딥러닝: 회귀분석

딥러닝

회귀분석

Author

김보람

Published

April 20, 2023

ref

파이썬 데이터 분석

보스톤 주택가격 예측

보스톤 주택가격 데이터 세트와 모형 구조

비선형 회귀분석의 경우 인공신경망 구조는 1개 이상의 은닉충 필요
주택가격(mediv)을 출력노드, 주택가격에 영향을 미치는 나머지 독립변수는 입력노드
0과 1사이의 값을 가지는 더미 변수 chas는 제외

활성화함수

딥러닝의 경우 ReLU 함수 설정하지만 회귀분석의 경우 출력 노드에는 설정 하지 않아도 되고 \(a(x)=x\)와 같이 선형함수가 활성화함수가 됨

비용함수

\(MSE=\dfrac{1}{n}\sum_{i=1}^n (y_i - \widehat y_i)^2\)

최적화 기법

Adam 사용

테스트 및 평가

평균절대오차 \(MAE=\dfrac{1}{n}\sum_{i=1}^n |y_i - \widehat y_i|^2\)

1. 패키지 설정

sklearn에서 2.1 이후로 해당 데이터는 사용할 수 없다.

from sklearn.datasets import load_boston

In this special case, you can fetch the dataset from the original source::

    import pandas as pd
    import numpy as np

    data_url = "http://lib.stat.cmu.edu/datasets/boston"
    raw_df = pd.read_csv(data_url, sep="\s+", skiprows=22, header=None)
    data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])
    target = raw_df.values[1::2, 2]


from sklearn.preprocessing import MinMaxScaler
from sklearn.model_selection import train_test_split  #학습용과 테스트용 분리
from sklearn.metrics import mean_absolute_error       #정규화
#딥러닝 모형화를 위해 keras를 사용
from keras.models import Sequential                   #Sequential 한층씩 추가하여 네트워크를 만든다.    
from keras.layers import Dense                        #Dense 층 간 노드들은 모두 연결되는 모형구조를 만든다.

import seaborn as sns
import matplotlib.pyplot as plt

import pandas as pd
import numpy as np

data_url = "http://lib.stat.cmu.edu/datasets/boston"
raw_df = pd.read_csv(data_url, sep="\s+", skiprows=22)
data = raw_df.values[:, :-1]
target = raw_df.values[:, -1]

import pandas as pd
import numpy as np

data_url = "http://lib.stat.cmu.edu/datasets/boston"
raw_df = pd.read_csv(data_url, sep="\s+", skiprows=21, header=None)

# 데이터셋에서 14번째 변수(MEDV)는 target 변수로 사용
# 데이터와 target을 분리
data2 = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :3]])

feautre_names=['CRIM','ZN','INDUS','CHAS','NOX','RM','AGE','DIS','RAD','TAX','PTRATIO','B','LSTAT']
# 데이터셋의 크기를 확인
print(data2.shape)  # (506, 14)

(506, 14)

data=data2[:,:-1]
target=data2[:,-1]

print(data.shape)  # (506, 13)
print(target.shape)  # (506,)

(506, 13)
(506,)

2. 데이터준비

X=pd.DataFrame(data, columns=feautre_names)
print(X)

        CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \
0    0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   
1    0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   
2    0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   
3    0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   
4    0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   
..       ...   ...    ...   ...    ...    ...   ...     ...  ...    ...   
501  0.06263   0.0  11.93   0.0  0.573  6.593  69.1  2.4786  1.0  273.0   
502  0.04527   0.0  11.93   0.0  0.573  6.120  76.7  2.2875  1.0  273.0   
503  0.06076   0.0  11.93   0.0  0.573  6.976  91.0  2.1675  1.0  273.0   
504  0.10959   0.0  11.93   0.0  0.573  6.794  89.3  2.3889  1.0  273.0   
505  0.04741   0.0  11.93   0.0  0.573  6.030  80.8  2.5050  1.0  273.0   

     PTRATIO       B  LSTAT  
0       15.3  396.90   4.98  
1       17.8  396.90   9.14  
2       17.8  392.83   4.03  
3       18.7  394.63   2.94  
4       18.7  396.90   5.33  
..       ...     ...    ...  
501     21.0  391.99   9.67  
502     21.0  396.90   9.08  
503     21.0  396.90   5.64  
504     21.0  393.45   6.48  
505     21.0  396.90   7.88  

[506 rows x 13 columns]

- 더미 변수 CHAS제외

X=X.drop(['CHAS'],axis=1)
print(X.head())

