Regression Logistic ສໍາລັບການປະຕິເສດກັບ API Core

ການທົບທວນຄືນ Content

ລະຫັດ QR
ດາວນ໌ໂຫລດ Data
Preprocessing ຂໍ້ມູນ
ລະຫັດ QR
ຄວາມຄິດເຫັນທີ່ Logistic Regression
ການເຮັດວຽກ Log Loss
ລະບົບການປັບປຸງ Gradient Descent
ການຝຶກອົບຮົມ Model
ການທົບທວນຄືນ
ດາວນ໌ໂຫລດ The Model
ພາສາລາວ

ຄູ່ມືນີ້ສະແດງໃຫ້ເຫັນວິທີການນໍາໃຊ້ API ຂອງ TensorFlow Core ທີ່ມີລະດັບຕ່ໍາເພື່ອນໍາໃຊ້ການສື່ຫຍໍ້ຂອງ binary ກັບການຍົກເລີກ logistic. ມັນນໍາໃຊ້ວິທະຍາໄລ Wisconsin Cancerປະເພດຂອງ tumor

ລະຫັດ QRມັນເປັນຫນຶ່ງໃນ algoritms ທີ່ດີທີ່ສຸດສໍາລັບການປະເພດສິລະປະ binary. ໃນຂະນະທີ່ມີຊຸດຕົວຢ່າງທີ່ມີຄຸນນະສົມບັດ, ການຄົ້ນຄວ້າຂອງການດໍາເນີນການ regression logistic ແມ່ນສໍາລັບການຜະລິດຄຸນນະສົມບັດລະຫວ່າງ 0 ແລະ 1, ເຊິ່ງສາມາດໄດ້ຮັບການອະນຸຍາດເປັນ probabilities ຂອງແຕ່ລະຕົວຢ່າງທີ່ກ່ຽວຂ້ອງກັບຄຸນນະສົມບັດພິເສດ.

ລະຫັດ QR

ການນໍາໃຊ້ tutorialປະເພດ Pandaການອ່ານເອກະສານ CSV ໃນ aລະຫັດ QRຂໍຂອບໃຈສີດໍາສໍາລັບການ plotting ການເຊື່ອມຕໍ່ Pairwise ໃນ dataset,ດາວໂຫລດສໍາລັບການຄອມພິວເຕີ matrix confusion, ແລະໂທລະສັບມືຖືການສ້າງ visualizations.

pip install -q seaborn

import tensorflow as tf
import pandas as pd
import matplotlib
from matplotlib import pyplot as plt
import seaborn as sns
import sklearn.metrics as sk_metrics
import tempfile
import os

# Preset matplotlib figure sizes.
matplotlib.rcParams['figure.figsize'] = [9, 6]

print(tf.__version__)
# To make the results reproducible, set the random seed value.
tf.random.set_seed(22)

2024-08-15 02:45:41.468739: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:485] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered
2024-08-15 02:45:41.489749: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:8454] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
2024-08-15 02:45:41.496228: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1452] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
2.17.0

ດາວນ໌ໂຫລດ Data

ຫຼັງຈາກນັ້ນ, load theວິທະຍາໄລ Wisconsin Cancerຈາກ Theການຝຶກອົບຮົມ UCI Machine Learningຊຸດຂໍ້ມູນນີ້ປະກອບມີຄຸນນະສົມບັດທີ່ແຕກຕ່າງກັນເຊັ່ນຕອງຂອງ tumor, texture, ແລະ concavity.

url = 'https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data'

features = ['radius', 'texture', 'perimeter', 'area', 'smoothness', 'compactness',
            'concavity', 'concave_poinits', 'symmetry', 'fractal_dimension']
column_names = ['id', 'diagnosis']

for attr in ['mean', 'ste', 'largest']:
  for feature in features:
    column_names.append(feature + "_" + attr)

ຊື່ຫຍໍ້ຂອງ : Read the dataset into a pandasລະຫັດ QR using pandas.read_csv:

dataset = pd.read_csv(url, names=column_names)

