Mashinali o‘qitishda gradientli tushish algoritmini chiziqli regressiya yordamida tadqiq qilish
![hosilalar deb ataladi. Berilgan p nuqtadagi n o‘lchamli f(x) funksiya uchun gradient
quyidagicha aniqlanadi:
∇ f( p ) =
[ ∂ f
∂ x
1 ( p )
:
∂ f
∂ x
n ( P ) ]
Teskari uchburchak nabla deb ataladigan belgidir va siz uni "del" deb o'qiysiz. Uni
qanday hisoblashni yaxshiroq tushunish uchun quyidagi ikki o'zgaruvchili funksiya
uchun qo'lda hisob-kitob qilaylik.
f(x)=0.5 x2+y2
Rasm 6.
f(x)=0.5 x2+y2 funksiyaning 3D grafigi
Faraz qilaylik, bizni p(10,10) nuqtadagi gradient qiziqtiradi:
∂ f ( x , y )
∂
x = x , ∂ f ( x , y )
∂
y = 2 y
shuning uchun
∇ f(x,y)=[
x
2y],∇ f(10,10 )=[
10
20 ]
11](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_11.png?v=1)
![umumlashtirilishini o'lchaydigan turli ko'rsatkichlar yordamida baholanishi
mumkin. Lineer regressiyada ishlatiladigan ba'zi umumiy ko'rsatkichlar:
Misol : Faraz qilaylik, bizda uyning kattaligiga qarab uy-joy narxini bashorat
qiluvchi chiziqli regressiya modeli mavjud. Bizda quyidagi haqiqiy narxlar (y) va
bashorat qilingan narxlar (y_hat) bo'lgan 10 ta ma'lumot nuqtasi mavjud:
y = [100, 150, 200, 250, 300, 350, 400, 450, 500, 550]
y_hat = [110, 140, 180, 240, 290, 320, 380, 420, 480, 520]
y_mean = yig'indi (y) / len (y) = 325
Kvadratlar regressiyasi yig'indisi (SSR): SSR prognoz qilingan qiymatlar va qaram
o'zgaruvchining o'rtacha qiymati o'rtasidagi kvadratik farqlar yig'indisini olish yo'li
bilan hisoblanadi. U mustaqil o'zgaruvchilar bilan izohlanadigan qaram
o'zgaruvchidagi o'zgaruvchanlikni ifodalaydi. Matematik jihatdan uni quyidagicha
ifodalash mumkin:
SSR = summa ((y_hat — y_mean)²) = 28300
Kvadratlar yig'indisi xatosi (SSE): SSE prognoz qilingan qiymatlar va qaram
o'zgaruvchining haqiqiy qiymatlari o'rtasidagi kvadratik farqlar yig'indisini olish
yo'li bilan hisoblanadi. Matematik jihatdan uni quyidagicha ifodalash mumkin:
SSE = summa((y — y_hat)²) = 26700
O'rtacha kvadrat xato (MSE): Bu ko'rsatkich bashorat qilingan va haqiqiy qiymatlar
o'rtasidagi o'rtacha kvadrat farqni o'lchaydi. U ma'lumotlar nuqtalari soniga
bo'lingan kvadrat qoldiqlar yig'indisi sifatida hisoblanadi. Pastroq MSE yaxshi
ishlashni ko'rsatadi. Matematik jihatdan uni quyidagicha ifodalash mumkin:
MSE = (1/n) * summa((y — y_hat)²) = 2670
Root Mean Squared Error (RMSE): Bu ko'rsatkich MSE ning kvadrat ildizini
o'lchaydi va bog'liq o'zgaruvchi bilan bir xil birliklardagi xatolarni izohlash uchun
foydalidir. Matematik jihatdan uni quyidagicha ifodalash mumkin:
RMSE = sqrt(MSE) = sqrt(2670) = 51,68
O'rtacha mutlaq xato (MAE): Bu ko'rsatkich bashorat qilingan va haqiqiy qiymatlar
o'rtasidagi o'rtacha mutlaq farqni o'lchaydi. U MSE ga qaraganda chetga
29](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_29.png?v=1)
![Ilovalar
import tkinter as tk
from tkinter import scrolledtext
from time import sleep, time
import threading
import sympy as sp
from math import sqrt
from copy import deepcopy
class NotSolvedException(Exception):
pass
class WrongParametr(Exception):
pass
class StopLoopException(Exception):
pass
def get_gradient(func: str) -> tuple[list[str], int]:
""" Funksiya gradientini aniqlaydigan funksiya.