      CRIM    ZN  INDUS    NOX     RM   AGE     DIS  RAD    TAX  PTRATIO  \
0  0.00632  18.0   2.31  0.538  6.575  65.2  4.0900  1.0  296.0     15.3   
1  0.02731   0.0   7.07  0.469  6.421  78.9  4.9671  2.0  242.0     17.8   
2  0.02729   0.0   7.07  0.469  7.185  61.1  4.9671  2.0  242.0     17.8   
3  0.03237   0.0   2.18  0.458  6.998  45.8  6.0622  3.0  222.0     18.7   
4  0.06905   0.0   2.18  0.458  7.147  54.2  6.0622  3.0  222.0     18.7   

        B  LSTAT  
0  396.90   4.98  
1  396.90   9.14  
2  392.83   4.03  
3  394.63   2.94  
4  396.90   5.33

X.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 506 entries, 0 to 505
Data columns (total 12 columns):
 #   Column   Non-Null Count  Dtype  
---  ------   --------------  -----  
 0   CRIM     506 non-null    float64
 1   ZN       506 non-null    float64
 2   INDUS    506 non-null    float64
 3   NOX      506 non-null    float64
 4   RM       506 non-null    float64
 5   AGE      506 non-null    float64
 6   DIS      506 non-null    float64
 7   RAD      506 non-null    float64
 8   TAX      506 non-null    float64
 9   PTRATIO  506 non-null    float64
 10  B        506 non-null    float64
 11  LSTAT    506 non-null    float64
dtypes: float64(12)
memory usage: 47.6 KB

y=pd.DataFrame(target)
print(y)

        0
0    24.0
1    21.6
2    34.7
3    33.4
4    36.2
..    ...
501  22.4
502  20.6
503  23.9
504  22.0
505  11.9

[506 rows x 1 columns]

3. 탐색적 데이터 분석

boston_df=pd.DataFrame(data=X)
boston_df["MEDIV"]=target
print(boston_df)

        CRIM    ZN  INDUS    NOX     RM   AGE     DIS  RAD    TAX  PTRATIO  \
0    0.00632  18.0   2.31  0.538  6.575  65.2  4.0900  1.0  296.0     15.3   
1    0.02731   0.0   7.07  0.469  6.421  78.9  4.9671  2.0  242.0     17.8   
2    0.02729   0.0   7.07  0.469  7.185  61.1  4.9671  2.0  242.0     17.8   
3    0.03237   0.0   2.18  0.458  6.998  45.8  6.0622  3.0  222.0     18.7   
4    0.06905   0.0   2.18  0.458  7.147  54.2  6.0622  3.0  222.0     18.7   
..       ...   ...    ...    ...    ...   ...     ...  ...    ...      ...   
501  0.06263   0.0  11.93  0.573  6.593  69.1  2.4786  1.0  273.0     21.0   
502  0.04527   0.0  11.93  0.573  6.120  76.7  2.2875  1.0  273.0     21.0   
503  0.06076   0.0  11.93  0.573  6.976  91.0  2.1675  1.0  273.0     21.0   
504  0.10959   0.0  11.93  0.573  6.794  89.3  2.3889  1.0  273.0     21.0   
505  0.04741   0.0  11.93  0.573  6.030  80.8  2.5050  1.0  273.0     21.0   

          B  LSTAT  MEDIV  
0    396.90   4.98   24.0  
1    396.90   9.14   21.6  
2    392.83   4.03   34.7  
3    394.63   2.94   33.4  
4    396.90   5.33   36.2  
..      ...    ...    ...  
501  391.99   9.67   22.4  
502  396.90   9.08   20.6  
503  396.90   5.64   23.9  
504  393.45   6.48   22.0  
505  396.90   7.88   11.9  

[506 rows x 13 columns]

- 히스토그램

#목표변수 값 히스토그램
sns.set(rc={'figure.figsize':(10,5)})
sns.distplot(boston_df['MEDIV'],bins=10)
plt.show()

