Aprendizado na Prática
Fazendo uso a regressão e classicação knn e logística!
Resultados Esperados
- Saber executar o KNN do SKlearn
- Praticar o pipeline completo de ICD
Sumário
#In:
# -*- coding: utf8
from scipy import stats as ss
import seaborn as sns
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
plt.rcParams['figure.figsize'] = (18, 10)
plt.rcParams['axes.labelsize'] = 20
plt.rcParams['axes.titlesize'] = 20
plt.rcParams['legend.fontsize'] = 20
plt.rcParams['xtick.labelsize'] = 20
plt.rcParams['ytick.labelsize'] = 20
plt.rcParams['lines.linewidth'] = 4
#In:
plt.ion()
plt.style.use('seaborn-colorblind')
plt.rcParams['figure.figsize'] = (12, 8)
#In:
def despine(ax=None):
if ax is None:
ax = plt.gca()
# Hide the right and top spines
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
# Only show ticks on the left and bottom spines
ax.yaxis.set_ticks_position('left')
ax.xaxis.set_ticks_position('bottom')
#In:
%%capture
! wget https://github.com/icd-ufmg/material/raw/master/aulas/23-MLPratica/fashion/train-images-idx3-ubyte.gz -P fashion
! wget https://github.com/icd-ufmg/material/raw/master/aulas/23-MLPratica/fashion/t10k-images-idx3-ubyte.gz -P fashion
! wget https://github.com/icd-ufmg/material/raw/master/aulas/23-MLPratica/fashion/train-labels-idx1-ubyte.gz -P fashion
! wget https://github.com/icd-ufmg/material/raw/master/aulas/23-MLPratica/fashion/t10k-labels-idx1-ubyte.gz -P fashion
#In:
def load_mnist(path, kind='train'):
import os
import gzip
import numpy as np
"""Load MNIST data from `path`"""
labels_path = os.path.join(path,
'%s-labels-idx1-ubyte.gz'
% kind)
images_path = os.path.join(path,
'%s-images-idx3-ubyte.gz'
% kind)
with gzip.open(labels_path, 'rb') as lbpath:
labels = np.frombuffer(lbpath.read(), dtype=np.uint8,
offset=8)
with gzip.open(images_path, 'rb') as imgpath:
images = np.frombuffer(imgpath.read(), dtype=np.uint8,
offset=16).reshape(len(labels), 784)
return images, labels
Classificação
Nesta aula vamos explorar aprendizado de máquina na prática. Em particular, vamos iniciar por algoritmos de classificação na base Fashion MNIST. Depois disso vamos explorar regressão.
Acima, temos alguns códigos auxiliares para carregar a base. Nesta, cada ponto é um vetor de 784 posições. Ao redimensionar os mesmos com:
#In:
x.reshape((28, 28))
Temos uma imagem de alguma peça de vestimento. Código para carregar os dados abaixo. Vamos usar apenas 500 instâncias para treino e teste. Lento usar muito mais do que isso no meu computador.
#In:
X_train, y_train = load_mnist('fashion', kind='train')
X_test, y_test = load_mnist('fashion', kind='t10k')
#In:
X_train = X_train[:500]
y_train = y_train[:500]
X_test = X_test[:500]
y_test = y_test[:500]
#In:
np.unique(y_test, return_counts=True)
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8),
array([53, 40, 63, 46, 55, 52, 49, 52, 43, 47]))
Observe como cada instância é um vetor. Cada valor é um tom de cinza. 0 == branco; 256 == preto.