dataset.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 569 entries, 0 to 568
Data columns (total 32 columns):
 #   Column                     Non-Null Count  Dtype  
---  ------                     --------------  -----  
 0   id                         569 non-null    int64  
 1   diagnosis                  569 non-null    object 
 2   radius_mean                569 non-null    float64
 3   texture_mean               569 non-null    float64
 4   perimeter_mean             569 non-null    float64
 5   area_mean                  569 non-null    float64
 6   smoothness_mean            569 non-null    float64
 7   compactness_mean           569 non-null    float64
 8   concavity_mean             569 non-null    float64
 9   concave_poinits_mean       569 non-null    float64
 10  symmetry_mean              569 non-null    float64
 11  fractal_dimension_mean     569 non-null    float64
 12  radius_ste                 569 non-null    float64
 13  texture_ste                569 non-null    float64
 14  perimeter_ste              569 non-null    float64
 15  area_ste                   569 non-null    float64
 16  smoothness_ste             569 non-null    float64
 17  compactness_ste            569 non-null    float64
 18  concavity_ste              569 non-null    float64
 19  concave_poinits_ste        569 non-null    float64
 20  symmetry_ste               569 non-null    float64
 21  fractal_dimension_ste      569 non-null    float64
 22  radius_largest             569 non-null    float64
 23  texture_largest            569 non-null    float64
 24  perimeter_largest          569 non-null    float64
 25  area_largest               569 non-null    float64
 26  smoothness_largest         569 non-null    float64
 27  compactness_largest        569 non-null    float64
 28  concavity_largest          569 non-null    float64
 29  concave_poinits_largest    569 non-null    float64
 30  symmetry_largest           569 non-null    float64
 31  fractal_dimension_largest  569 non-null    float64
dtypes: float64(30), int64(1), object(1)
memory usage: 142.4+ KB

Display the first five rows:

dataset.head()

id	diagnosis	radius_mean	texture_mean	perimeter_mean	area_mean	smoothness_mean	compactness_mean	concavity_mean	concave_poinits_mean	...	radius_largest	texture_largest	perimeter_largest	area_largest	smoothness_largest	compactness_largest	concavity_largest	concave_poinits_largest	symmetry_largest	fractal_dimension_largest

0 842302 M 17.99 10.38 122.80 1001.0 0.11840 0.27760 0.3001 0.14710 ... 25.38 17.33 184.60 2019.0 0.1622 0.6656 0.7119 0.2654 0.4601 0.11890 1 842517 M 20.57 17.77 132.90 1326.0 0.08474 0.07864 0.0869 0.07017 ... 24.99 23.41 158.80 1956.0 0.1238 0.1866 0.24 0.1860 0.274850 0.08902 2 84300903 M 19.25 21.25 130.00 1203.00.10960 0.15990 0.1974 0.12790 ... 23.57 25.53 152.508.07 1707.014 0.444 0.4245 0.4504 0.30 0.13875 3 84348301 M 11.42 20.38 77.58 386.

ຊື່ຫຍໍ້ຂອງ : Divide the dataset into training and test sets usingpandas.DataFrame.sampleຂໍຂອບໃຈpandas.DataFrame.dropແລະpandas.DataFrame.ilocຊຸດທົດສອບຖືກນໍາໃຊ້ເພື່ອ evaluating generalizability ຂອງມາດຕະຖານຂອງທ່ານກັບຂໍ້ມູນທີ່ບໍ່ຮູ້ຈັກ.

train_dataset = dataset.sample(frac=0.75, random_state=1)

len(train_dataset)

test_dataset = dataset.drop(train_dataset.index)

len(test_dataset)

# The `id` column can be dropped since each row is unique
x_train, y_train = train_dataset.iloc[:, 2:], train_dataset.iloc[:, 1]
x_test, y_test = test_dataset.iloc[:, 2:], test_dataset.iloc[:, 1]

Preprocessing ຂໍ້ມູນ

ລະບົບຂໍ້ມູນນີ້ປະກອບມີຂະຫນາດກາງ, ລະບົບປະເພດ, ແລະຂະຫນາດໃຫຍ່ທີ່ສຸດສໍາລັບທຸກໆ 10 ການຂະຫນາດໃຫຍ່ຂອງ tumor ທີ່ໄດ້ຮັບການກວດສອບໂດຍສະເພາະ."diagnosis"ລະຫັດ QR ທີ່ຖືກເຂົ້າລະຫັດໂດຍການເຂົ້າລະຫັດ QR'M'ການຢັ້ງຢືນການປິ່ນປົວຂອງ tumor malignant ແລະ'B'ການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນການຢັ້ງຢືນ

ການpandas.Series.mapລະຫັດ QR ເອກະຊົນບໍລິການບໍລິການລູກຄ້າຂອງພວກເຮົາ

ຊຸດຂໍ້ມູນຍັງຄວນໄດ້ຮັບການປ່ຽນແປງກັບ tensor ກັບtf.convert_to_tensorການເຮັດວຽກຫຼັງຈາກການ preprocessing ແມ່ນ completed.

y_train, y_test = y_train.map({'B': 0, 'M': 1}), y_test.map({'B': 0, 'M': 1})
x_train, y_train = tf.convert_to_tensor(x_train, dtype=tf.float32), tf.convert_to_tensor(y_train, dtype=tf.float32)
x_test, y_test = tf.convert_to_tensor(x_test, dtype=tf.float32), tf.convert_to_tensor(y_test, dtype=tf.float32)

WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1723689945.265757  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.269593  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.273290  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.276976  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.288712  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.292180  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.295550  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.299093  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.302584  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.306098  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.309484  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689945.312921  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.538105  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.540233  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.542239  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.544278  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.546323  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.548257  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.550168  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.552143  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.554591  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.556540  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.558447  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.560412  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.599852  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.601910  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.604061  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.606104  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.608094  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.610074  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.611985  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.613947  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.615903  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.618356  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.620668  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355
I0000 00:00:1723689946.623031  132290 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355

Use seaborn.pairplotການທົບທວນຄືນການຈັດການຮ່ວມເພດຂອງຄູ່ເພື່ອນຂອງຄຸນນະສົມບັດປະມານທີ່ແຕກຕ່າງກັນຈາກຄຸນນະສົມບັດການຝຶກອົບຮົມແລະເບິ່ງວິທີທີ່ພວກເຂົາເຈົ້າກ່ຽວຂ້ອງກັບຈຸດປະສົງ:

sns.pairplot(train_dataset.iloc[:, 1:6], hue = 'diagnosis', diag_kind='kde');

ການຄາດຄະເນດິນດີຕ້ອນຮັບຂອງພວກເຮົາແມ່ນການຄາດຄະເນດິນດີຕ້ອນຮັບຂອງພວກເຮົາ. ການຄາດຄະເນດິນດີຕ້ອນຮັບຂອງພວກເຮົາແມ່ນການຄາດຄະເນດິນດີຕ້ອນຮັບຂອງພວກເຮົາ.

ຖ້າຫາກວ່າທ່ານກໍາລັງຊອກຫາຂໍ້ມູນເພີ່ມເຕີມ, ກະລຸນາຊອກຫາຂໍ້ມູນເພີ່ມເຕີມກ່ຽວກັບການຊອກຫາຂໍ້ມູນເພີ່ມເຕີມ.

train_dataset.describe().transpose()[:10]

	count	mean	std	min	25%	50%	75%	max
id	427.0	2.756014e+07	1.162735e+08	8670.00000	865427.500000	905539.00000	8.810829e+06	9.113205e+08
radius_mean	427.0	1.414331e+01	3.528717e+00	6.98100	11.695000	13.43000	1.594000e+01	2.811000e+01
texture_mean	427.0	1.924468e+01	4.113131e+00	10.38000	16.330000	18.84000	2.168000e+01	3.381000e+01
perimeter_mean	427.0	9.206759e+01	2.431431e+01	43.79000	75.235000	86.87000	1.060000e+02	1.885000e+02
area_mean	427.0	6.563190e+02	3.489106e+02	143.50000	420.050000	553.50000	7.908500e+02	2.499000e+03
smoothness_mean	427.0	9.633618e-02	1.436820e-02	0.05263	0.085850	0.09566	1.050000e-01	1.634000e-01
compactness_mean	427.0	1.036597e-01	5.351893e-02	0.02344	0.063515	0.09182	1.296500e-01	3.454000e-01
concavity_mean	427.0	8.833008e-02	7.965884e-02	0.00000	0.029570	0.05999	1.297500e-01	4.268000e-01
concave_poinits_mean	427.0	4.872688e-02	3.853594e-02	0.00000	0.019650	0.03390	7.409500e-02	2.012000e-01
symmetry_mean	427.0	1.804597e-01	2.637837e-02	0.12030	0.161700	0.17840	1.947000e-01	2.906000e-01