Bunda o'zgaruvchilar x1,x2,x3,x4,x5 ... x100 ko'rinishida bo'lishi shart
(ya'ni a,b,c va hokazolar qabul qilinmaydi).
Ushbu funksiya grafikda faqat qozon shaklini hosil qilgandagina ishlaydi.
"""
def _(s: str) -> str:
return s.replace(' ', '').replace('\n', '').replace('\t', '')
vars = []
38](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_38.png?v=1)
![var_count = 0
for i in range(1, 101):
if f'x{i}' in func:
vars.append(f'x{i}')
var_count = 0 + i
vars = ','.join([f'x{i}' for i in range(1, var_count + 1)])
if var_count == 1:
var_list = [sp.symbols(vars)]
else:
var_list = list(sp.symbols(vars))
new_func = func + ""
for i in range(var_list.__len__()):
new_func = new_func.replace(f'x{var_list.__len__() - i}', '1')
try:
eval(new_func)
except Exception:
raise WrongParametr("Funksiyada ortiqcha belgilar mavjud.\nFaqat quyidagi
o'zgaruvchilarni ishlating: x1,x2,x3,x4 ...")
gradient = [str(sp.diff(func, var)) for var in var_list]
is_access = False
for i in range(var_count):
grad_two = str(sp.diff(gradient[i], var_list[i]))
if _(grad_two) != '0':
is_access = is_access or True
grad_three = str(sp.diff(grad_two, var_list[i]))
if _(grad_three) != '0':
raise WrongParametr("Funksiya talabga javob bermaydi")
if not is_access:
raise WrongParametr("Funksiya talabga javob bermaydi")
return gradient, var_count
def norm(vc: list[float]):
""" vektorning normasini hisoblaydi """
return sqrt(sum(list(map(lambda x: x*x, vc))))
def solve_with_gradient(gradient: list[str], values: list[float]):
""" gradient va vektorni birgalikda hisoblaydi """
def _(func: str, _values: list[float]):
for i in range(len(_values)):
func = func.replace(f'x{i+1}', str(_values[i]))
try:
return eval(func)
except:
raise NotSolvedException
if len(gradient) != len(values):
raise WrongParametr("Gradient va qiymatlar vektori o'lchovi mos emas")
return list(map(lambda x: _(x, values), gradient))
def subtract_two_vc(vc1: list[float], vc2: list[float]):
39](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_39.png?v=1)
![if len(vc1) != len(vc2):
raise WrongParametr("vc1 va vc2 o'lchamlari mos emas")
return list(map(lambda i: vc1[i]-vc2[i], range(vc2.__len__())))
def multiple_vc_and_num(vc: list[float], num: float):
return list(map(lambda x: x*num, vc))
def f_solve(func: str, values: list[float]):
for i in range(len(values)):
func = func.replace(f'x{i+1}', str(values[i]))
return eval(func)
class GetCoordinateZero:
def __init__(self) -> None:
self.stop_flag = False
def get_coordinate_zero(self, func: str, *, eps: float = None,
x0: list[float] = None, t: float = None):
""" Matematik funksiyaning boshlang'ich qiymatini aniqlaydigan funksiya """
eps = eps or 0.01
t = t or 0.5
gradient, var_count = get_gradient(func)
x0 = x0 or [1] * var_count
xk: list[float] = deepcopy(x0)
if t == 1.0:
raise WrongParametr("t`ning qiymati 1.0 bo'lishi mumkin emas")
counter = 0
last_grad_norm = 0
last_grad_norm_counter = 0
while True:
counter += 1
if self.stop_flag:
raise StopLoopException
grad_vc_solve = solve_with_gradient(gradient, xk)
norm_dvs = norm(grad_vc_solve)
if norm_dvs < eps:
return xk, counter
xk_p_1: list[float] = subtract_two_vc(xk, multiple_vc_and_num(grad_vc_solve, t))
xk = deepcopy(xk_p_1)
if last_grad_norm <= norm_dvs:
last_grad_norm_counter += 1
if last_grad_norm_counter == 20:
raise NotSolvedException
last_grad_norm = deepcopy(norm_dvs)
class GUI:
def __init__(self) -> None:
self.window = tk.Tk(className="Gradient tushish")
self.window.geometry('800x500+100+100')
40](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_40.png?v=1)
![self._eps_label = tk.Label(self.window, text="Aniqlik koeffitsentini kiriting",font=('Arial
10'))
self._eps_label.place(x=410, y=105)
self._solve_label = scrolledtext.ScrolledText(self.window, wrap=tk.WORD, font=('Arial 12'),
bd=0, highlightthickness=0)
self._solve_label.place(x=10, y=180, width=780, height=200)
self._solve_label.config(state=tk.DISABLED)
def set_text(self, txt: str):
self._solve_label.config(state=tk.NORMAL)
self._solve_label.delete('1.0', tk.END)
self._solve_label.insert(tk.INSERT, txt)
self._solve_label.config(state=tk.DISABLED)
def force_thread_func(self):
func = self._func_input.get()
t = self._t_input.get()
eps = self._eps_input.get()
func = func.replace('^', '**')
if func.replace(' ', '').__len__() == 0:
self.set_text("Funksiyani kiriting !")