#In:
X_train[10]
array([ 0, 0, 0, 0, 1, 0, 0, 0, 0, 41, 162, 167, 84,
30, 38, 94, 177, 176, 26, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 41, 147, 228, 242, 228,
236, 251, 251, 251, 255, 242, 230, 247, 221, 125, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 91, 216, 228, 222,
219, 219, 218, 222, 200, 224, 230, 221, 222, 222, 227, 237, 183,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 202, 208,
212, 217, 219, 222, 222, 219, 219, 220, 218, 222, 224, 224, 221,
210, 227, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 102,
225, 210, 216, 218, 222, 221, 219, 225, 225, 221, 222, 224, 222,
224, 224, 215, 215, 218, 28, 0, 0, 0, 0, 0, 0, 0,
0, 189, 222, 220, 213, 219, 220, 218, 221, 220, 219, 222, 226,
222, 220, 221, 216, 215, 218, 229, 148, 0, 0, 0, 0, 0,
0, 0, 11, 240, 210, 227, 213, 214, 220, 217, 220, 224, 220,
221, 217, 206, 209, 208, 212, 220, 224, 218, 234, 0, 0, 0,
0, 0, 0, 0, 118, 214, 208, 224, 216, 211, 226, 212, 219,
213, 193, 192, 179, 194, 213, 216, 216, 217, 227, 216, 221, 91,
0, 0, 0, 0, 0, 0, 170, 221, 205, 225, 219, 217, 232,
232, 226, 182, 182, 211, 226, 220, 212, 217, 216, 216, 225, 213,
226, 184, 0, 0, 0, 0, 0, 0, 0, 181, 229, 219, 220,
213, 227, 226, 222, 214, 222, 220, 216, 215, 213, 214, 216, 215,
220, 233, 211, 0, 0, 0, 0, 0, 0, 0, 0, 0, 164,
242, 222, 210, 214, 211, 215, 215, 216, 217, 215, 215, 215, 215,
213, 222, 238, 184, 0, 0, 0, 0, 0, 0, 0, 0, 2,
0, 0, 60, 222, 217, 214, 214, 215, 219, 202, 217, 210, 203,
216, 212, 221, 200, 60, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 193, 222, 208, 216, 215, 216, 218, 220,
219, 215, 216, 204, 222, 148, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 194, 222, 206, 216, 216, 217,
218, 217, 218, 216, 218, 208, 219, 179, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 192, 224, 213, 217,
217, 218, 217, 217, 217, 215, 216, 209, 215, 176, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 194, 221,
214, 217, 216, 216, 217, 217, 217, 216, 214, 210, 214, 177, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
193, 220, 214, 218, 217, 216, 217, 217, 216, 216, 215, 212, 214,
183, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 197, 220, 214, 219, 218, 218, 218, 218, 217, 217, 219,
214, 217, 189, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 201, 222, 214, 219, 218, 219, 219, 218, 218,
217, 219, 216, 220, 196, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 209, 222, 216, 220, 219, 219, 220,
220, 218, 217, 219, 216, 222, 203, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 209, 221, 216, 220, 219,
219, 221, 221, 219, 219, 221, 217, 222, 210, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 208, 222, 218,
221, 220, 220, 221, 222, 220, 220, 222, 219, 222, 216, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 210,
226, 220, 221, 220, 221, 222, 222, 220, 220, 224, 221, 224, 221,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 217, 227, 219, 222, 224, 219, 219, 221, 222, 220, 221, 222,
225, 220, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 183, 228, 221, 225, 221, 215, 217, 221, 222, 221,
222, 224, 224, 193, 0, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 179, 225, 218, 221, 219, 213, 213, 217,
220, 219, 218, 221, 222, 197, 0, 0, 2, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 240, 233, 228, 235, 232, 229,
228, 229, 231, 231, 231, 228, 229, 212, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 157, 148, 148,
167, 180, 182, 179, 176, 172, 171, 164, 177, 163, 0, 0, 1,
0, 0, 0, 0], dtype=uint8)
Ao redimensionar temos uma peça de roupa! Fashion!
#In:
I = X_train[0].reshape(28, 28)
print(I.shape)
(28, 28)
#In:
plt.imshow(X_train[100].reshape(28, 28))
<matplotlib.image.AxesImage at 0x7f8cda558fa0>
#In:
plt.imshow(X_train[1].reshape(28, 28))
<matplotlib.image.AxesImage at 0x7f8cd8252110>
#In:
M = np.array([[1, 2], [2, 3]])
M.flatten()
array([1, 2, 2, 3])
Temos 10 classes.
#In:
len(set(y_train))
10
#In:
text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat', 'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
index = np.arange(len(text_labels))
labels = pd.Series(text_labels, index=index)
labels
0 t-shirt
1 trouser
2 pullover
3 dress
4 coat
5 sandal
6 shirt
7 sneaker
8 bag
9 ankle boot
dtype: object
Executando o Scikit-Learn
Agora, vamos executar o código do sklearn na nossa base. Lembrando que temos que separar a mesma em Treino, Validação e Teste. Para tal, vamos fazer uso da classe StratifiedKFold. A mesma serve para realizar n-fold cross validation. A biblioteca sklearn não cria grupos de validação para você, a mesma só usa o conceito de treino/teste. De qualquer forma, validação nada mais é do que um conjunto a mais de teste. Então, vamos fazer 5-fold no nosso treino, separando em treino/validação. Note que NUNCA avaliamos nada no teste, apenas reportamos os números no fim!!