ລະຫັດ QR

427.0

2.756014e+07

1.162735e+08

8670.00000

865427.500000

905539.00000

8.810829e+06

9.113205e+08

ລະຫັດ QR

427.0

1.414331e+01

3.528717e+00

6.98100

11.695000

13.43000

1.594000e+01

2.811000e+01

texture_mean

427.0

1.924468e+01

4.113131e+00

10.38000

16.330000

18.84000

2.168000e+01

3.381000e+01

ຊື່ຫຍໍ້ຂອງ : perimeter

427.0

9.206759e+01

2.431431e+01

43.79000

75.235000

86.87000

1.060000e+02

1.885000e+02

ຫນ້າທໍາອິດ / Mean

427.0

6.563190e+02

3.489106e+02

143.50000

420.050000

553.50000

7.908500e+02

2.499000e+03

ຄວາມຄິດເຫັນທີ່ Smoothness

427.0

9.633618e-02

1.436820e-02

0.05263

0.085850

0.09566

1.050000e-01

1.634000e-01

ລະຫັດ QR

427.0

1.036597e-01

5.351893e-02

0.02344

0.063515

0.09182

1.296500e-01

3.454000e-01

ຄວາມຄິດເຫັນທີ່ concavity

427.0

8.833008e-02

7.965884e-02

0.00000

0.029570

0.05999

1.297500e-01

4.268000e-01

ຊື່ຫຍໍ້ຂອງ : concave

427.0

4.872688e-02

3.853594e-02

0.00000

0.019650

0.03390

7.409500e-02

2.012000e-01

symmetry_mean

427.0

1.804597e-01

2.637837e-02

0.12030

0.161700

0.17840

1.947000e-01

2.906000e-01

ມີການຄາດຄະເນດຽວກັນ, ມັນເປັນປະໂຫຍດທີ່ຈະມາດຕະຖານຂໍ້ມູນເຊັ່ນດຽວກັນກັບການຄາດຄະເນດຽວກັນກັບການຄາດຄະເນດຽວກັນກັບການຄາດຄະເນດຽວກັນ.normalization.

class Normalize(tf.Module):
  def __init__(self, x):
    # Initialize the mean and standard deviation for normalization
    self.mean = tf.Variable(tf.math.reduce_mean(x, axis=0))
    self.std = tf.Variable(tf.math.reduce_std(x, axis=0))

  def norm(self, x):
    # Normalize the input
    return (x - self.mean)/self.std

  def unnorm(self, x):
    # Unnormalize the input
    return (x * self.std) + self.mean

norm_x = Normalize(x_train)
x_train_norm, x_test_norm = norm_x.norm(x_train), norm_x.norm(x_test)

ລະຫັດ QR

Before building a logistic regression model, it is crucial to understand the method's differences compared to traditional linear regression.

ຄວາມຄິດເຫັນທີ່ Logistic Regression

ການຍົກເລີກ Linear returns a linear combination of its inputs; this output is unlimited. ການຍົກເລີກຂອງລະຫັດ QRມັນແມ່ນໃນ(0, 1)ປະເພດ: ປະເພດ: ປະເພດ: ປະເພດ: ປະເພດ: ປະເພດ: ປະເພດ: ປະເພດທີ່ດີເລີດລະຫັດ QR

Logistic regression maps the continuous outputs of traditional linear regression, (-∞, ∞)ປະເພດ probabilities(0, 1)ການປ່ຽນແປງນີ້ຍັງເປັນ symmetrical ດັ່ງນັ້ນຈຶ່ງເພື່ອ flipping ລະຫັດຂອງ output linear ມີຜົນປະໂຫຍດທີ່ທັນສະໄຫມຂອງ probabilities ທີ່ເລີ່ມຕົ້ນ.

ສະ ຫນັບ ສະ ຫນູນ ສະ ຫນູນ ສະ ຫນູນ ສະ ຫນູນ ສະ ຫນູນ ສະ ຫນູນ ສະ ຫນູນ ສະ ຫນູນ ສະ ຫນູນ ສະ ຫນູນ ສະ ຫນູນ1ການກັ່ນຕອງທີ່ຕ້ອງການສາມາດໄດ້ຮັບໂດຍ interpreting output linear regression ເປັນlog oddsຄວາມຄິດເຫັນທີ່ Being In Class1ປະເພດ0:

ln⁡(Y1−Y)=wX+b

ໂດຍການຕິດຕັ້ງ wX + b = z, ການຄາດຄະເນດຽວກັນນີ້ສາມາດແກ້ໄຂສໍາລັບ Y:

Y=ez1+ez=11+e−z

ການອະນຸຍາດ 11+e−z ແມ່ນຮູ້ຈັກເປັນລະຫັດ QR σ(z). Hence, the equation for logistic regression can be written as Y=σ(wX+b).

ລະບົບຂໍ້ມູນຂອງການຝຶກອົບຮົມນີ້ແມ່ນການປິ່ນປົວ matrix feature high-dimensional. Therefore, the equation above must be rewritten in a matrix vector form as follows:

Y=σ(Xw+b)

ວິທີການ:

Ym×1 - Vector ປະລິມານ
Xm×n: a feature matrix
ລະຫັດ QR
ຊື່ຫຍໍ້ຂອງ : A bias
σ: ຄຸນນະສົມບັດ sigmoid ທີ່ຖືກນໍາໃຊ້ກັບແຕ່ລະອຽດຂອງ vector output

ການເລີ່ມຕົ້ນໂດຍ visualizing ລະບົບ sigmoid, ເຊິ່ງການປ່ຽນແປງ output linear,(-∞, ∞)ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈ0ແລະ1ຄຸນນະສົມບັດ Sigmoid ແມ່ນມີຢູ່ໃນtf.math.sigmoid.

x = tf.linspace(-10, 10, 500)
x = tf.cast(x, tf.float32)
f = lambda x : (1/20)*x + 0.6
plt.plot(x, tf.math.sigmoid(x))
plt.ylim((-0.1,1.1))
plt.title("Sigmoid function");

