https://www.kaggle.com/uciml/pima-indians-diabetes-database
1.Import relevant commands for numpy, pandas, sklearn.
import numpy as np
import pandas as pd
from pandas import DataFrame, read_csv, to_numeric
from sklearn.model_selection import train_test_split, KFold
from sklearn.naive_bayes import GaussianNB
from sklearn.linear_model import LogisticRegression
from sklearn.neighbors import KNeighborsClassifier
import math
import scipy.stats as stats2.Using the appropriate pandas function, read the diabetes.csv into a dataframe. Pay good attention to the necessary arguments.
data = read_csv('diabetes.csv', sep=",")
a = pd.DataFrame(data)
print(a)<br/><br/> Pregnancies Glucose BloodPressure SkinThickness Insulin BMI \
0 6 148 72 35 0 33.6
1 1 85 66 29 0 26.6
2 8 183 64 0 0 23.3
3 1 89 66 23 94 28.1
4 0 137 40 35 168 43.1
.. ... ... ... ... ... ...
763 10 101 76 48 180 32.9
764 2 122 70 27 0 36.8
765 5 121 72 23 112 26.2
766 1 126 60 0 0 30.1
767 1 93 70 31 0 30.4
DiabetesPedigreeFunction Age Outcome
0 0.627 50 1
1 0.351 31 0
2 0.672 32 1
3 0.167 21 0
4 2.288 33 1
.. ... ... ...
763 0.171 63 0
764 0.340 27 0
765 0.245 30 0
766 0.349 47 1
767 0.315 23 0
[768 rows x 9 columns]
3.use naivebayes, logistic regression and 3-nn classifiers (library) to train on the training sets and compute training and validation errors for each fold. The target label is Outcome.
X=a.iloc[:,0:8].values
y=a.iloc[:,-1].values
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state=0)
kf = KFold(n_splits=10)
kf.get_n_splits()
#print(kf)
for train_index, test_index in kf.split(X):
print("TRAIN:", train_index, "TEST:", test_index)
X_train, X_test = X[train_index], X[test_index]
y_train, y_test = y[train_index], y[test_index]
nb_model = GaussianNB()
lr_model = LogisticRegression(solver= 'liblinear')
knn_model = KNeighborsClassifier(n_neighbors=3)
nb_error = []
lr_error = []
knn_error =[]
for train, validation in kf.split(X_train):
nb_fit = nb_model.fit(X_train[train], y_train[train])
nb_pred = nb_model.predict(X_train[validation])
#print(nb_pred)
error = np.sum(nb_pred!= y_train[validation])/len(nb_pred)
nb_error.append(error)
lr_fit = lr_model.fit(X_train[train], y_train[train])
lr_pred = lr_model.predict(X_train[validation])
#print(lr_pred)
error = np.sum(lr_pred!=y_train[validation])/len(lr_pred)
lr_error.append(error)
knn_fit = knn_model.fit(X_train[train], y_train[train])
knn_pred = knn_model.predict(X_train[validation])
#print(knn_pred)
error = np.sum(lr_pred!=y_train[validation])/len(knn_pred)
knn_error.append(error)
Error_list=np.transpose([nb_error,lr_error,knn_error])
z = pd.DataFrame(data=Error_list, columns =("Naivebayes","logistic regression","KNN"))
print(z)TRAIN: [ 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94
95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112
113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148
149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166
167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184
185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202
203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220
221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238
239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256
257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274
275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292
293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310
311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328
329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346
347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364
365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382
383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400
401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418
419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436
437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454
455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472
473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490
491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508
509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526
527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544
545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562
563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580
581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598
599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616
617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634
635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652
653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670
671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688
689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706
707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724
725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742
743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760
761 762 763 764 765 766 767] TEST: [ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
72 73 74 75 76]
Naivebayes logistic regression KNN
0 0.328571 0.314286 0.314286
1 0.157143 0.171429 0.171429
2 0.231884 0.188406 0.188406
3 0.333333 0.304348 0.304348
4 0.304348 0.333333 0.333333
5 0.217391 0.202899 0.202899
6 0.173913 0.159420 0.159420
7 0.202899 0.188406 0.188406
8 0.202899 0.159420 0.159420
9 0.246377 0.260870 0.260870
4.is the error of naive bayes <0.2 with confidence 0.9
x=np.std(nb_error)
y=np.mean(nb_error)
z= math.sqrt(10)*(y-0.2)/x
print(z)
a=stats.t.ppf(0.9,9)
if z > a :
print("No")
else :
print("Yes")2.122373130045732
No
5.have naive bayes and knn the same error?