#In:
from sklearn.model_selection import StratifiedKFold
Ao gerar o split, teremos 20 conjuntos (muito eu sei).
#In:
skf = StratifiedKFold(n_splits=20, shuffle=True)
Cada passo do laço retorna indices do vetor
#In:
for treino, validacao in skf.split(X_train, y_train):
count_train = np.unique(y_train[treino], return_counts=True)
print(count_train)
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 37, 42, 62, 48, 39, 58, 49, 43, 48]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 37, 42, 62, 48, 39, 58, 49, 43, 48]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 36, 42, 62, 48, 39, 58, 50, 43, 48]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 36, 42, 62, 48, 39, 58, 50, 43, 48]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 36, 42, 62, 49, 38, 58, 50, 43, 48]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 36, 43, 62, 49, 39, 58, 50, 42, 47]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 36, 43, 62, 49, 39, 58, 50, 42, 47]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 36, 43, 62, 49, 39, 58, 50, 42, 47]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([50, 36, 43, 61, 49, 39, 58, 50, 42, 47]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([50, 36, 43, 61, 49, 39, 58, 50, 42, 47]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([50, 36, 43, 61, 49, 39, 58, 49, 43, 47]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([50, 36, 43, 61, 49, 39, 58, 49, 43, 47]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([50, 36, 43, 61, 49, 39, 58, 49, 43, 47]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([50, 36, 43, 62, 48, 39, 58, 49, 43, 47]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([50, 36, 43, 62, 48, 39, 58, 49, 43, 47]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([50, 36, 43, 62, 48, 39, 57, 49, 43, 48]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 36, 43, 62, 48, 39, 58, 49, 43, 48]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 36, 43, 62, 48, 39, 58, 49, 43, 48]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 36, 43, 62, 48, 39, 58, 49, 43, 48]))
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8), array([49, 36, 43, 62, 48, 39, 58, 49, 43, 48]))
Vamos quebrar nos conjuntos e avaliar o KNN. De um mundo de métricas, vamos fazer uso de 4 neste notebook:
- Precisão
- Revocação
- F1
- Acurácia
Na figura acima, assuma que o termo busca indica as previsões do seu classificador (sem tempo para alterar a figura irmão). Sendo y_p (y-pred) um conjunto de elementos da previsão e y_t (y-true) os rótulos reais. Por clareza, vamos assumir duas classes 1 e 0. Afinal, o caso multiclasse pode ser reduzido para este. Assim, cada elemento dos vetores y_p e y_t $\in {0, 1}$. Os verdadeiros positivos, true positive (TP), é o conjunto de previsões da classe 1 que foram corretas. Podemos formalizar como:
$\mathbb{1}{y_t[i] = 1}$ retorna 1 quando $y_t[i] = 1$, 0 caso contrário. O mesmo vale para $\mathbb{1}{y_t[i] = y_p[i]}$ que retorna um quando $y_p[i] = 1$. Usando a mesma notação, os verdadeiros negativos é definido como:
\[TN = \sum_i \mathbb{1}_{y_t[i] = 0} \mathbb{1}_{y_t[i] = 0}\]Os falsos positivos e negativos capturam os erros da previsão. Note que nos dois a previsão é o oposto do real:
\[FP = \sum_i \mathbb{1}_{y_t[i] = 0} \mathbb{1}_{y_p[i] = 1}\] \[FN = \sum_i \mathbb{1}_{y_t[i] = 1} \mathbb{1}_{y_p[i] = 0}\]Assim, a acurácia do classificador é definida como a fração total de acertos:
\[Acuracia = \frac{TP + TN}{TP + TN + FP + FN}\]A precisão é definida como a fração dos elementos classificados como 1 que foram corretos:
\[Precisão = \frac{TP}{TP + FP}\]A revocação é a fração de todos os elementos do conjunto 1 que foram acertados. Diferente da precisão, aqui focamos nos elementos reais! Na precisão focamos nas previsões.