return
try:
t = float(t)
except:
self.set_text(f"t`ning qiymati haqiqiy son bo'lishi kerak !")
return
try:
eps = float(eps)
except:
self.set_text("Aniqlik koeffitsenti haqiqiy son bo'lishi kerak!")
return
try:
start = time()
points, counter = self.solve_obj.get_coordinate_zero(func, t=t,eps=eps)
finish = time()
except NotSolvedException:
self.set_text("Yechimni aniqlab bo'lmadi. \nIltimos parametrlarni qayta ko'rib chiqing.")
return
except WrongParametr as wp:
self.set_text(str(wp.args[0]))
return
except StopLoopException:
self.set_text("To'xtatildi")
return
except Exception as ex:
self.set_text(f'Nomalum xatolik yuz berdi: {ex}')
return
txt = ""
f_zero = "" + func
42](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_42.png?v=1)
![for i in range(len(points)):
txt += f'x{i+1} = {points[i]:.12f}\n'
f_zero = f_zero.replace(f'x{len(points) - i}', f'({points[len(points) - i - 1]})')
txt += f'F = {eval(f_zero):.12f}\n'
txt += f"\n\nIteratsiyalar soni: {counter}\nHisoblash vaqti: {(finish-start):.5f} sekund."
self.set_text(txt)
if __name__ == '__main__':
GUI()
import tkinter as tk
import os
from tkinter import filedialog, messagebox
import pandas as pd
from math import fabs
from sklearn import linear_model
import warnings
"""
Ushbu kod ishlashi uchun bir nechta paketlar kerak bo'ladi.
Ularni yuklab olish uchun terminalga ushbu kodlarni yozasiz
Windows uchun:
pip install pandas
pip install scikit-learn
Ubuntu yoki Linux uchun:
sudo apt install python3-tk
pip install pandas
pip install scikit-learn
"""
def get_solve_in_csv(csv_file_path: str, result_key: str, target_values: list[float]):
""" .csv fayldan ma'lumotni o'qib oladi va ushbu modelga yarasha model tayyorlaydi.
* csv_file_path: str - bu fayl manzili
* result_key: str - bu fayldagi asosiy kelib chiqishi kerak bo'lgan qiymat
* target_values: list[str] - bu bashorat qilinishi kerak bo'lgan ma'lumot
43](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_43.png?v=1)
![Qaytish: dict[Any]
* koeffitsentlar
* korrelyatsiya koefftisenti
* bashorat qiymati
"""
data = pd.read_csv(csv_file_path)
data = data.fillna(0)
X = data.drop(result_key, axis=1)
y = data[result_key]
model = linear_model.LinearRegression()
model.fit(X, y)
r_squared = model.score(X, y)
returned_dict = {}
returned_dict['coef'] = model.coef_
returned_dict['free'] = model.intercept_
returned_dict['r'] = r_squared
returned_dict['target_result'] = model.predict([target_values])[0]
return returned_dict
class CustomInput:
def __init__(self,window: tk.Tk, width: int, height: int, position_x: int, position_y: int, *args,
**kwargs):
self.input = tk.Entry(window, font=('Arial 10'), *args, **kwargs)
self.input.place(height=height, width=width, x=position_x, y=position_y)
def get_text(self):
return self.input.get()
def set_text(self, text: str):
self.input.delete(0, tk.END)
self.input.insert(0, text)
def delete(self):
self.input.destroy()
class CustomButton:
def __init__(self, window: tk.Tk, text: str, width: int, height: int, position_x: int, position_y: int,
*args, **kwargs):
self.button = tk.Button(window, text=text, *args, **kwargs)
self.button.place(height=height, width=width, x=position_x, y=position_y)
def delete(self):
self.button.destroy()
class GUI:
def __init__(self, *args, **_) -> None:
self.filename: str = None
self.data: pd.DataFrame = None
self.columns: list[str] = None
self.value_inside = None
44](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_44.png?v=1)
![self.window = tk.Tk(className=_['window_name'])
self.window.geometry(f'{_["screen_width"]}x{_["screen_height"]}')
self.window.configure(bg='#e6e6ff')
self.keys_info: list[tk.Widget] = []
self.value_inputs: list[CustomInput] = []
self.coeffitsents: list[tk.Label] = []
self.buttons_draw()
self.labels_draw()
self.inputs_draw()
