import warnings
warnings.filterwarnings('ignore')
import numpy as np
import pandas as pd
np.random.seed(12345)
import matplotlib.pyplot as plt
plt.rc('figure', figsize=(10, 6))
PREVIOUS_MAX_ROWS = pd.options.display.max_rows
pd.options.display.max_columns = 20
pd.options.display.max_rows = 20
pd.options.display.max_colwidth = 80
np.set_printoptions(precision=4, suppress=True)
import matplotlib.pyplot as plt
# Matplotlib 한글 폰트 설정 (macOS용)
plt.rc('font', family='AppleGothic')
plt.rc('axes', unicode_minus=False)11 12장: 파이썬 모델링 라이브러리 소개
데이터 분석을 넘어 기계 학습 모델링으로 나아가기 위한 기초 인터페이스를 다룹니다.
11.1 pandas와 모델 코드의 인터페이스
데이터프레임을 NumPy 배열로 변환하여 모델 라이브러리에 전달하는 과정을 이해합니다.
data = pd.DataFrame({
'x0': [1, 2, 3, 4, 5],
'x1': [0.01, -0.01, 0.25, -4.1, 0.],
'y': [-1.5, 0., 3.6, 1.3, -2.]})
data
data.columns
data.to_numpy()array([[ 1. , 0.01, -1.5 ],
[ 2. , -0.01, 0. ],
[ 3. , 0.25, 3.6 ],
[ 4. , -4.1 , 1.3 ],
[ 5. , 0. , -2. ]])df2 = pd.DataFrame(data.to_numpy(), columns=['one', 'two', 'three'])
df2| one | two | three | |
|---|---|---|---|
| 0 | 1.0 | 0.01 | -1.5 |
| 1 | 2.0 | -0.01 | 0.0 |
| 2 | 3.0 | 0.25 | 3.6 |
| 3 | 4.0 | -4.10 | 1.3 |
| 4 | 5.0 | 0.00 | -2.0 |
df3 = data.copy()
df3['strings'] = ['a', 'b', 'c', 'd', 'e']
df3
df3.to_numpy()array([[1, 0.01, -1.5, 'a'],
[2, -0.01, 0.0, 'b'],
[3, 0.25, 3.6, 'c'],
[4, -4.1, 1.3, 'd'],
[5, 0.0, -2.0, 'e']], dtype=object)model_cols = ['x0', 'x1']
data.loc[:, model_cols].to_numpy()array([[ 1. , 0.01],
[ 2. , -0.01],
[ 3. , 0.25],
[ 4. , -4.1 ],
[ 5. , 0. ]])data['category'] = pd.Categorical(['a', 'b', 'a', 'a', 'b'],
categories=['a', 'b'])
data| x0 | x1 | y | category | |
|---|---|---|---|---|
| 0 | 1 | 0.01 | -1.5 | a |
| 1 | 2 | -0.01 | 0.0 | b |
| 2 | 3 | 0.25 | 3.6 | a |
| 3 | 4 | -4.10 | 1.3 | a |
| 4 | 5 | 0.00 | -2.0 | b |
dummies = pd.get_dummies(data.category, prefix='category',
dtype=float)
data_with_dummies = data.drop('category', axis=1).join(dummies)
data_with_dummies| x0 | x1 | y | category_a | category_b | |
|---|---|---|---|---|---|
| 0 | 1 | 0.01 | -1.5 | 1.0 | 0.0 |
| 1 | 2 | -0.01 | 0.0 | 0.0 | 1.0 |
| 2 | 3 | 0.25 | 3.6 | 1.0 | 0.0 |
| 3 | 4 | -4.10 | 1.3 | 1.0 | 0.0 |
| 4 | 5 | 0.00 | -2.0 | 0.0 | 1.0 |
11.2 Patsy를 이용한 모델 설명
수식 형태의 문자열을 사용하여 통계 모델의 디자인 행렬을 생성합니다.