- 상관계수

# 각 변수별 상관계수
correlation_matrix=boston_df.corr().round(2)
correlation_matrix

	CRIM	ZN	INDUS	NOX	RM	AGE	DIS	RAD	TAX	PTRATIO	B	LSTAT	MEDIV
CRIM	1.00	-0.20	0.41	0.42	-0.22	0.35	-0.38	0.63	0.58	0.29	-0.39	0.46	-0.39
ZN	-0.20	1.00	-0.53	-0.52	0.31	-0.57	0.66	-0.31	-0.31	-0.39	0.18	-0.41	0.36
INDUS	0.41	-0.53	1.00	0.76	-0.39	0.64	-0.71	0.60	0.72	0.38	-0.36	0.60	-0.48
NOX	0.42	-0.52	0.76	1.00	-0.30	0.73	-0.77	0.61	0.67	0.19	-0.38	0.59	-0.43
RM	-0.22	0.31	-0.39	-0.30	1.00	-0.24	0.21	-0.21	-0.29	-0.36	0.13	-0.61	0.70
AGE	0.35	-0.57	0.64	0.73	-0.24	1.00	-0.75	0.46	0.51	0.26	-0.27	0.60	-0.38
DIS	-0.38	0.66	-0.71	-0.77	0.21	-0.75	1.00	-0.49	-0.53	-0.23	0.29	-0.50	0.25
RAD	0.63	-0.31	0.60	0.61	-0.21	0.46	-0.49	1.00	0.91	0.46	-0.44	0.49	-0.38
TAX	0.58	-0.31	0.72	0.67	-0.29	0.51	-0.53	0.91	1.00	0.46	-0.44	0.54	-0.47
PTRATIO	0.29	-0.39	0.38	0.19	-0.36	0.26	-0.23	0.46	0.46	1.00	-0.18	0.37	-0.51
B	-0.39	0.18	-0.36	-0.38	0.13	-0.27	0.29	-0.44	-0.44	-0.18	1.00	-0.37	0.33
LSTAT	0.46	-0.41	0.60	0.59	-0.61	0.60	-0.50	0.49	0.54	0.37	-0.37	1.00	-0.74
MEDIV	-0.39	0.36	-0.48	-0.43	0.70	-0.38	0.25	-0.38	-0.47	-0.51	0.33	-0.74	1.00

sns.set(rc={'figure.figsize':(10,8)})
sns.heatmap(data=correlation_matrix,annot=True)
plt.show()

4. 데이터분리

학습용과 테스트용 데이터를 7:3으로 분리하자.

X.shape

(506, 13)

X=X.drop(['MEDIV'],axis=1)
X

	CRIM	ZN	INDUS	NOX	RM	AGE	DIS	RAD	TAX	PTRATIO	B	LSTAT
0	0.00632	18.0	2.31	0.538	6.575	65.2	4.0900	1.0	296.0	15.3	396.90	4.98
1	0.02731	0.0	7.07	0.469	6.421	78.9	4.9671	2.0	242.0	17.8	396.90	9.14
2	0.02729	0.0	7.07	0.469	7.185	61.1	4.9671	2.0	242.0	17.8	392.83	4.03
3	0.03237	0.0	2.18	0.458	6.998	45.8	6.0622	3.0	222.0	18.7	394.63	2.94
4	0.06905	0.0	2.18	0.458	7.147	54.2	6.0622	3.0	222.0	18.7	396.90	5.33
...	...	...	...	...	...	...	...	...	...	...	...	...
501	0.06263	0.0	11.93	0.573	6.593	69.1	2.4786	1.0	273.0	21.0	391.99	9.67
502	0.04527	0.0	11.93	0.573	6.120	76.7	2.2875	1.0	273.0	21.0	396.90	9.08
503	0.06076	0.0	11.93	0.573	6.976	91.0	2.1675	1.0	273.0	21.0	396.90	5.64
504	0.10959	0.0	11.93	0.573	6.794	89.3	2.3889	1.0	273.0	21.0	393.45	6.48
505	0.04741	0.0	11.93	0.573	6.030	80.8	2.5050	1.0	273.0	21.0	396.90	7.88

506 rows × 12 columns

X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.3)

5. 피처 스케일링

학습용 입력 데이터에 대한 정규화 스케일러 만들고 입력데이터를 0~1로 정규화하기

# 정규화 스케일러 생성
scalerX=MinMaxScaler()

# 정규화 스케일러를 학습용 데이터에 맞춤
scalerX.fit(X_train)

# 정규화 스케일러로 학습용 데이터 변환
X_train_norm=scalerX.transform(X_train)

# 정규화 스케일러로 테스트용 데이터 변환
X_test_norm = scalerX.transform(X_test)

print(X_train_norm)

[[0.00680253 0.2        0.11962963 ... 0.04255319 0.98184477 0.08724646]
 [0.07235853 0.         0.64296296 ... 0.80851064 0.24617984 0.27924423]
 [0.1610363  0.         0.64296296 ... 0.80851064 0.93953301 0.7957766 ]
 ...
 [0.11494542 0.         0.64296296 ... 0.80851064 0.95662918 0.44595721]
 [0.1717624  0.         0.64296296 ... 0.80851064 0.91456957 0.59071964]
 [0.00187693 0.         0.33148148 ... 0.70212766 1.         0.27868852]]

X_train_norm.shape

(354, 12)

print(X_test_norm)

