<02> CHIZIQLI MODEL

Chiziqli model haqida tushuncha va xatolikni hisoblash

Chiziqli modelni qo'llanilishi haqida qo'shimcha ma'lumotlar.

CHIZIQLI MODEL

Statistikada chiziqli model qo'llanilishiga qarab turlicha tasvrilanadi. Bulardan ko'p uchraydiganlari regressiyaga modellarga aloqdorlaridir, shu sababli chiziqli model va chiziqli regressiya sinonim sifatida qo'llaniladi. Ma'lumotlarning o'zgarishi chiziqli teksi tarzda ortib borishi yoki kamayib borishi bilan ham chiziqli modelni boshqalaridan ajratish qiyinchilik tug'dirmaydi.

O'RTACHA KVADRATIK XATOLIK (MEAN SQUARED ERROR-->MSE)

Demak, chiziqli modelning xatoligini hisoblashda biz MSE xatolik funksiyasidan foydalandik. Yuqoridagi ifodada barcha o'zgaruvchilar aniq berilgan.

MODEL&LOSS(Python)

#Kutubxonalrni chaqirib olish
import matplotlib.pyplot as plt
import numpy as np

#Ma'lumotlarni kiritish
x_soat = np.array([1.0, 2.0, 3.0])
y_baho = np.array([2.0, 4.0, 6.0 ])

#To'g'ri hisoblash uchun funksiya
def forward(x):
    return x*w
#Xatolik (Loss) ning funksiyasi
def loss(x,y):
    y_pred = forward(x)
    return (y_pred-y)**2

#Grafikni yaratib olishimiz uchun kontaynerlar
w_list=[]
mse_list=[]

#w ni 0 dan 4 gacha oralig'ida hisblash 
for w in np.arange(0.0,4.1,0.1):
    print("w={:.3f}".format(w))
    L_umum=0
    
    for x_hb_qiym, y_hb_qiym in zip(x_soat, y_baho):
        y_hb_bash = forward(x_hb_qiym)
        L_hb_qiym = loss(x_hb_qiym, y_hb_qiym)
        L_umum += L_hb_qiym
        print("\t", "{:.2f}, {:.2f}, {:.2f}, {:.2f}".format(x_hb_qiym, y_hb_qiym, y_hb_bash, L_hb_qiym))
    
    # Har bir ma'lumot uchun MSE ni hisoblaymiz
    print("MSE=", L_umum / len(x_soat))  #len(x_soat)--> N
    w_list.append(w)
    mse_list.append(L_umum / len(x_soat))

#Grafik natija
plt.plot(w_list, mse_list)
plt.ylabel('Loss')
plt.xlabel('w')
ax= plt.axes()
ax.set_facecolor('#030101')
plt.show()

BIROR QIZIQARALI CHIZIQLI MA'LUMOT TOPIB UNI MODELLASHTIRING HAMDA XATOLIGINI MSE YORDAMIDA ANIQLANG.
MSE XATOLIK VA w QIYMATLARINI GRAFIK KO'RINISHIDA TASVIRLANG.

MASALAN:

Previous<01> KIRISH Next<03> GRADIENT PASTLASH

Last updated 3 years ago

CHIZIQLI MODEL

MODEL&LOSS(Python)

#Kutubxonalrni chaqirib olish
import matplotlib.pyplot as plt
import numpy as np

#Ma'lumotlarni kiritish
x_soat = np.array([1.0, 2.0, 3.0])
y_baho = np.array([2.0, 4.0, 6.0 ])

#To'g'ri hisoblash uchun funksiya
def forward(x):
    return x*w
#Xatolik (Loss) ning funksiyasi
def loss(x,y):
    y_pred = forward(x)
    return (y_pred-y)**2

#Grafikni yaratib olishimiz uchun kontaynerlar
w_list=[]
mse_list=[]

#w ni 0 dan 4 gacha oralig'ida hisblash 
for w in np.arange(0.0,4.1,0.1):
    print("w={:.3f}".format(w))
    L_umum=0
    
    for x_hb_qiym, y_hb_qiym in zip(x_soat, y_baho):
        y_hb_bash = forward(x_hb_qiym)
        L_hb_qiym = loss(x_hb_qiym, y_hb_qiym)
        L_umum += L_hb_qiym
        print("\t", "{:.2f}, {:.2f}, {:.2f}, {:.2f}".format(x_hb_qiym, y_hb_qiym, y_hb_bash, L_hb_qiym))
    
    # Har bir ma'lumot uchun MSE ni hisoblaymiz
    print("MSE=", L_umum / len(x_soat))  #len(x_soat)--> N
    w_list.append(w)
    mse_list.append(L_umum / len(x_soat))

#Grafik natija
plt.plot(w_list, mse_list)
plt.ylabel('Loss')
plt.xlabel('w')
ax= plt.axes()
ax.set_facecolor('#030101')
plt.show()