ການເຮັດວຽກ Log Loss

ການດາວໂຫລດ, or binary cross-entropy loss, is the ideal loss function for a binary classification problem with logistic regression. For each example, the log loss quantifies the similarity between a predicted probability and the example's true value. It is determined by the following equation:

L=−1m∑i=1myi⋅log⁡(y^i)+(1−yi)⋅log⁡(1−y^i)

ວິທີການ:

y^: vector ຂອງ probabilities predicted
y: Vector ຂອງຈຸດປະສົງທີ່ແທ້ຈິງ

You can use the tf.nn.sigmoid_cross_entropy_with_logitsFunction to calculate the log loss. This function automatically applies the sigmoid activation to the regression output:

def log_loss(y_pred, y):
  # Compute the log loss function
  ce = tf.nn.sigmoid_cross_entropy_with_logits(labels=y, logits=y_pred)
  return tf.reduce_mean(ce)

ລະບົບການປັບປຸງ Gradient Descent

The TensorFlow Core APIs support automatic differentiation with tf.GradientTapeຖ້າຫາກວ່າທ່ານກໍາລັງຊອກຫາສໍາລັບການຄອມພິວເຕີທີ່ຢູ່ໃກ້ກັບການ regression logisticການປັບປຸງ Gradientຂໍຂອບໃຈວ່າທ່ານກໍາລັງຊອກຫາຂໍ້ມູນເພີ່ມເຕີມ.

ໃນອຸປະກອນທີ່ຜ່ານມາສໍາລັບການ lost log, ກະລຸນາຮູ້ວ່າແຕ່ລະ y^i ສາມາດໄດ້ຮັບ rewrite ໃນຕອນທ້າຍຂອງ input ເປັນ σ(Xiw + b).

ການຄົ້ນຄວ້າແມ່ນເພື່ອຊອກຫາ w ແລະ b ທີ່ຫຼຸດຜ່ອນການປະທັບໃຈຂອງບັນຊີລາຍຊື່:

L=−1m∑i=1myi⋅log⁡(σ(Xiw+b))+(1−yi)⋅log⁡(1−σ(Xiw+b))

By taking the gradient L with respect to w, you get the following:

∂L∂w=1m(σ(Xw+b)−y)X

ໂດຍການນໍາໃຊ້ gradient L ກັບ b, ທ່ານໄດ້ຮັບການນີ້:

∂L∂b=1m∑i=1mσ(Xiw+b)−yi

ໃນປັດຈຸບັນ, ສ້າງຮູບແບບການ regression logistic.

class LogisticRegression(tf.Module):

  def __init__(self):
    self.built = False

  def __call__(self, x, train=True):
    # Initialize the model parameters on the first call
    if not self.built:
      # Randomly generate the weights and the bias term
      rand_w = tf.random.uniform(shape=[x.shape[-1], 1], seed=22)
      rand_b = tf.random.uniform(shape=[], seed=22)
      self.w = tf.Variable(rand_w)
      self.b = tf.Variable(rand_b)
      self.built = True
    # Compute the model output
    z = tf.add(tf.matmul(x, self.w), self.b)
    z = tf.squeeze(z, axis=1)
    if train:
      return z
    return tf.sigmoid(z)

ການຢັ້ງຢືນ, ໃຫ້ແນ່ໃຈວ່າມາດຕະຖານທີ່ບໍ່ໄດ້ຮັບການຝຶກອົບຮົມ outputs ຄຸນນະພາບໃນຂະຫນາດຂອງ(0, 1)ສໍາລັບ subset ຂະຫນາດນ້ອຍຂອງຂໍ້ມູນການຝຶກອົບຮົມ.

log_reg = LogisticRegression()

y_pred = log_reg(x_train_norm[:5], train=False)
y_pred.numpy()

array([0.9994985 , 0.9978607 , 0.29620072, 0.01979049, 0.3314926 ],
      dtype=float32)

ຫຼັງຈາກນັ້ນ, ດາວນ໌ໂຫລດ Function accuracy ສໍາລັບການຄາດຄະເນຜົນປະໂຫຍດປະສິດທິພາບໃນໄລຍະການຝຶກອົບຮົມ. ສໍາລັບການດາວໂຫລດ Classifications ຈາກ probabilities predicted, sett a threshold for which all probabilities higher than the threshold belong to class.1. ນີ້ແມ່ນ hyperparameter configurable ທີ່ສາມາດຕິດຕັ້ງເພື່ອ0.5ໃນຖານະເປັນ default.

