpha):
lr = LinearRegressionRidge(learning_rate=lr,epochs=iteration,is_print_loss=True,lamda=alpha)
lr.fit(X,target)

return lr
In [ ]:
lr = linear_regression_Ridge(lr=0.001,iteration=1000,X=X[:200,:],target=y[:200],alpha=0.001)
In [ ]:
plt.plot(list(range(999)),lr.cost_arr[1:])
plt.show()
In [ ]:
## different penalty
cost_all = []
alpha_all =[0.1,0.2,0.3,0.4]
for p in alpha_all:
lr = linear_regression_Ridge(lr=0.001,iteration=1000,X=X[:200,:],target=y[:200],alpha=p)
cost_all.append(lr.cost_arr[1:])
In [ ]:
cost_all = np.asarray(cost_all)
In [ ]:

In [ ]:
for idx,p in enumerate(alpha_all):
plt.plot(list(range(999)),cost_all[idx],label=’alpha={}’.format(str(p)))
plt.legend()
In [ ]:

In [ ]:

In [ ]:
plt.scatter(x=X[:200,-1],y=y[:200])
In [ ]:
plt.scatter(x=pred,y=y[:100])

1.5¶
In [ ]:
class LinearRegressionRidgeMomentum(object):
def __init__(self,learning_rate,epochs,lamda,momentum,is_print_loss=True):
self.lr = learning_rate
self.epochs = epochs
self.lam = lamda
self.theta = None
self.baise = None
self.print_loss = is_print_loss
self.momentum = momentum

def cost(self,y,update):
loss = np.dot((y-update).T, y-update)/len(y)+self.lam*np.square(self.theta,self.theta).sum()
return loss.mean()

def gradient(self,x,y,update):
dleta = -(2/x.shape[0])*np.dot((y-update).T,x)
return dleta*self.momentum

def fit(self,X,y):
cost_arr = []
self.theta = np.ones(shape=(1,X.shape[1]))
self.baise = np.asarray([1])
self.cost_arr = []
for epoch in range(self.epochs):
update = np.dot(X,self.theta.T)+self.baise
loss = self.cost(y,update)
theta_update= self.gradient(X,y,update)
biase_update = -2*np.dot((y-update).T,
np.ones(shape=[X.shape[0],1]))/X.shape[0]

self.theta=self.theta-self.lr*theta_update
self.baise=self.baise-self.lr*biase_update
self.cost_arr.append(loss)
if self.print_loss:
print(‘epoch: {}\tloss: {:.4f}’.format(epoch,loss))

#return cost_arr

def predict(self,X):
pred = np.dot(X, self.theta[0,:]) + self.baise[0]
return pred

In [ ]:
def linear_regression_Ridge_momentum(lr,X,target,iteration,alpha,momentum):
lr = LinearRegressionRidgeMomentum(learning_rate=lr,
epochs=iteration,
lamda=alpha,momentum=momentum,
is_print_loss=True)
lr.fit(X,target)

return lr
In [ ]:
lr = linear_regression_Ridge_momentum(lr=0.001,X=X[:200,:],target=y[:200],alpha=0.1,momentum=0.1,iteration=1000)
In [ ]:
plt.plot(list(range(999)),lr.cost_arr[1:])
plt.show()
In [ ]:
### Try different momenta and plot the learning curves with and without momentum for a fixed learning rate
# with momenta

cost_all = []
lr_all =[0.1,0.0001,0.003]
momenta_all = [0.1,0.2,0.3]
for l in lr_all:
tmp = []
for m in momenta_all:
lr = linear_regression_Ridge_momentum(lr=l,iteration=1000,X=X[:200,:],
target=y[:200],alpha=0.1,
momentum=m)
tmp.append(lr.cost_arr[1:])
cost_all.append(tmp)

cost_all = np.asarray(cost_all)
In [ ]:
for l_idx,l in enumerate(lr_all):
for m_idx, m in enumerate(momenta_all):
plt.plot(list(range(999)),cost_all[l_idx][m_idx],label=’lr={} moment = {}’.format(str(l),str(m)))
plt.legend()
In [ ]:
# without momenta

cost_all = []
lr_all =[0.1,0.0001,0.003]
for l in lr_all:
lr = linear_regression_Ridge(lr=l,iteration=1000,X=X[:200,:],
target=y[:200],alpha=0.1)
cost_all.append(lr.cost_arr[1:])

cost_all = np.asarray(cost_all)
In [ ]:
for l_idx,l in enumerate(lr_all):
plt.plot(list(range(999)),cost_all[l_idx],label=’lr={}’.format(str(l)))
plt.legend()
In [ ]:
pred = predict(X=X[:200],params=lr)
In [ ]:
from sklearn.metrics import mean_squared_error
In [ ]:
print(‘mse=’,mean_squared_error(y[:200],pred))