11.3 Patsy를 이용한 모델 설명
설명 변수와 반응 변수를 수식 형태로 기술하는 방법을 배웁니다.
data = pd.DataFrame({
'x0': [1, 2, 3, 4, 5],
'x1': [0.01, -0.01, 0.25, -4.1, 0.],
'y': [-1.5, 0., 3.6, 1.3, -2.]})
data
import patsy
y, X = patsy.dmatrices('y ~ x0 + x1', data)y
XDesignMatrix with shape (5, 3)
Intercept x0 x1
1 1 0.01
1 2 -0.01
1 3 0.25
1 4 -4.10
1 5 0.00
Terms:
'Intercept' (column 0)
'x0' (column 1)
'x1' (column 2)np.asarray(y)
np.asarray(X)array([[ 1. , 1. , 0.01],
[ 1. , 2. , -0.01],
[ 1. , 3. , 0.25],
[ 1. , 4. , -4.1 ],
[ 1. , 5. , 0. ]])patsy.dmatrices('y ~ x0 + x1 + 0', data)[1]DesignMatrix with shape (5, 2)
x0 x1
1 0.01
2 -0.01
3 0.25
4 -4.10
5 0.00
Terms:
'x0' (column 0)
'x1' (column 1)coef, resid, _, _ = np.linalg.lstsq(X, y, rcond=None)coef
coef = pd.Series(coef.squeeze(), index=X.design_info.column_names)
coefIntercept 0.312910
x0 -0.079106
x1 -0.265464
dtype: float64y, X = patsy.dmatrices('y ~ x0 + np.log(np.abs(x1) + 1)', data)
XDesignMatrix with shape (5, 3)
Intercept x0 np.log(np.abs(x1) + 1)
1 1 0.00995
1 2 0.00995
1 3 0.22314
1 4 1.62924
1 5 0.00000
Terms:
'Intercept' (column 0)
'x0' (column 1)
'np.log(np.abs(x1) + 1)' (column 2)y, X = patsy.dmatrices('y ~ standardize(x0) + center(x1)', data)
XDesignMatrix with shape (5, 3)
Intercept standardize(x0) center(x1)
1 -1.41421 0.78
1 -0.70711 0.76
1 0.00000 1.02
1 0.70711 -3.33
1 1.41421 0.77
Terms:
'Intercept' (column 0)
'standardize(x0)' (column 1)
'center(x1)' (column 2)new_data = pd.DataFrame({
'x0': [6, 7, 8, 9],
'x1': [3.1, -0.5, 0, 2.3],
'y': [1, 2, 3, 4]})
new_X = patsy.build_design_matrices([X.design_info], new_data)
new_X[DesignMatrix with shape (4, 3)
Intercept standardize(x0) center(x1)
1 2.12132 3.87
1 2.82843 0.27
1 3.53553 0.77
1 4.24264 3.07
Terms:
'Intercept' (column 0)
'standardize(x0)' (column 1)
'center(x1)' (column 2)]y, X = patsy.dmatrices('y ~ I(x0 + x1)', data)
XDesignMatrix with shape (5, 2)
Intercept I(x0 + x1)
1 1.01
1 1.99
1 3.25
1 -0.10
1 5.00
Terms:
'Intercept' (column 0)
'I(x0 + x1)' (column 1)data = pd.DataFrame({
'key1': ['a', 'a', 'b', 'b', 'a', 'b', 'a', 'b'],
'key2': [0, 1, 0, 1, 0, 1, 0, 0],
'v1': [1, 2, 3, 4, 5, 6, 7, 8],
'v2': [-1, 0, 2.5, -0.5, 4.0, -1.2, 0.2, -1.7]
})
y, X = patsy.dmatrices('v2 ~ key1', data)
XDesignMatrix with shape (8, 2)
Intercept key1[T.b]
1 0
1 0
1 1
1 1
1 0
1 1
1 0
1 1
Terms:
'Intercept' (column 0)
'key1' (column 1)y, X = patsy.dmatrices('v2 ~ key1 + 0', data)
XDesignMatrix with shape (8, 2)
key1[a] key1[b]
1 0
1 0
0 1
0 1
1 0
0 1
1 0
0 1
Terms:
'key1' (columns 0:2)y, X = patsy.dmatrices('v2 ~ C(key2)', data)
XDesignMatrix with shape (8, 2)
Intercept C(key2)[T.1]
1 0
1 1
1 0
1 1
1 0
1 1
1 0
1 0
Terms:
'Intercept' (column 0)