[[ 2.05400974e-02  0.00000000e+00  6.97777778e-01 ...  2.23404255e-01
   9.81617832e-01 -1.66712976e-03]
 [ 1.09008802e-02  0.00000000e+00  7.83333333e-01 ...  9.14893617e-01
   6.61758031e-01  4.25951653e-01]
 [ 4.66707160e-01  0.00000000e+00  6.42962963e-01 ...  8.08510638e-01
   8.29946039e-01  7.05751598e-01]
 ...
 [ 1.61036297e-01  0.00000000e+00  6.42962963e-01 ...  8.08510638e-01
   9.65757224e-01  3.09252570e-01]
 [ 9.47848868e-04  2.00000000e-01  2.30370370e-01 ...  6.38297872e-01
   9.85980130e-01  3.24256738e-01]
 [ 4.01371790e-04  2.80000000e-01  5.29629630e-01 ...  5.95744681e-01
   9.95234253e-01  1.71714365e-01]]

X_test_norm.shape

(152, 12)

# 정규화 스케일러 생성
scalerY=MinMaxScaler()

# 정규화 스케일러를 학습용 데이터에 맞춤
scalerY.fit(y_train)

# 정규화 스케일러로 학습용 데이터 변환
y_train_norm=scalerY.transform(y_train)

# 정규화 스케일러로 테스트용 데이터 변환
y_test_norm = scalerY.transform(y_test)

print(y_train_norm[0:10])

[[1.        ]
 [0.24666667]
 [0.11555556]
 [0.3       ]
 [0.17111111]
 [0.30888889]
 [0.28444444]
 [0.32666667]
 [0.33111111]
 [0.52444444]]

y_train_norm.shape

(354, 1)

print(y_test_norm[0:10])

[[1.        ]
 [0.23555556]
 [0.07777778]
 [0.12222222]
 [0.53555556]
 [0.92666667]
 [0.40222222]
 [0.58      ]
 [0.57333333]
 [0.34888889]]

y_test_norm.shape

(152, 1)

6. 모형화 및 학습

model=Sequential() # 순차모형
model.add(Dense(60,activation='relu', input_shape=(12,))) # 제 1은닉충과 입력층
model.add(Dense(60,activation='relu')) # 제 2은닉충
model.add(Dense(30,activation='relu')) # 제 3은닉충
model.add(Dense(1)) # 출력층 (선형 활섬화함수)

model.summary()

Model: "sequential_3"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 dense_12 (Dense)            (None, 60)                780       
                                                                 
 dense_13 (Dense)            (None, 60)                3660      
                                                                 
 dense_14 (Dense)            (None, 30)                1830      
                                                                 
 dense_15 (Dense)            (None, 1)                 31        
                                                                 
=================================================================
Total params: 6,301
Trainable params: 6,301
Non-trainable params: 0
_________________________________________________________________

Param : 가중치 12x60=720, 편향:60

model.compile(optimizer='adam',
              loss='mse',
              metrics=['mae'])

- 학습

results=model.fit(X_train_norm, y_train_norm,
                  validation_data=(X_test_norm, y_test_norm),
                  epochs=200, batch_size=32)