\[Revocação = \frac{TP}{TP + FN}\]Tanto a previsão quanto a revocação importam. Na primeira, precisão, queremos saber o quão bom o classificador é em retornar acertos. Na segunda, o quanto de elementos reais o classificador captura. Observe como um classificador que sempre retorna 1 tem revocação máxima, porém precisão baixa. Um classificador que sempre retorna 0 tem precisão máxima e revocação baixa. Para captura a média harmônica dos dois usamos o F1-score:
\[F1 = MediaHarmonica(Precisao, Revocacao)\]Dependendo do problema uma métrica pode importar mais do que a outra. Aqui, trabalhamos com classes balanceadas, então a acurácia já é boa suficiente. Vamos avaliar a acurácia nos conjuntos abaixo:
#In:
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import accuracy_score
Observe como o laço abaixo guarda o melhor valor de n para cada fold de validação!
#In:
fold = 0
melhores = []
for treino, validacao in skf.split(X_train, y_train):
X_tt = X_train[treino]
y_tt = y_train[treino]
X_v = X_train[validacao]
y_v = y_train[validacao]
best = (0, 0)
for nn in [2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 100]: # Vamos testar tais valores de n
model = KNeighborsClassifier(n_neighbors=nn)
model.fit(X_tt, y_tt) # treina no conjunto de treino
y_pv = model.predict(X_v) # previsões no conjunto de validação
# Resultado com melhor acurácia!
accuracy = accuracy_score(y_v, y_pv)
if accuracy > best[0]:
best = (accuracy, nn)
melhores.append(best[1])
fold += 1
print('Fold-{}, melhor nn = {}, acc = {}'.format(fold, best[1], best[0]))
Fold-1, melhor nn = 2, acc = 0.84
Fold-2, melhor nn = 4, acc = 0.84
Fold-3, melhor nn = 4, acc = 0.68
Fold-4, melhor nn = 2, acc = 0.68
Fold-5, melhor nn = 30, acc = 0.6
Fold-6, melhor nn = 5, acc = 0.8
Fold-7, melhor nn = 2, acc = 0.76
Fold-8, melhor nn = 5, acc = 0.92
Fold-9, melhor nn = 2, acc = 0.72
Fold-10, melhor nn = 9, acc = 0.68
Fold-11, melhor nn = 3, acc = 0.68
Fold-12, melhor nn = 2, acc = 0.68
Fold-13, melhor nn = 3, acc = 0.76
Fold-14, melhor nn = 8, acc = 0.88
Fold-15, melhor nn = 30, acc = 0.84
Fold-16, melhor nn = 8, acc = 0.84
Fold-17, melhor nn = 40, acc = 0.76
Fold-18, melhor nn = 7, acc = 0.92
Fold-19, melhor nn = 9, acc = 0.68
Fold-20, melhor nn = 20, acc = 0.88
Vamos ver quantas vezes cada escolha de número de vizinhos, nn, ganhou na validação.
#In:
unique, counts = np.unique(melhores, return_counts=True)
plt.bar(unique, counts)
despine()
plt.title('Número de vezes que n ganhou na validação')
plt.xlabel('NN')
plt.ylabel('Count na validação')
Text(0, 0.5, 'Count na validação')
Agora, podemos finalmente avaliar o modelo no conjunto de teste! Vamos escolher n como a médiana dos folds.
#In:
print(np.median(melhores))
5.0
Vamos verificar as outras métricas e todas as classes.
#In:
from sklearn.metrics import classification_report
model = KNeighborsClassifier(n_neighbors=5)
model.fit(X_train, y_train)
print(classification_report(y_test, model.predict(X_test)))
precision recall f1-score support
0 0.71 0.77 0.74 53
1 0.95 0.97 0.96 40
2 0.53 0.62 0.57 63
3 0.86 0.93 0.90 46
4 0.63 0.60 0.62 55
5 0.94 0.60 0.73 52
6 0.53 0.43 0.47 49
7 0.71 0.87 0.78 52
8 0.94 0.79 0.86 43
9 0.83 0.96 0.89 47
accuracy 0.74 500
macro avg 0.76 0.75 0.75 500
weighted avg 0.75 0.74 0.74 500
Parece que erramos muito a classe 4, coat. Casacos se parecem com camisas, vestidos etc. Podemos investigar isto usando a matriz de confusão.