'C(key2)' (column 1)data['key2'] = data['key2'].map({0: 'zero', 1: 'one'})
data
y, X = patsy.dmatrices('v2 ~ key1 + key2', data)
X
y, X = patsy.dmatrices('v2 ~ key1 + key2 + key1:key2', data)
XDesignMatrix with shape (8, 4)
Intercept key1[T.b] key2[T.zero] key1[T.b]:key2[T.zero]
1 0 1 0
1 0 0 0
1 1 1 1
1 1 0 0
1 0 1 0
1 1 0 0
1 0 1 0
1 1 1 1
Terms:
'Intercept' (column 0)
'key1' (column 1)
'key2' (column 2)
'key1:key2' (column 3)import statsmodels.api as sm
import statsmodels.formula.api as smf11.4 statsmodels 소개
파이썬에서 통계 모델을 추정하고 분석하는 방법을 알아봅니다.
# To make the example reproducible
rng = np.random.default_rng(seed=12345)
def dnorm(mean, variance, size=1):
if isinstance(size, int):
size = size,
return mean + np.sqrt(variance) * rng.standard_normal(*size)
N = 100
X = np.c_[dnorm(0, 0.4, size=N),
dnorm(0, 0.6, size=N),
dnorm(0, 0.2, size=N)]
eps = dnorm(0, 0.1, size=N)
beta = [0.1, 0.3, 0.5]
y = np.dot(X, beta) + epsX[:5]
y[:5]array([-0.5995, -0.5885, 0.1856, -0.0075, -0.0154])X_model = sm.add_constant(X)
X_model[:5]array([[ 1. , -0.9005, -0.1894, -1.0279],
[ 1. , 0.7993, -1.546 , -0.3274],
[ 1. , -0.5507, -0.1203, 0.3294],
[ 1. , -0.1639, 0.824 , 0.2083],
[ 1. , -0.0477, -0.2131, -0.0482]])model = sm.OLS(y, X)results = model.fit()
results.paramsarray([0.0668, 0.268 , 0.4505])print(results.summary()) OLS Regression Results
=======================================================================================
Dep. Variable: y R-squared (uncentered): 0.469
Model: OLS Adj. R-squared (uncentered): 0.452
Method: Least Squares F-statistic: 28.51
Date: Thu, 26 Feb 2026 Prob (F-statistic): 2.66e-13
Time: 20:53:04 Log-Likelihood: -25.611
No. Observations: 100 AIC: 57.22
Df Residuals: 97 BIC: 65.04
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
x1 0.0668 0.054 1.243 0.217 -0.040 0.174
x2 0.2680 0.042 6.313 0.000 0.184 0.352
x3 0.4505 0.068 6.605 0.000 0.315 0.586
==============================================================================
Omnibus: 0.435 Durbin-Watson: 1.869
Prob(Omnibus): 0.805 Jarque-Bera (JB): 0.301
Skew: 0.134 Prob(JB): 0.860
Kurtosis: 2.995 Cond. No. 1.64
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.data = pd.DataFrame(X, columns=['col0', 'col1', 'col2'])
data['y'] = y
data[:5]| col0 | col1 | col2 | y | |
|---|---|---|---|---|
| 0 | -0.900506 | -0.189430 | -1.027870 | -0.599527 |
| 1 | 0.799252 | -1.545984 | -0.327397 | -0.588454 |
| 2 | -0.550655 | -0.120254 | 0.329359 | 0.185634 |
| 3 | -0.163916 | 0.824040 | 0.208275 | -0.007477 |
| 4 | -0.047651 | -0.213147 | -0.048244 | -0.015374 |
results = smf.ols('y ~ col0 + col1 + col2', data=data).fit()
results.params
results.tvaluesIntercept -0.652501
col0 1.219768
col1 6.312369
col2 6.567428
dtype: float64results.predict(data[:5])0 -0.592959
