Mashinali o’qitish Mustaqil ish Guruh: 210-18 Bajardi: Mahmudova Dilnoza Tekshirdi: Ochilov Mannon Toshkent 2021

Python dasturini amalga oshirish

def weightInitialization(n_features):
w = np.zeros((1,n_features))
b = 0
return w,bdef sigmoid_activation(result):
final_result = 1/(1+np.exp(-result))
return final_result
def model_optimize(w, b, X, Y):
m = X.shape[0]

#Prediction
final_result = sigmoid_activation(np.dot(w,X.T)+b)
Y_T = Y.T
cost = (-1/m)*(np.sum((Y_T*np.log(final_result)) + ((1-Y_T)*(np.log(1-final_result)))))
#

#Gradient calculation
dw = (1/m)*(np.dot(X.T, (final_result-Y.T).T))
db = (1/m)*(np.sum(final_result-Y.T))

grads = {"dw": dw, "db": db}

return grads, costdef model_predict(w, b, X, Y, learning_rate, no_iterations):
costs = []
for i in range(no_iterations):
#
grads, cost = model_optimize(w,b,X,Y)
#
dw = grads["dw"]
db = grads["db"]
#weight update
w = w - (learning_rate * (dw.T))
b = b - (learning_rate * db)
#

if (i % 100 == 0):
costs.append(cost)
#print("Cost after %i iteration is %f" %(i, cost))

#final parameters
coeff = {"w": w, "b": b}
gradient = {"dw": dw, "db": db}

return coeff, gradient, costsdef predict(final_pred, m):
y_pred = np.zeros((1,m))
for i in range(final_pred.shape[1]):
if final_pred[0][i] > 0.5:
y_pred[0][i] = 1
return y_pred

O'zgarishlar soni va soni

13-rasm: costni pasaytirish

Tizimning poezd va sinov aniqligi 100%

Ushbu dastur ikkilik logistik regressiya uchun mo'ljallangan. Ikki sinfdan ko'proq ma'lumot uchun softmax regressiyasidan foydalanish kerak.

1-ilova. Ikkilik logistic regressiya

import csv

import numpy as np

import matplotlib.pyplot as plt

def loadCSV(filename):

'''

function to load dataset

'''

with open(filename,"r") as csvfile:

lines = csv.reader(csvfile)

dataset = list(lines)

for i in range(len(dataset)):

dataset[i] = [float(x) for x in dataset[i]]

return np.array(dataset)

def normalize(X):

'''

function to normalize feature matrix, X

'''

mins = np.min(X, axis = 0)

maxs = np.max(X, axis = 0)

rng = maxs - mins

norm_X = 1 - ((maxs - X)/rng)

return norm_X

def logistic_func(beta, X):

'''

logistic(sigmoid) function

'''

return 1.0/(1 + np.exp(-np.dot(X, beta.T)))

def log_gradient(beta, X, y):

'''

logistic gradient function

'''

first_calc = logistic_func(beta, X) - y.reshape(X.shape[0], -1)

final_calc = np.dot(first_calc.T, X)

return final_calc

def cost_func(beta, X, y):

'''

cost function, J

'''

log_func_v = logistic_func(beta, X)

y = np.squeeze(y)

step1 = y * np.log(log_func_v)

step2 = (1 - y) * np.log(1 - log_func_v)

final = -step1 - step2

return np.mean(final)

def grad_desc(X, y, beta, lr=.01, converge_change=.001):

'''

gradient descent function

'''

cost = cost_func(beta, X, y)

change_cost = 1

num_iter = 1

while(change_cost > converge_change):

old_cost = cost

beta = beta - (lr * log_gradient(beta, X, y))

cost = cost_func(beta, X, y)

change_cost = old_cost - cost

num_iter += 1

return beta, num_iter

def pred_values(beta, X):

'''

function to predict labels

'''

pred_prob = logistic_func(beta, X)

pred_value = np.where(pred_prob >= .5, 1, 0)

return np.squeeze(pred_value)

def plot_reg(X, y, beta):

'''

function to plot decision boundary

'''

# labelled observations

x_0 = X[np.where(y == 0.0)]

x_1 = X[np.where(y == 1.0)]