Epoch 1/200
12/12 [==============================] - 0s 7ms/step - loss: 0.1031 - mae: 0.2534 - val_loss: 0.0570 - val_mae: 0.1836
Epoch 2/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0472 - mae: 0.1690 - val_loss: 0.0401 - val_mae: 0.1482
Epoch 3/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0326 - mae: 0.1291 - val_loss: 0.0295 - val_mae: 0.1203
Epoch 4/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0244 - mae: 0.1095 - val_loss: 0.0234 - val_mae: 0.1124
Epoch 5/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0224 - mae: 0.1113 - val_loss: 0.0205 - val_mae: 0.0991
Epoch 6/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0176 - mae: 0.0876 - val_loss: 0.0162 - val_mae: 0.0880
Epoch 7/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0144 - mae: 0.0785 - val_loss: 0.0135 - val_mae: 0.0801
Epoch 8/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0123 - mae: 0.0711 - val_loss: 0.0118 - val_mae: 0.0791
Epoch 9/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0110 - mae: 0.0675 - val_loss: 0.0108 - val_mae: 0.0707
Epoch 10/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0100 - mae: 0.0645 - val_loss: 0.0105 - val_mae: 0.0756
Epoch 11/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0097 - mae: 0.0650 - val_loss: 0.0095 - val_mae: 0.0690
Epoch 12/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0089 - mae: 0.0612 - val_loss: 0.0092 - val_mae: 0.0682
Epoch 13/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0082 - mae: 0.0588 - val_loss: 0.0090 - val_mae: 0.0672
Epoch 14/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0080 - mae: 0.0565 - val_loss: 0.0102 - val_mae: 0.0783
Epoch 15/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0089 - mae: 0.0635 - val_loss: 0.0090 - val_mae: 0.0702
Epoch 16/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0121 - mae: 0.0826 - val_loss: 0.0117 - val_mae: 0.0826
Epoch 17/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0088 - mae: 0.0666 - val_loss: 0.0088 - val_mae: 0.0703
Epoch 18/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0069 - mae: 0.0544 - val_loss: 0.0077 - val_mae: 0.0625
Epoch 19/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0067 - mae: 0.0540 - val_loss: 0.0073 - val_mae: 0.0614
Epoch 20/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0062 - mae: 0.0518 - val_loss: 0.0072 - val_mae: 0.0605
Epoch 21/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0063 - mae: 0.0513 - val_loss: 0.0070 - val_mae: 0.0599
Epoch 22/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0059 - mae: 0.0507 - val_loss: 0.0069 - val_mae: 0.0594
Epoch 23/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0064 - mae: 0.0518 - val_loss: 0.0075 - val_mae: 0.0646
Epoch 24/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0061 - mae: 0.0507 - val_loss: 0.0065 - val_mae: 0.0573
Epoch 25/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0057 - mae: 0.0495 - val_loss: 0.0064 - val_mae: 0.0568
Epoch 26/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0055 - mae: 0.0504 - val_loss: 0.0067 - val_mae: 0.0580
Epoch 27/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0058 - mae: 0.0512 - val_loss: 0.0066 - val_mae: 0.0570
Epoch 28/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0056 - mae: 0.0487 - val_loss: 0.0064 - val_mae: 0.0564
Epoch 29/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0052 - mae: 0.0484 - val_loss: 0.0063 - val_mae: 0.0554
Epoch 30/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0049 - mae: 0.0469 - val_loss: 0.0063 - val_mae: 0.0560
Epoch 31/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0049 - mae: 0.0472 - val_loss: 0.0061 - val_mae: 0.0545
Epoch 32/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0045 - mae: 0.0448 - val_loss: 0.0063 - val_mae: 0.0546
Epoch 33/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0045 - mae: 0.0452 - val_loss: 0.0061 - val_mae: 0.0537
Epoch 34/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0044 - mae: 0.0456 - val_loss: 0.0061 - val_mae: 0.0540
Epoch 35/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0045 - mae: 0.0454 - val_loss: 0.0061 - val_mae: 0.0533
Epoch 36/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0041 - mae: 0.0436 - val_loss: 0.0060 - val_mae: 0.0520
Epoch 37/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0043 - mae: 0.0449 - val_loss: 0.0062 - val_mae: 0.0529
Epoch 38/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0041 - mae: 0.0444 - val_loss: 0.0060 - val_mae: 0.0529
Epoch 39/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0040 - mae: 0.0439 - val_loss: 0.0060 - val_mae: 0.0518
Epoch 40/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0046 - mae: 0.0481 - val_loss: 0.0087 - val_mae: 0.0648
Epoch 41/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0046 - mae: 0.0467 - val_loss: 0.0060 - val_mae: 0.0524
Epoch 42/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0041 - mae: 0.0453 - val_loss: 0.0060 - val_mae: 0.0533
Epoch 43/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0043 - mae: 0.0454 - val_loss: 0.0067 - val_mae: 0.0548
Epoch 44/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0045 - mae: 0.0501 - val_loss: 0.0060 - val_mae: 0.0503
Epoch 45/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0039 - mae: 0.0451 - val_loss: 0.0063 - val_mae: 0.0548
Epoch 46/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0038 - mae: 0.0446 - val_loss: 0.0056 - val_mae: 0.0494
Epoch 47/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0035 - mae: 0.0423 - val_loss: 0.0057 - val_mae: 0.0496
Epoch 48/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0037 - mae: 0.0426 - val_loss: 0.0060 - val_mae: 0.0509