def predict_class(y_pred, thresh=0.5):
  # Return a tensor with  `1` if `y_pred` > `0.5`, and `0` otherwise
  return tf.cast(y_pred > thresh, tf.float32)

def accuracy(y_pred, y):
  # Return the proportion of matches between `y_pred` and `y`
  y_pred = tf.math.sigmoid(y_pred)
  y_pred_class = predict_class(y_pred)
  check_equal = tf.cast(y_pred_class == y,tf.float32)
  acc_val = tf.reduce_mean(check_equal)
  return acc_val

ການຝຶກອົບຮົມ Model

ການນໍາໃຊ້ mini-batches ສໍາລັບການຝຶກອົບຮົມສະຫນອງການປະສິດທິພາບຂອງລັກສະນະແລະການເຊື່ອມຕໍ່ຢ່າງໄວວາ.tf.data.DatasetAPI ມີຄຸນນະສົມບັດທີ່ດີສໍາລັບການ batching ແລະ shuffling. API ເຮັດໃຫ້ທ່ານສາມາດສ້າງ pipelines ການເຂົ້າເຖິງທີ່ສົມບູນແບບຈາກເອກະສານທີ່ທັນສະໄຫມແລະສາມາດນໍາໃຊ້ຢ່າງຕໍ່ເນື່ອງ.

batch_size = 64
train_dataset = tf.data.Dataset.from_tensor_slices((x_train_norm, y_train))
train_dataset = train_dataset.shuffle(buffer_size=x_train.shape[0]).batch(batch_size)
test_dataset = tf.data.Dataset.from_tensor_slices((x_test_norm, y_test))
test_dataset = test_dataset.shuffle(buffer_size=x_test.shape[0]).batch(batch_size)

ໃນປັດຈຸບັນຂຽນການຝຶກອົບຮົມ loop ສໍາລັບຮູບແບບ regression logistic. The loop utilizes the log loss function and its gradients with respect to the input in order to iteratively update the model's parameters.

# Set training parameters
epochs = 200
learning_rate = 0.01
train_losses, test_losses = [], []
train_accs, test_accs = [], []

# Set up the training loop and begin training
for epoch in range(epochs):
  batch_losses_train, batch_accs_train = [], []
  batch_losses_test, batch_accs_test = [], []

  # Iterate over the training data
  for x_batch, y_batch in train_dataset:
    with tf.GradientTape() as tape:
      y_pred_batch = log_reg(x_batch)
      batch_loss = log_loss(y_pred_batch, y_batch)
    batch_acc = accuracy(y_pred_batch, y_batch)
    # Update the parameters with respect to the gradient calculations
    grads = tape.gradient(batch_loss, log_reg.variables)
    for g,v in zip(grads, log_reg.variables):
      v.assign_sub(learning_rate * g)
    # Keep track of batch-level training performance
    batch_losses_train.append(batch_loss)
    batch_accs_train.append(batch_acc)

  # Iterate over the testing data
  for x_batch, y_batch in test_dataset:
    y_pred_batch = log_reg(x_batch)
    batch_loss = log_loss(y_pred_batch, y_batch)
    batch_acc = accuracy(y_pred_batch, y_batch)
    # Keep track of batch-level testing performance
    batch_losses_test.append(batch_loss)
    batch_accs_test.append(batch_acc)

  # Keep track of epoch-level model performance
  train_loss, train_acc = tf.reduce_mean(batch_losses_train), tf.reduce_mean(batch_accs_train)
  test_loss, test_acc = tf.reduce_mean(batch_losses_test), tf.reduce_mean(batch_accs_test)
  train_losses.append(train_loss)
  train_accs.append(train_acc)
  test_losses.append(test_loss)
  test_accs.append(test_acc)
  if epoch % 20 == 0:
    print(f"Epoch: {epoch}, Training log loss: {train_loss:.3f}")

Epoch: 0, Training log loss: 0.661
Epoch: 20, Training log loss: 0.418
Epoch: 40, Training log loss: 0.269
Epoch: 60, Training log loss: 0.178
Epoch: 80, Training log loss: 0.137
Epoch: 100, Training log loss: 0.116
Epoch: 120, Training log loss: 0.106
Epoch: 140, Training log loss: 0.096
Epoch: 160, Training log loss: 0.094
Epoch: 180, Training log loss: 0.089

ການທົບທວນຄືນ

ເບິ່ງການປ່ຽນແປງໃນຄວາມງາມແລະຄວາມຖືກຕ້ອງຂອງຮູບແບບຂອງທ່ານໃນໄລຍະເວລາ.

plt.plot(range(epochs), train_losses, label = "Training loss")
plt.plot(range(epochs), test_losses, label = "Testing loss")
plt.xlabel("Epoch")
plt.ylabel("Log loss")
plt.legend()
plt.title("Log loss vs training iterations");

plt.plot(range(epochs), train_accs, label = "Training accuracy")
plt.plot(range(epochs), test_accs, label = "Testing accuracy")
plt.xlabel("Epoch")
plt.ylabel("Accuracy (%)")
plt.legend()
plt.title("Accuracy vs training iterations");

print(f"Final training log loss: {train_losses[-1]:.3f}")
print(f"Final testing log Loss: {test_losses[-1]:.3f}")