self.others_draw()
self.window.mainloop()
def buttons_draw(self):
""" Barcha boshlang'ich buttonlar shu yerda chiziladi """
self.button_open_file_dialog = CustomButton(self.window, text='CSV faylni tanlang',
font=('Arial 10'), width=440, height=30, position_x=10, position_y=0, command=self.select_file)
self.button_solve = CustomButton(self.window, text='Hisoblash', font=('Arial 10'),
width=440, height=30, position_x=550, position_y=260, command=self.solve_action)
self.button_clear = CustomButton(self.window, text='Tozalash', font=('Arial 10'), width=440,
height=30, position_x=550, position_y=290, command=self.clear_action)
def clear_action(self):
""" Tozalash tugmasi bosilganda shu funksiya ishlaydi """
if self.filename:
self.draw_target_inputs(self.value_inside.get())
for i in self.value_inputs:
i.set_text('')
self.r_input.set_text('0.5')
self.show_target_res.config(text="Umumiy natija: Mavjud emas")
def solve_action(self):
""" Hisoblash tugmasi bosilganda shu funksiya ishlaydi """
if not self.filename:
self.error_view("Fayl tanlanmagan", "Iltimos avval kerakli faylni tanlang !")
return
absolute_error = self.r_input.get_text()
if not absolute_error:
self.error_view("Ma'lumot to'liq emas", "Iltimos korrelyatsiya koeffitsientini kiriting")
return
try:
absolute_error = float(absolute_error)
except:
self.error_view("String konvertatsiya xatoligi", "Korrelyatsiya koeffitsienti son bo'lishi
kerak")
return
if fabs(absolute_error) > 1.0:
self.error_view("Noto'g'ri qiymat", "Korrelyatsiya koeffitsienti moduli 1 dan kichik
bo'lishi shart")
45](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_45.png?v=1)
![return
target_values: list[float] = []
for i in range(len(self.value_inputs)):
text = self.value_inputs[i].get_text()
if not text:
self.error_view("Ma'lumotlar to'liq emas", f"Iltimos `{self.keys_info[i]['text']}`ning
qiymatini kiriting")
return
try:
target_values.append(float(text))
except:
self.error_view("String konvertatsiya xatoligi", f"`{self.keys_info[i]['text']}` maydoniga
son kiriting!")
return
res = get_solve_in_csv(self.filename, self.value_inside.get(), target_values)
if res['r'] < absolute_error:
self.error_view("Natijalar yaxshi emas!", "Modeldagi korrelyatsiya koeffitsenti talabga
javob bermaydi")
return
self.show_target_res.config(text="Umumiy natija: " + str(res['target_result']))
def inputs_draw(self):
""" Boshlang'ich inputlar shu yerda chiziladi """
self.r_input = CustomInput(self.window, 440, 30, 10, 290)
self.r_input.set_text(0.5)
def labels_draw(self):
""" Boshlang'ich labellar shu yerda chiziladi """
self.file_name_info = tk.Label(self.window, text='Fayl: Tanlanmagan', font=('Arial 10'),
relief=tk.FLAT)
self.file_name_info.place(x=10, y=40, width=440, height=30)
self.file_cols_info = tk.Label(self.window, text='Ustunlar: Tanlanmagan', font=('Arial 10'),
relief=tk.FLAT)
self.file_cols_info.place(x=10, y=70, width=440, height=30)
self.file_rows_info = tk.Label(self.window, text='Ma\'lumotlar hajmi: Tanlanmagan',
font=('Arial 10'), relief=tk.FLAT)
self.file_rows_info.place(x=10, y=100, width=440, height=30)
self.key_select_info = tk.Label(self.window, text='Asosiy qiymat kalitini tanlang',
font=('Arial 10'), relief=tk.FLAT)
self.key_select_info.place(y=0, x=550, width=440, height=30)
tk.Label(self.window, text='Nomlar:', font=('Arial 10'), relief=tk.RIDGE).place(y=150, x=10,
width=80, height=30)
tk.Label(self.window, text='Qiymatlar:', font=('Arial 10'), relief=tk.RIDGE).place(y=180,
x=10, width=80, height=30)
tk.Label(self.window, text='Koeffitsentlar:', font=('Arial 9'), relief=tk.RIDGE).place(y=210,
x=10, width=80, height=30)
46](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_46.png?v=1)
![tk.Label(self.window, text='Minimal korrelyatsiya koeffitsientini kiriting', font=('Arial 10'),