Epoch 49/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0036 - mae: 0.0425 - val_loss: 0.0071 - val_mae: 0.0555
Epoch 50/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0092 - mae: 0.0708 - val_loss: 0.0089 - val_mae: 0.0701
Epoch 51/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0050 - mae: 0.0526 - val_loss: 0.0069 - val_mae: 0.0579
Epoch 52/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0041 - mae: 0.0456 - val_loss: 0.0060 - val_mae: 0.0510
Epoch 53/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0041 - mae: 0.0462 - val_loss: 0.0062 - val_mae: 0.0528
Epoch 54/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0033 - mae: 0.0409 - val_loss: 0.0063 - val_mae: 0.0516
Epoch 55/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0034 - mae: 0.0414 - val_loss: 0.0064 - val_mae: 0.0529
Epoch 56/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0034 - mae: 0.0414 - val_loss: 0.0064 - val_mae: 0.0545
Epoch 57/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0035 - mae: 0.0401 - val_loss: 0.0062 - val_mae: 0.0504
Epoch 58/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0031 - mae: 0.0387 - val_loss: 0.0065 - val_mae: 0.0525
Epoch 59/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0030 - mae: 0.0385 - val_loss: 0.0068 - val_mae: 0.0541
Epoch 60/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0031 - mae: 0.0404 - val_loss: 0.0061 - val_mae: 0.0506
Epoch 61/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0034 - mae: 0.0425 - val_loss: 0.0071 - val_mae: 0.0564
Epoch 62/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0033 - mae: 0.0405 - val_loss: 0.0070 - val_mae: 0.0545
Epoch 63/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0031 - mae: 0.0395 - val_loss: 0.0068 - val_mae: 0.0534
Epoch 64/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0029 - mae: 0.0399 - val_loss: 0.0064 - val_mae: 0.0527
Epoch 65/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0028 - mae: 0.0382 - val_loss: 0.0062 - val_mae: 0.0517
Epoch 66/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0028 - mae: 0.0379 - val_loss: 0.0063 - val_mae: 0.0512
Epoch 67/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0027 - mae: 0.0379 - val_loss: 0.0062 - val_mae: 0.0505
Epoch 68/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0026 - mae: 0.0365 - val_loss: 0.0063 - val_mae: 0.0513
Epoch 69/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0029 - mae: 0.0383 - val_loss: 0.0066 - val_mae: 0.0514
Epoch 70/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0027 - mae: 0.0370 - val_loss: 0.0066 - val_mae: 0.0505
Epoch 71/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0029 - mae: 0.0386 - val_loss: 0.0066 - val_mae: 0.0520
Epoch 72/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0026 - mae: 0.0373 - val_loss: 0.0067 - val_mae: 0.0515
Epoch 73/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0025 - mae: 0.0367 - val_loss: 0.0063 - val_mae: 0.0509
Epoch 74/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0026 - mae: 0.0364 - val_loss: 0.0064 - val_mae: 0.0519
Epoch 75/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0034 - mae: 0.0422 - val_loss: 0.0060 - val_mae: 0.0496
Epoch 76/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0026 - mae: 0.0353 - val_loss: 0.0068 - val_mae: 0.0534
Epoch 77/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0027 - mae: 0.0381 - val_loss: 0.0064 - val_mae: 0.0499
Epoch 78/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0024 - mae: 0.0357 - val_loss: 0.0060 - val_mae: 0.0495
Epoch 79/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0024 - mae: 0.0353 - val_loss: 0.0059 - val_mae: 0.0490
Epoch 80/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0025 - mae: 0.0366 - val_loss: 0.0065 - val_mae: 0.0517
Epoch 81/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0024 - mae: 0.0363 - val_loss: 0.0064 - val_mae: 0.0507
Epoch 82/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0023 - mae: 0.0350 - val_loss: 0.0062 - val_mae: 0.0499
Epoch 83/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0342 - val_loss: 0.0064 - val_mae: 0.0513
Epoch 84/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0023 - mae: 0.0351 - val_loss: 0.0062 - val_mae: 0.0499
Epoch 85/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0335 - val_loss: 0.0061 - val_mae: 0.0500
Epoch 86/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0346 - val_loss: 0.0062 - val_mae: 0.0517
Epoch 87/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0345 - val_loss: 0.0061 - val_mae: 0.0507
Epoch 88/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0021 - mae: 0.0331 - val_loss: 0.0061 - val_mae: 0.0500
Epoch 89/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0020 - mae: 0.0331 - val_loss: 0.0062 - val_mae: 0.0512
Epoch 90/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0021 - mae: 0.0330 - val_loss: 0.0062 - val_mae: 0.0498
Epoch 91/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0020 - mae: 0.0327 - val_loss: 0.0062 - val_mae: 0.0496
Epoch 92/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0020 - mae: 0.0328 - val_loss: 0.0061 - val_mae: 0.0496
Epoch 93/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0019 - mae: 0.0319 - val_loss: 0.0063 - val_mae: 0.0506
Epoch 94/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0020 - mae: 0.0329 - val_loss: 0.0062 - val_mae: 0.0506
Epoch 95/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0019 - mae: 0.0318 - val_loss: 0.0061 - val_mae: 0.0503
Epoch 96/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0315 - val_loss: 0.0062 - val_mae: 0.0507