#In:
from sklearn.metrics import confusion_matrix
plt.imshow(confusion_matrix(y_test, model.predict(X_test)))
plt.xticks(labels.index, labels, rotation=90)
plt.yticks(labels.index, labels);
Logística
Vamos repetir tudo para a regressão logística. Felizmente, o sklearn tem uma versão da logística que já faz treino/validação internamente. Para alguns modelos, existem atalhos para fazer isto. Caso queira entender, leia:
https://robjhyndman.com/hyndsight/crossvalidation/
#In:
from sklearn.linear_model import LogisticRegressionCV
#In:
# O LogisticCV tenta várias regularizações.
model = LogisticRegressionCV(Cs=100,
penalty='l2', #ridge
cv=5, #5 folds internos
fit_intercept=False,
solver='liblinear',
multi_class='ovr')
model.fit(X_train, y_train)
LogisticRegressionCV(Cs=100, cv=5, fit_intercept=False, multi_class='ovr',
solver='liblinear')
#In:
model.C_
array([0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001, 0.0001,
0.0001, 0.0001])
#In:
print(classification_report(y_test, model.predict(X_test)))
precision recall f1-score support
0 0.83 0.64 0.72 53
1 1.00 0.97 0.99 40
2 0.69 0.54 0.61 63
3 0.75 0.91 0.82 46
4 0.59 0.75 0.66 55
5 1.00 0.69 0.82 52
6 0.52 0.65 0.58 49
7 0.85 0.87 0.86 52
8 0.89 0.79 0.84 43
9 0.82 0.98 0.89 47
accuracy 0.77 500
macro avg 0.79 0.78 0.78 500
weighted avg 0.79 0.77 0.77 500
#In:
plt.imshow(confusion_matrix(y_test, model.predict(X_test)))
plt.xticks(labels.index, labels, rotation=90)
plt.yticks(labels.index, labels);
Regressão
Agora vamos avaliar modelos de regressão em dados tabulares. Primeiro, vamos carregar os dados. Obsevre que cada atributo é diferente. Data, numéricos categóricos, etc…
#In:
df = pd.read_csv('walmart.csv', on_bad_lines='skip')
df = df.iloc[:, :-1]
df.head()
| Store | Date | Weekly_Sales_Store | IsHoliday | Temperature | Fuel_Price | MarkDown1 | MarkDown2 | MarkDown3 | MarkDown4 | MarkDown5 | CPI | Unemployment | Type | Size | Total Markdown | Total Sales | SalesPerSqFt | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 5/2/2010 | 1643690.90 | False | 42.31 | 2.572 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 211.096358 | 8.106 | A | 151315 | 0.0 | 1643690.90 | 10.862710 |
| 1 | 1 | 12/2/2010 | 1641957.44 | True | 38.51 | 2.548 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 211.242170 | 8.106 | A | 151315 | 0.0 | 1641957.44 | 10.851254 |
| 2 | 1 | 19/2/2010 | 1611968.17 | False | 39.93 | 2.514 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 211.289143 | 8.106 | A | 151315 | 0.0 | 1611968.17 | 10.653063 |
| 3 | 1 | 26/2/2010 | 1409727.59 | False | 46.63 | 2.561 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 211.319643 | 8.106 | A | 151315 | 0.0 | 1409727.59 | 9.316509 |
| 4 | 1 | 5/3/2010 | 1554806.68 | False | 46.50 | 2.625 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 211.350143 | 8.106 | A | 151315 | 0.0 | 1554806.68 | 10.275298 |
Vamos criar o treino e teste
#In:
from sklearn.model_selection import train_test_split
#In:
train_df, test_df = train_test_split(df, test_size=0.2)
#In:
df.shape
(6435, 18)
#In:
train_df.shape
(5148, 18)
#In:
test_df.shape
(1287, 18)
Segundo, temos que converter os atributos categóricos em colunas novas. Para isto, fazemos uso de one hot encoding. Cada categoria vira uma coluna de 1/0. Algoritmos como KNN e Logistic não sabem fazer uso de categorias por padrão. Mesmo se as categorias representarem números, faça uso de one hot. Sempre se pergunte: faz sentido computar uma distância nessa coluna? Se não, one-hot (ou outra abordagem).