Final training log loss: 0.089
Final testing log Loss: 0.077

print(f"Final training accuracy: {train_accs[-1]:.3f}")
print(f"Final testing accuracy: {test_accs[-1]:.3f}")

Final training accuracy: 0.968
Final testing accuracy: 0.979

ຮູບແບບນີ້ສະແດງໃຫ້ເຫັນຄວາມແມ່ນຍໍາສູງແລະຄວາມເສຍຫາຍຕ່ໍາໃນຂະນະທີ່ຂ້າງຂວາງກ່ຽວກັບການສອບເສັງ tumors ໃນຊຸດຂໍ້ມູນການຝຶກອົບຮົມແລະຍັງເປັນການທົ່ວໄປທີ່ດີກັບຂໍ້ມູນການທົດສອບທີ່ບໍ່ຖືກເບິ່ງ. ສໍາລັບການຂົນສົ່ງຫນຶ່ງຫຼັງຈາກນັ້ນ, ທ່ານສາມາດທົດສອບລະດັບຄວາມຜິດພາດທີ່ໃຫ້ຄວາມຮູ້ເພີ່ມເຕີມຫຼາຍກ່ວາລະດັບຄວາມແມ່ນຍໍາທົ່ວໄປ. ລະດັບຄວາມຜິດພາດທີ່ດີທີ່ສຸດສອງສໍາລັບບັນຫາການສອບເສັງ binary ແມ່ນລະດັບຄວາມຫມັ້ນຄົງ (FPR) ແລະລະດັບຄວາມຫມັ້ນຄົງ (FNR).

ສໍາລັບບັນຫານີ້, FPR ແມ່ນຂະຫນາດໃຫຍ່ຂອງການຄາດຄະເນດິບ malignant ໃນລະຫວ່າງການຢາທີ່ເປັນຕົວແທນ benign. Inversely, FNR ແມ່ນຂະຫນາດໃຫຍ່ຂອງການຄາດຄະເນດິບ benign ໃນລະຫວ່າງການຢາທີ່ເປັນຕົວແທນ malignant.

ການຄຸ້ມຄອງ matrix confusionsklearn.metrics.confusion_matrix, ເຊິ່ງກວດສອບຄວາມຖືກຕ້ອງຂອງການກວດສອບ, ແລະໃຊ້ matplotlib ເພື່ອພິມ matrix:

def show_confusion_matrix(y, y_classes, typ):
  # Compute the confusion matrix and normalize it
  plt.figure(figsize=(10,10))
  confusion = sk_metrics.confusion_matrix(y.numpy(), y_classes.numpy())
  confusion_normalized = confusion / confusion.sum(axis=1, keepdims=True)
  axis_labels = range(2)
  ax = sns.heatmap(
      confusion_normalized, xticklabels=axis_labels, yticklabels=axis_labels,
      cmap='Blues', annot=True, fmt='.4f', square=True)
  plt.title(f"Confusion matrix: {typ}")
  plt.ylabel("True label")
  plt.xlabel("Predicted label")

y_pred_train, y_pred_test = log_reg(x_train_norm, train=False), log_reg(x_test_norm, train=False)
train_classes, test_classes = predict_class(y_pred_train), predict_class(y_pred_test)

show_confusion_matrix(y_train, train_classes, 'Training')

show_confusion_matrix(y_test, test_classes, 'Testing')

ໃນໄລຍະການທົດສອບທາງດ້ານວິຊາການຈໍານວນຫຼາຍເຊັ່ນດຽວກັນກັບການກວດສອບການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນປົວຂອງການປິ່ນ

ສໍາລັບການຄວບຄຸມສໍາລັບ FPR ແລະ FNR, ກະລຸນາປ່ຽນແປງ hyperparameter threshold ໃນຂະນະທີ່ກໍານົດຄຸນນະພາບຄຸນນະພາບ. threshold ນ້ອຍກ່ວາການຄຸນນະພາບສູງກ່ວາການຄຸນນະພາບສູງກ່ວາການຄຸນນະພາບສູງກ່ວາການຄຸນນະພາບສູງກ່ວາການຄຸນນະພາບສູງກ່ວາການຄຸນນະພາບສູງ. This inevitably increases the number of false positives and the FPR but it also helps to reduce the number of false negatives and the FNR.