# plotting points with diff color for diff label

plt.scatter([x_0[:, 1]], [x_0[:, 2]], c='b', label='y = 0')

plt.scatter([x_1[:, 1]], [x_1[:, 2]], c='r', label='y = 1')

# plotting decision boundary

x1 = np.arange(0, 1, 0.1)

x2 = -(beta[0,0] + beta[0,1]*x1)/beta[0,2]

plt.plot(x1, x2, c='k', label='reg line')

plt.xlabel('x1')

plt.ylabel('x2')

plt.legend()

plt.show()

if __name__ == "__main__":

# load the dataset

dataset = loadCSV('dataset1.csv')

# normalizing feature matrix

X = normalize(dataset[:, :-1])

# stacking columns wth all ones in feature matrix

X = np.hstack((np.matrix(np.ones(X.shape[0])).T, X))

# response vector

y = dataset[:, -1]

# initial beta values

beta = np.matrix(np.zeros(X.shape[1]))

# beta values after running gradient descent

beta, num_iter = grad_desc(X, y, beta)

# estimated beta values and number of iterations

print("Estimated regression coefficients:", beta)

print("No. of iterations:", num_iter)

# predicted labels

y_pred = pred_values(beta, X)

# number of correctly predicted labels

print("Correctly predicted labels:", np.sum(y == y_pred))

# plotting regression line

plot_reg(X, y, beta)

2-ilova. Multinomial Logistik regressiya

from sklearn import datasets, linear_model, metrics

# load the digit dataset

digits = datasets.load_digits()

# defining feature matrix(X) and response vector(y)

X = digits.data

y = digits.target

# splitting X and y into training and testing sets

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=1)

# create logistic regression object

reg = linear_model.LogisticRegression()

# train the model using the training sets

reg.fit(X_train, y_train)

# making predictions on the testing set

y_pred = reg.predict(X_test)

# comparing actual response values (y_test) with predicted response values (y_pred)

print("Logistic Regression model accuracy(in %):",

metrics.accuracy_score(y_test, y_pred)*100)

Xulosa

Logistik regressiya kuchli vositadir, ayniqsa epidemiologik tadqiqotlarda, bir vaqtning o'zida bir nechta tushuntirish o'zgaruvchilarini tahlil qilishga imkon beradi, shu bilan birga chalkash omillar ta'sirini kamaytiradi. Biroq, tadqiqotchilar modellarni yaratishga e'tibor berishlari kerak, dasturiy ta'minotni faqat xom ma'lumotlar bilan oziqlantirishdan va natijalarga erishishdan qochish kerak. Model qurish bo'yicha ba'zi qiyin qarorlar butunlay tadqiqotchining ushbu sohadagi tajribasiga bog'liq bo'ladi.

Logistik regressiya haqida ba'zi fikrlar:

• 
  Bog'liq o'zgaruvchi va mustaqil o'zgaruvchilar o'rtasida chiziqli bog'liqlik mavjud emas, lekin tushuntiruvchi o'zgaruvchilar logiti va javob o'rtasida chiziqli bog'liqlik mavjud .
  
• 
  Mustaqil o'zgaruvchilar, hatto dastlabki mustaqil o'zgaruvchilarning kuch atamalari yoki boshqa ba'zi bir chiziqli bo'lmagan o'zgarishlar bo'lishi mumkin.
  
• 
  Bog'liq o'zgaruvchini odatda taqsimlash shart emas, lekin u odatda eksponent oiladan (masalan, binomial, Poisson, multinomial, normal,…) taqsimotni qabul qiladi; ikkilik logistik regressiya javobning binomial taqsimlanishini o'z zimmasiga oladi.
  
• 
  Variantlarning bir xilligi qondirilishi shart emas.
  
• 
  Xatolar mustaqil bo'lishi kerak, lekin odatda taqsimlanmaydi.
  
• 
  Parametrlarni baholash uchun oddiy kichik kvadratchalar (OLS) emas, balki maksimal ehtimollik bahosidan (MLE) foydalanadi va shuning uchun katta namunali taxminlarga tayanadi .
  

Foydalanilgan adabiyotlar

• 
  http://cs229.stanford.edu/notes/cs229-notes1.pdf
  
• 
  http://machinelearningmastery.com/logistic-regression-for-machine-learning/
  
• 
  https://onlinecourses.science.psu.edu/stat504/node/164