#In:
train_df = train_df.drop(['MarkDown1', 'MarkDown2', 'MarkDown3', 'MarkDown4', 'MarkDown5'], axis='columns')
test_df = test_df.drop(['MarkDown1', 'MarkDown2', 'MarkDown3', 'MarkDown4', 'MarkDown5'], axis='columns')
#In:
train_df.head()
| Store | Date | Weekly_Sales_Store | IsHoliday | Temperature | Fuel_Price | CPI | Unemployment | Type | Size | Total Markdown | Total Sales | SalesPerSqFt | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 5798 | 41 | 5/8/2011 | 1402233.69 | False | 72.19 | 3.554 | 193.911013 | 6.901 | A | 196321 | 0.00 | 1402233.69 | 7.142556 |
| 5518 | 39 | 16/9/2011 | 1372500.63 | False | 83.11 | 3.526 | 214.793411 | 8.177 | A | 184109 | 0.00 | 1372500.63 | 7.454826 |
| 1608 | 12 | 8/10/2010 | 918335.68 | False | 71.82 | 3.013 | 126.279167 | 14.313 | B | 112238 | 0.00 | 918335.68 | 8.182039 |
| 848 | 6 | 24/8/2012 | 1501095.49 | False | 79.03 | 3.620 | 223.786018 | 5.668 | A | 202505 | 17191.42 | 1518286.91 | 7.497528 |
| 1756 | 13 | 12/11/2010 | 1939964.63 | False | 42.55 | 2.831 | 126.546161 | 7.795 | A | 219622 | 0.00 | 1939964.63 | 8.833198 |
#In:
train_df.dtypes
Store int64
Date object
Weekly_Sales_Store float64
IsHoliday bool
Temperature float64
Fuel_Price float64
CPI float64
Unemployment float64
Type object
Size int64
Total Markdown float64
Total Sales float64
SalesPerSqFt float64
dtype: object
Vamos inicialmente converter a data. Note que a mesma existe em uma escala completamente diferente do resto. O split abaixo quebra o texto da data.
#In:
train_df['Date'].str.split('/')
5798 [5, 8, 2011]
5518 [16, 9, 2011]
1608 [8, 10, 2010]
848 [24, 8, 2012]
1756 [12, 11, 2010]
...
449 [25, 6, 2010]
1783 [20, 5, 2011]
3804 [30, 9, 2011]
5437 [26, 2, 2010]
5714 [21, 9, 2012]
Name: Date, Length: 5148, dtype: object
Agora pegamos o mês
#In:
for split in train_df['Date'].str.split('/'):
print(split[1])
break
8
#In:
train_df['Month'] = [split[1] for split in train_df['Date'].str.split('/')]
test_df['Month'] = [split[1] for split in test_df['Date'].str.split('/')]
#In:
test_df.head()
| Store | Date | Weekly_Sales_Store | IsHoliday | Temperature | Fuel_Price | CPI | Unemployment | Type | Size | Total Markdown | Total Sales | SalesPerSqFt | Month | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2765 | 20 | 7/1/2011 | 1843030.95 | False | 31.43 | 3.193 | 204.648780 | 7.343 | A | 203742 | 0.00 | 1843030.95 | 9.045906 | 1 |
| 4573 | 32 | 12/10/2012 | 1176681.31 | False | 43.49 | 3.760 | 199.053937 | 7.557 | A | 203007 | 8937.26 | 1185618.57 | 5.840284 | 10 |
| 4736 | 34 | 4/6/2010 | 966187.51 | False | 72.17 | 2.701 | 126.136065 | 9.593 | A | 158114 | 0.00 | 966187.51 | 6.110702 | 6 |
| 3667 | 26 | 11/11/2011 | 1077640.13 | False | 40.08 | 3.570 | 136.461806 | 7.598 | A | 152513 | 18336.76 | 1095976.89 | 7.186121 | 11 |
| 2503 | 18 | 24/6/2011 | 920719.98 | False | 67.41 | 3.851 | 135.265267 | 8.975 | B | 120653 | 0.00 | 920719.98 | 7.631140 | 6 |
Removendo a data
#In:
train_df = train_df.drop(['Date'], axis='columns')
test_df = test_df.drop(['Date'], axis='columns')
train_df.shape
(5148, 13)
One hot encoding do resto categórico
#In:
cols_usar = ['Temperature', 'Fuel_Price', 'CPI', 'Unemployment', 'Size',
'Weekly_Sales_Store',
'Store', 'Month', 'Type', 'IsHoliday']
cols_cat = ['Store', 'Month', 'Type', 'IsHoliday']
train_df = pd.get_dummies(train_df[cols_usar],
columns=cols_cat)
test_df = pd.get_dummies(test_df[cols_usar],
columns=cols_cat)
Vamos focar em poucos pontos para o notebook executar e só olhar para o teste no fim de tudo!