ດາວນ໌ໂຫລດ The Model

ຂ້າພະເຈົ້າສືບຕໍ່ໄດ້ຮັບການປະທັບໃຈກໍໂດຍການບໍລິການລູກຄ້າຂອງພວກເຮົາ

ລະຫັດ QR
ການຄາດຄະເນ
ການຄາດຄະເນ

class ExportModule(tf.Module):
  def __init__(self, model, norm_x, class_pred):
    # Initialize pre- and post-processing functions
    self.model = model
    self.norm_x = norm_x
    self.class_pred = class_pred

  @tf.function(input_signature=[tf.TensorSpec(shape=[None, None], dtype=tf.float32)])
  def __call__(self, x):
    # Run the `ExportModule` for new data points
    x = self.norm_x.norm(x)
    y = self.model(x, train=False)
    y = self.class_pred(y)
    return y

log_reg_export = ExportModule(model=log_reg,
                              norm_x=norm_x,
                              class_pred=predict_class)

ຖ້າຫາກວ່າທ່ານຕ້ອງການໃຫ້ມາດຕະຖານໃນສະພາບອາກາດຂອງຕົນ, ທ່ານສາມາດເຮັດວຽກກັບtf.saved_model.saveການດາວໂຫລດຮູບແບບທີ່ຖືກເກັບຮັກສາແລະການຄາດຄະເນດຽວກັນtf.saved_model.loadລະຫັດ QR

models = tempfile.mkdtemp()
save_path = os.path.join(models, 'log_reg_export')
tf.saved_model.save(log_reg_export, save_path)

INFO:tensorflow:Assets written to: /tmpfs/tmp/tmp9k_sar52/log_reg_export/assets
INFO:tensorflow:Assets written to: /tmpfs/tmp/tmp9k_sar52/log_reg_export/assets

log_reg_loaded = tf.saved_model.load(save_path)
test_preds = log_reg_loaded(x_test)
test_preds[:10].numpy()

array([1., 1., 1., 1., 0., 1., 1., 1., 1., 1.], dtype=float32)

ພາສາລາວ

ຊື່ຫຍໍ້ຂອງ : This notebook introduced a few techniques to handle a logistic regression problem. Here are a few more tips that may help:

API ຂອງ TensorFlow Core ສາມາດຖືກນໍາໃຊ້ເພື່ອສ້າງ workflows ການຝຶກອົບຮົມເຄື່ອງທີ່ມີລະດັບຄວາມສູງຂອງການຕິດຕັ້ງ
ການທົດສອບລະດັບຄວາມຜິດພາດແມ່ນວິທີທີ່ດີທີ່ຈະຊອກຫາຄວາມຮູ້ເພີ່ມເຕີມກ່ຽວກັບຜົນປະໂຫຍດຂອງມະນຸດຄົ້ນຄວ້າຫຼາຍກ່ວາລະດັບຄວາມຖືກຕ້ອງທັງຫມົດຂອງຕົນ.
Overfitting ແມ່ນບັນຫາທີ່ແຕກຕ່າງກັນສໍາລັບຮູບແບບ regression logistic, ແຕ່ມັນບໍ່ແມ່ນບັນຫາສໍາລັບການ tutorial ນີ້. ດາວນ໌ໂຫລດ Overfit ແລະ underfit tutorial ສໍາລັບການຊ່ວຍເຫຼືອເພີ່ມເຕີມກ່ຽວກັບການນີ້.

ສໍາລັບຕົວຢ່າງເພີ່ມເຕີມຂອງການນໍາໃຊ້ TensorFlow Core API, ດາວນ໌ໂຫລດguideຖ້າຫາກວ່າທ່ານຕ້ອງການຮູ້ເພີ່ມເຕີມກ່ຽວກັບການດາວໂຫລດແລະການ preparing data, ກະລຸນາເບິ່ງ tutorials ຢູ່ຮູບພາບ ສໍາ ລັບ Data Loadingປະເພດລະຫັດ QR.

ທີ່ຜ່ານມາ: Published on theປະເພດ TensorFlow website, this article appears here under a new headline and is licensed under CC BY 4.0. Code samples shared under the Apache 2.0 License

ທີ່ຜ່ານມາ: Published on theປະເພດ TensorFlowເວັບໄຊທ໌ເວັບໄຊທ໌ນີ້ສະແດງໃຫ້ເຫັນນີ້ພາຍໃຕ້ຊື່ໃຫມ່ແລະໄດ້ຮັບການອະນຸຍາດພາຍໃຕ້ CC BY 4.0. ລະຫັດຕົວຢ່າງຖືກຈັດຂຶ້ນພາຍໃຕ້ Apache 2.0 License

ປະເພດ TensorFlow

Regression Logistic ສໍາລັບການປະຕິເສດກັບ API Core

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ການເຮັດວຽກ Log Loss

ລະບົບການປັບປຸງ Gradient Descent

ການຝຶກອົບຮົມ Model

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