x=np.absolute(np.subtract(np.array(knn_error),np.array(nb_error)))
print(x)
y=np.std(x)
z=np.mean(x)
a= math.sqrt(10)*z/y
print(a)
b=stats.t.ppf(0.9,9)
if a > b :
print("No")
else :
print("Yes")[0.01428571 0.01428571 0.04347826 0.02898551 0.02898551 0.01449275
0.01449275 0.01449275 0.04347826 0.01449275]
6.296258830957976
No
6.do the three classifiers have different errors?
e_table = np.array(np.transpose([nb_error,lr_error,knn_error]))
No_of_models = 3
Folds= 10
average_of_models =np.mean(e_table, axis=0)
bet_same_model = Folds*np.var(average_of_models)
bet_all_model = np.sum(np.var(e_table,axis=0)/No_of_models)
x=stats.f.ppf(0.9,dfn=No_of_models-1 ,dfd= No_of_models*(Folds-1))
ratio= bet_same_model/bet_all_model
print("F-statistic",x)
print("Estimater ratio",ratio)
if x < ratio:
print("All models have same error")
else:
print("All models have differnt error")F-statistic 2.5106086665585408
Estimater ratio 0.0753450085421447
All models have differnt error
7.Use Bayes rule to decide on the label using the Glucose feature. Compute the mean and std of Glucose feature on the whole dataset (marginal distribution) and for each class separately, (class condition distribution Prob(x|C=0), Prob(x|C=1))). Assume that the feature is distributed according to the mean and std you computed. Compute the predictions for the 10 validation sets. Compare with the naivebayes classifier (library) using only the Glucose feature
from sklearn.naive_bayes import GaussianNB
data_g = data.Glucose.values
data_o = data.Outcome.values
err_model = []
err_lib = []
def Gaussian(x,mean,var):
numerator = np.exp(-((x-mean )**2)/(2*var))
denominator = np.sqrt(2*np.pi*var)
return numerator/denominator
for train, validation in kf.split(data_o):
x_train = data_g[train]
y_train = data_o[train]
var_0 = np.var(x_train[y_train==0])
var_1 = np.var(x_train[y_train==1])
p_prob_0 = len(x_train[y_train==0]/len(x_train))
p_prob_1 = len(x_train[y_train==1]/len(x_train))
mean_0 = np.mean(x_train[y_train==0])
mean_1 = np.mean(x_train[y_train==1])
prediction= []
for x in data_g[validation]:
gaussian_0= Gaussian(x,mean_0,var_0)
gaussian_1= Gaussian(x,mean_1,var_1)
class_0 = p_prob_0*gaussian_0
class_1 = p_prob_1*gaussian_1
if class_0 > class_1:
prediction.append(0)
else:
prediction.append(1)
err_model.append(np.sum(np.array(prediction)!=data_o[validation])/len(prediction))
nb_classifier = GaussianNB()
nb_classifier.fit(data_g.reshape(-1,1), data_o.reshape(-1,1))
nb_pred = nb_classifier.predict(data_g[validation].reshape(-1,1))
error = np.sum(nb_pred!=data_o[validation])/len(data_g[validation])
err_lib.append(error)
Error_list = np.transpose([err_model, err_lib])
z= pd.DataFrame(data=Error_list , columns =("My model Error","Library Model error"))
print("\n",z)
print("\n Both model have same error\n") My model Error Library Model error
0 0.337662 0.337662
1 0.246753 0.246753
2 0.298701 0.298701
3 0.324675 0.324675
4 0.246753 0.246753
5 0.220779 0.194805
6 0.181818 0.181818
7 0.207792 0.207792
8 0.210526 0.210526
9 0.250000 0.250000
Both model have same error