#In:
train_df = train_df.sample(1000)
test_df = test_df.sample(1000)
Normalizando dados: Como trabalhar com esse mundo de valores distintos? Solução!? Normalizar!
#In:
y_train_df = train_df['Weekly_Sales_Store']
X_train_df = train_df.drop('Weekly_Sales_Store', axis='columns')
#In:
X_train_df
| Temperature | Fuel_Price | CPI | Unemployment | Size | Store_1 | Store_2 | Store_3 | Store_4 | Store_5 | ... | Month_5 | Month_6 | Month_7 | Month_8 | Month_9 | Type_A | Type_B | Type_C | IsHoliday_False | IsHoliday_True | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 525 | 31.64 | 3.153 | 129.855533 | 5.143 | 205863 | 0 | 0 | 0 | 1 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| 5266 | 76.55 | 3.688 | 220.407558 | 6.989 | 39910 | 0 | 0 | 0 | 0 | 0 | ... | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
| 4853 | 75.89 | 3.646 | 130.885355 | 9.285 | 158114 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
| 4439 | 42.43 | 2.692 | 189.734262 | 9.014 | 203007 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| 1471 | 58.63 | 2.771 | 215.207452 | 7.564 | 207499 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 3575 | 9.55 | 2.788 | 131.527903 | 8.488 | 152513 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| 1299 | 69.76 | 3.105 | 126.380567 | 9.524 | 126512 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
| 2770 | 25.38 | 3.239 | 206.076386 | 7.343 | 203742 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
| 3392 | 31.92 | 3.737 | 136.959839 | 8.659 | 203819 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| 788 | 87.00 | 3.524 | 216.725739 | 6.925 | 202505 | 0 | 0 | 0 | 0 | 0 | ... | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
1000 rows × 67 columns
#In:
from sklearn.preprocessing import StandardScaler
IMPORTANTE SÓ NORMALIZE O TREINO!!! DEPOIS USE A MÉDIA E DESVIO DO TREINO PARA NORMALIZAR O TESTE!!
O TESTE É UM FUTURO! NÃO EXISTE, VOCÊ NÃO SABE NADA DO MESMO
#In:
scaler_x = StandardScaler()
scaler_y = StandardScaler()
X_train = scaler_x.fit_transform(X_train_df.values)
y_train = scaler_y.fit_transform(y_train_df.values[:, np.newaxis])
#In:
X_train
array([[-1.47899696, -0.37784933, -1.08529399, ..., -0.39166636,
0.29287596, -0.29287596],
[ 0.89990939, 0.797513 , 1.21462889, ..., 2.55319349,
0.29287596, -0.29287596],
[ 0.86494884, 0.70524157, -1.05913764, ..., -0.39166636,
0.29287596, -0.29287596],
...,
[-1.81059246, -0.18891258, 0.85063272, ..., -0.39166636,
-3.41441472, 3.41441472],
[-1.46416522, 0.90516301, -0.90485236, ..., -0.39166636,
0.29287596, -0.29287596],
[ 1.4534514 , 0.43721502, 1.12111469, ..., -0.39166636,
0.29287596, -0.29287596]])
#In:
y_train
array([[ 2.62453291e+00],
[-9.11982774e-01],
[-1.88058619e-01],
[ 3.74069171e-02],
[ 4.52591455e-01],
[-9.77094958e-01],
[ 4.02472469e-01],
[-3.61349552e-01],
[ 8.28706692e-02],
[-3.48086075e-01],
[ 9.55379822e-01],
[-2.75153083e-01],
[ 5.33213308e-01],
[-8.13621395e-01],
[-6.36005303e-02],
[ 1.54425972e-01],
[ 1.72205727e+00],
[-1.42171707e+00],
[ 1.62484616e+00],
[-1.19794621e+00],
[ 3.90878783e-01],
[-2.88423915e-01],
[-9.43327418e-01],
[ 8.70980877e-02],
[ 1.40786373e+00],
[-1.04198434e+00],
[ 6.06612877e-03],
[-1.04759308e+00],
[-1.31008988e+00],
[-1.03809762e+00],
[-2.34465051e-01],
[-2.39539942e-01],
[-1.09658018e+00],
[-9.67785169e-01],
[ 5.12377672e-01],
[ 1.84777424e+00],
[-9.82714848e-01],
[-8.50257605e-01],