Epoch 97/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0317 - val_loss: 0.0061 - val_mae: 0.0501
Epoch 98/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0315 - val_loss: 0.0063 - val_mae: 0.0505
Epoch 99/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0019 - mae: 0.0330 - val_loss: 0.0062 - val_mae: 0.0498
Epoch 100/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0019 - mae: 0.0313 - val_loss: 0.0067 - val_mae: 0.0527
Epoch 101/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0310 - val_loss: 0.0063 - val_mae: 0.0507
Epoch 102/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0318 - val_loss: 0.0066 - val_mae: 0.0519
Epoch 103/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0021 - mae: 0.0343 - val_loss: 0.0063 - val_mae: 0.0517
Epoch 104/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0317 - val_loss: 0.0063 - val_mae: 0.0508
Epoch 105/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0019 - mae: 0.0325 - val_loss: 0.0065 - val_mae: 0.0513
Epoch 106/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0021 - mae: 0.0339 - val_loss: 0.0060 - val_mae: 0.0501
Epoch 107/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0311 - val_loss: 0.0068 - val_mae: 0.0528
Epoch 108/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0026 - mae: 0.0386 - val_loss: 0.0067 - val_mae: 0.0512
Epoch 109/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0020 - mae: 0.0335 - val_loss: 0.0070 - val_mae: 0.0530
Epoch 110/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0028 - mae: 0.0404 - val_loss: 0.0065 - val_mae: 0.0517
Epoch 111/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0029 - mae: 0.0407 - val_loss: 0.0058 - val_mae: 0.0501
Epoch 112/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0019 - mae: 0.0328 - val_loss: 0.0060 - val_mae: 0.0507
Epoch 113/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0019 - mae: 0.0331 - val_loss: 0.0059 - val_mae: 0.0495
Epoch 114/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0021 - mae: 0.0341 - val_loss: 0.0064 - val_mae: 0.0505
Epoch 115/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0020 - mae: 0.0324 - val_loss: 0.0065 - val_mae: 0.0518
Epoch 116/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0017 - mae: 0.0303 - val_loss: 0.0061 - val_mae: 0.0500
Epoch 117/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0017 - mae: 0.0303 - val_loss: 0.0060 - val_mae: 0.0502
Epoch 118/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0320 - val_loss: 0.0062 - val_mae: 0.0509
Epoch 119/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0317 - val_loss: 0.0060 - val_mae: 0.0499
Epoch 120/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0017 - mae: 0.0309 - val_loss: 0.0064 - val_mae: 0.0512
Epoch 121/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0024 - mae: 0.0355 - val_loss: 0.0063 - val_mae: 0.0514
Epoch 122/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0024 - mae: 0.0379 - val_loss: 0.0075 - val_mae: 0.0617
Epoch 123/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0028 - mae: 0.0388 - val_loss: 0.0055 - val_mae: 0.0484
Epoch 124/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0020 - mae: 0.0330 - val_loss: 0.0065 - val_mae: 0.0531
Epoch 125/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0325 - val_loss: 0.0063 - val_mae: 0.0504
Epoch 126/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0017 - mae: 0.0306 - val_loss: 0.0065 - val_mae: 0.0512
Epoch 127/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0317 - val_loss: 0.0061 - val_mae: 0.0503
Epoch 128/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0292 - val_loss: 0.0060 - val_mae: 0.0502
Epoch 129/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0297 - val_loss: 0.0065 - val_mae: 0.0531
Epoch 130/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0302 - val_loss: 0.0063 - val_mae: 0.0503
Epoch 131/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0015 - mae: 0.0293 - val_loss: 0.0066 - val_mae: 0.0525
Epoch 132/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0305 - val_loss: 0.0060 - val_mae: 0.0499
Epoch 133/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0315 - val_loss: 0.0061 - val_mae: 0.0505
Epoch 134/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0299 - val_loss: 0.0066 - val_mae: 0.0515
Epoch 135/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0301 - val_loss: 0.0065 - val_mae: 0.0520
Epoch 136/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0321 - val_loss: 0.0064 - val_mae: 0.0509
Epoch 137/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0021 - mae: 0.0343 - val_loss: 0.0059 - val_mae: 0.0505
Epoch 138/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0303 - val_loss: 0.0058 - val_mae: 0.0489
Epoch 139/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0017 - mae: 0.0308 - val_loss: 0.0061 - val_mae: 0.0500
Epoch 140/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0015 - mae: 0.0287 - val_loss: 0.0062 - val_mae: 0.0494
Epoch 141/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0015 - mae: 0.0285 - val_loss: 0.0062 - val_mae: 0.0496
Epoch 142/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0280 - val_loss: 0.0061 - val_mae: 0.0497
Epoch 143/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0279 - val_loss: 0.0061 - val_mae: 0.0499
Epoch 144/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0300 - val_loss: 0.0061 - val_mae: 0.0492
Epoch 145/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0015 - mae: 0.0293 - val_loss: 0.0064 - val_mae: 0.0512
Epoch 146/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0017 - mae: 0.0304 - val_loss: 0.0065 - val_mae: 0.0515