relief=tk.FLAT).place(y=260, x=10, width=440, height=30)
self.show_r = tk.Label(self.window, text="Korrelyatsiya koeffitsienti: Fayl tanlanmagan",
relief=tk.FLAT, font=('Arial 10'))
self.show_r.place(y=330, x=10, width=440, height=30)
self.show_target_res = tk.Label(self.window, text="Umumiy natija: Mavjud emas",
relief=tk.FLAT, font=('Arial 10'))
self.show_target_res.place(y=360, x=10, width=440, height=30)
self.show_free_coef = tk.Label(self.window, text="Ozod koeffitsent: Fayl tanlanmagan",
relief=tk.FLAT, font=('Arial 10'))
self.show_free_coef.place(y=390, x=10, width=440, height=30)
def others_draw(self):
""" OptionMenu shu yerda chiziladi """
self.value_inside = tk.StringVar(self.window)
self.value_inside.set("Fayl tanlanmagan")
self.select_main_key = tk.OptionMenu(self.window, self.value_inside, value='')
self.select_main_key.place(y=40, x=550, width=440, height=30)
self.select_main_key.config(state=tk.DISABLED, relief=tk.GROOVE)
def select_file(self):
""" Open File Dialog ochilishida ishlaydihgan funksiya """
filename = filedialog.askopenfilename(initialdir=os.getcwd(), title="CSV faylni tanlang",
filetypes=(('CSV fayllar', '*csv'),))
if not (not filename or filename == ()):
self.filename = filename
data = pd.read_csv(self.filename)
self.columns = data.columns
self.file_name_info.config(text='Fayl: ' + self.filename.split('/')[-1])
self.file_cols_info.config(text='Ustunlar: ' + ','.join(self.columns))
self.file_rows_info.config(text='Ma\'lumotlar hajmi: ' + str(len(data)))
self.select_main_key.destroy()
self.value_inside = tk.StringVar(self.window)
self.value_inside.set(self.columns[-1])
self.select_main_key = tk.OptionMenu(self.window, self.value_inside, *self.columns,
command=self.select_func)
self.select_main_key.place(y=40, x=550, width=440, height=30)
self.select_main_key.config(relief=tk.GROOVE)
self.show_target_res.config(text="Umumiy natija: Mavjud emas")
self.draw_target_inputs(self.value_inside.get())
def select_func(self, *args, **kwarg):
47](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_47.png?v=1)
![""" OptionMenu qayta tanlangan vaqtda shu funksiya ishlaydi """
self.draw_target_inputs(self.value_inside.get())
def draw_target_inputs(self, ignore: str):
""" Yangilanish vaqtida inputlarni qayta chizadigan funksiya """
for i in range(len(self.keys_info)):
self.keys_info[i].destroy()
self.value_inputs[i].delete()
self.coeffitsents[i].destroy()
self.value_inputs.clear()
self.keys_info.clear()
self.coeffitsents.clear()
res = get_solve_in_csv(self.filename, self.value_inside.get(), list(map(float,
'0'*(len(self.columns)-1))))
counter = 0
for i in range(len(self.columns)):
if self.columns[i] == ignore:
continue
label = tk.Label(self.window, text=self.columns[i], font=('Arial 10'), relief=tk.RIDGE)
label.place(x=90 + counter*80, y=150, width=80, height=30)
self.keys_info.append(label)
self.value_inputs.append(CustomInput(self.window, 80, 30, 90+counter*80, 180))
label = tk.Label(self.window, text=f"{res['coef'][counter]:.7f}", relief=tk.FLAT,
font=('Arial 10'))
label.place(x=90 + counter*80, y=210, width=80, height=30)
self.coeffitsents.append(label)
counter += 1
self.show_r.config(text="Korrelyatsiya koeffitsienti: " + str(res['r']))
self.show_free_coef.config(text="Ozod koeffitsient: " + str(res['free']))
def error_view(self, error_screen: str, error_text: str):
""" Xatolik xabarini ekranga chiqaradi """
messagebox.showerror(error_screen, error_text)
if __name__ == '__main__':
warnings.filterwarnings('ignore')
GUI(
window_name = "Liner prediction problem solver",
screen_width = 1000,
screen_height = 450
)
48](https://docx.uz/documents/81a56dd1-d9df-4fb5-b68c-41d84db327d3/page_48.png?v=1)
Mashinali o‘qitishda gradientli tushish algoritmini chiziqli regressiya yordamida tadqiq qilish