[ 6.30126891e-01],
[ 1.73396906e+00],
[-9.03445727e-01],
[-6.44217310e-01],
[ 1.77278823e+00],
[ 6.60681673e-01],
[-5.46228154e-01],
[-2.58561896e-01],
[-8.50122998e-01],
[-4.82123830e-02],
[-3.99420526e-01],
[ 8.09129939e-01],
[-7.56418995e-01],
[-2.15915400e-01],
[ 1.91070846e+00],
[-8.69161841e-01],
[-5.69915876e-01],
[-1.98333921e-01],
[ 2.12706837e-01],
[ 4.12762624e-01],
[-2.83251336e-01],
[-1.13757894e+00],
[-1.05822086e-01],
[-1.30333045e+00],
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[ 1.07209265e+00],
[-1.25428881e+00],
[-2.88224093e-01],
[ 7.09604225e-01],
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[ 1.55103688e+00],
[-9.23001808e-01],
[ 6.39292558e-01],
[ 9.08511441e-01],
[ 7.15383607e-02],
[ 2.90754888e-01],
[-6.36226975e-01],
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[ 5.83262313e-01],
[-5.61722041e-01],
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[ 1.29876939e+00],
[-9.75751777e-01],
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#In:
from sklearn.linear_model import LinearRegression # sem regularizar
from sklearn.linear_model import Lasso # com regularização l1
from sklearn.linear_model import Ridge # com regularização l2
from sklearn.neighbors import KNeighborsRegressor
from sklearn.model_selection import GridSearchCV
O gridsearch cv faz o laço que fizemos na mão acima (conjuntos de validação)
#In:
linear = LinearRegression(fit_intercept=False)
lasso = GridSearchCV(Lasso(fit_intercept=False),
cv=10,
refit=True,
param_grid={'alpha': [0.001, 0.01, 0.1, 1, 10, 100]})
ridge = GridSearchCV(Ridge(fit_intercept=False),
cv=10,
refit=True,
param_grid={'alpha': [0.001, 0.01, 0.1, 1, 10, 100]})
knn = GridSearchCV(KNeighborsRegressor(),
cv=10,
refit=True,
param_grid={'n_neighbors': [2, 3, 5, 7, 11, 13],
'weights': ['uniform', 'distance']})
#In:
linear = linear.fit(X_train, y_train)
linear.score(X_train, y_train)
0.9316391152834318
#In:
lasso = lasso.fit(X_train, y_train)
lasso.score(X_train, y_train)
0.9318514675371551
#In:
ridge = ridge.fit(X_train, y_train)
ridge.score(X_train, y_train)
0.9319223512617757
#In:
knn = knn.fit(X_train, y_train)
knn.score(X_train, y_train)
1.0
#In:
knn.best_params_
{'n_neighbors': 13, 'weights': 'distance'}
Agora vamos usar o Bootstrap para entender o erro dos modelos caso eu repita o experimento.
#In:
from sklearn.metrics import mean_squared_error
#In:
y_pred = linear.predict(X_train)
mean_squared_error(y_train, y_pred)
0.06836088471656822
#In:
def bootstrap_score(X, y, model, n=1000):
size = len(y)
samples = np.zeros(size)
for i in range(size):
# Gera amostras com reposição
idx = np.random.choice(size, size)
Xb = X[idx]
yb = y[idx]
err = mean_squared_error(yb, model.predict(Xb))
samples[i] = err
return samples
#In:
y_test_df = test_df['Weekly_Sales_Store']
X_test_df = test_df.drop('Weekly_Sales_Store', axis='columns')
#In:
X_test = scaler_x.transform(X_test_df.values)
y_test = scaler_y.transform(y_test_df.values[:, np.newaxis])
#In:
samples = bootstrap_score(X_test, y_test, knn)
plt.hist(samples, edgecolor='k')
plt.title('({}, {})'.format(ss.scoreatpercentile(samples, 2.5),
ss.scoreatpercentile(samples, 97.5)))
despine()
#In:
samples = bootstrap_score(X_test, y_test, lasso)
plt.hist(samples, edgecolor='k')
plt.title('({}, {})'.format(ss.scoreatpercentile(samples, 2.5),
ss.scoreatpercentile(samples, 97.5)))
despine()