1 -0.531160
2 0.058636
3 0.283658
4 -0.102947
dtype: float64init_x = 4
values = [init_x, init_x]
N = 1000
b0 = 0.8
b1 = -0.4
noise = dnorm(0, 0.1, N)
for i in range(N):
new_x = values[-1] * b0 + values[-2] * b1 + noise[i]
values.append(new_x)from statsmodels.tsa.ar_model import AutoReg
MAXLAGS = 5
model = AutoReg(values, MAXLAGS)
results = model.fit()results.paramsarray([ 0.0235, 0.8097, -0.4287, -0.0334, 0.0427, -0.0567])train = pd.read_csv('datasets/titanic/train.csv')
test = pd.read_csv('datasets/titanic/test.csv')
train.head(4)| PassengerId | Survived | Pclass | Name | Sex | Age | SibSp | Parch | Ticket | Fare | Cabin | Embarked | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0 | 3 | Braund, Mr. Owen Harris | male | 22.0 | 1 | 0 | A/5 21171 | 7.2500 | NaN | S |
| 1 | 2 | 1 | 1 | Cumings, Mrs. John Bradley (Florence Briggs Thayer) | female | 38.0 | 1 | 0 | PC 17599 | 71.2833 | C85 | C |
| 2 | 3 | 1 | 3 | Heikkinen, Miss. Laina | female | 26.0 | 0 | 0 | STON/O2. 3101282 | 7.9250 | NaN | S |
| 3 | 4 | 1 | 1 | Futrelle, Mrs. Jacques Heath (Lily May Peel) | female | 35.0 | 1 | 0 | 113803 | 53.1000 | C123 | S |
11.5 scikit-learn 소개
가장 인기 있는 머신러닝 라이브러리를 사용하여 예측 모델을 구축하는 기초를 학습합니다.
train.isna().sum()
test.isna().sum()PassengerId 0
Pclass 0
Name 0
Sex 0
Age 86
SibSp 0
Parch 0
Ticket 0
Fare 1
Cabin 327
Embarked 0
dtype: int64impute_value = train['Age'].median()
train['Age'] = train['Age'].fillna(impute_value)
test['Age'] = test['Age'].fillna(impute_value)train['IsFemale'] = (train['Sex'] == 'female').astype(int)
test['IsFemale'] = (test['Sex'] == 'female').astype(int)predictors = ['Pclass', 'IsFemale', 'Age']
X_train = train[predictors].to_numpy()
X_test = test[predictors].to_numpy()
y_train = train['Survived'].to_numpy()
X_train[:5]
y_train[:5]array([0, 1, 1, 1, 0])11.6 scikit-learn
가장 대중적인 머신러닝 라이브러리의 표준 워크플로우를 경험합니다.
from sklearn.linear_model import LogisticRegression
model = LogisticRegression()model.fit(X_train, y_train)LogisticRegression()In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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Parameters
y_predict = model.predict(X_test)
y_predict[:10]array([0, 0, 0, 0, 1, 0, 1, 0, 1, 0])from sklearn.linear_model import LogisticRegressionCV
model_cv = LogisticRegressionCV(Cs=10)
model_cv.fit(X_train, y_train)LogisticRegressionCV()In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
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Parameters
from sklearn.model_selection import cross_val_score
model = LogisticRegression(C=10)
scores = cross_val_score(model, X_train, y_train, cv=4)
scoresarray([0.7758, 0.7982, 0.7758, 0.7883])pd.options.display.max_rows = PREVIOUS_MAX_ROWS