Epoch 147/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0024 - mae: 0.0374 - val_loss: 0.0062 - val_mae: 0.0497
Epoch 148/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0017 - mae: 0.0316 - val_loss: 0.0061 - val_mae: 0.0515
Epoch 149/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0017 - mae: 0.0305 - val_loss: 0.0062 - val_mae: 0.0523
Epoch 150/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0015 - mae: 0.0281 - val_loss: 0.0059 - val_mae: 0.0492
Epoch 151/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0015 - mae: 0.0283 - val_loss: 0.0062 - val_mae: 0.0512
Epoch 152/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0015 - mae: 0.0289 - val_loss: 0.0062 - val_mae: 0.0501
Epoch 153/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0283 - val_loss: 0.0061 - val_mae: 0.0488
Epoch 154/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0277 - val_loss: 0.0061 - val_mae: 0.0492
Epoch 155/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0272 - val_loss: 0.0063 - val_mae: 0.0489
Epoch 156/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0268 - val_loss: 0.0063 - val_mae: 0.0494
Epoch 157/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0269 - val_loss: 0.0062 - val_mae: 0.0494
Epoch 158/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0012 - mae: 0.0259 - val_loss: 0.0063 - val_mae: 0.0489
Epoch 159/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0260 - val_loss: 0.0062 - val_mae: 0.0500
Epoch 160/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0263 - val_loss: 0.0073 - val_mae: 0.0537
Epoch 161/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0023 - mae: 0.0360 - val_loss: 0.0071 - val_mae: 0.0572
Epoch 162/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0360 - val_loss: 0.0069 - val_mae: 0.0546
Epoch 163/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0342 - val_loss: 0.0066 - val_mae: 0.0527
Epoch 164/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0356 - val_loss: 0.0061 - val_mae: 0.0509
Epoch 165/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0331 - val_loss: 0.0065 - val_mae: 0.0516
Epoch 166/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0019 - mae: 0.0319 - val_loss: 0.0063 - val_mae: 0.0499
Epoch 167/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0325 - val_loss: 0.0077 - val_mae: 0.0570
Epoch 168/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0374 - val_loss: 0.0066 - val_mae: 0.0519
Epoch 169/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0365 - val_loss: 0.0066 - val_mae: 0.0520
Epoch 170/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0023 - mae: 0.0377 - val_loss: 0.0058 - val_mae: 0.0501
Epoch 171/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0311 - val_loss: 0.0061 - val_mae: 0.0517
Epoch 172/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0300 - val_loss: 0.0060 - val_mae: 0.0501
Epoch 173/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0018 - mae: 0.0322 - val_loss: 0.0060 - val_mae: 0.0498
Epoch 174/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0274 - val_loss: 0.0061 - val_mae: 0.0494
Epoch 175/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0269 - val_loss: 0.0063 - val_mae: 0.0495
Epoch 176/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0012 - mae: 0.0263 - val_loss: 0.0061 - val_mae: 0.0495
Epoch 177/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0012 - mae: 0.0258 - val_loss: 0.0060 - val_mae: 0.0501
Epoch 178/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0027 - mae: 0.0401 - val_loss: 0.0057 - val_mae: 0.0493
Epoch 179/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0022 - mae: 0.0354 - val_loss: 0.0061 - val_mae: 0.0501
Epoch 180/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0301 - val_loss: 0.0063 - val_mae: 0.0511
Epoch 181/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0275 - val_loss: 0.0070 - val_mae: 0.0533
Epoch 182/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0277 - val_loss: 0.0059 - val_mae: 0.0485
Epoch 183/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0015 - mae: 0.0289 - val_loss: 0.0061 - val_mae: 0.0484
Epoch 184/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0271 - val_loss: 0.0071 - val_mae: 0.0546
Epoch 185/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0305 - val_loss: 0.0066 - val_mae: 0.0513
Epoch 186/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0270 - val_loss: 0.0061 - val_mae: 0.0483
Epoch 187/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0267 - val_loss: 0.0062 - val_mae: 0.0481
Epoch 188/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0283 - val_loss: 0.0066 - val_mae: 0.0496
Epoch 189/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0261 - val_loss: 0.0060 - val_mae: 0.0476
Epoch 190/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0266 - val_loss: 0.0062 - val_mae: 0.0483
Epoch 191/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0016 - mae: 0.0300 - val_loss: 0.0070 - val_mae: 0.0524
Epoch 192/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0287 - val_loss: 0.0065 - val_mae: 0.0515
Epoch 193/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0283 - val_loss: 0.0062 - val_mae: 0.0481
Epoch 194/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0269 - val_loss: 0.0059 - val_mae: 0.0482
Epoch 195/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0264 - val_loss: 0.0060 - val_mae: 0.0490
Epoch 196/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0012 - mae: 0.0251 - val_loss: 0.0059 - val_mae: 0.0480
Epoch 197/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0012 - mae: 0.0255 - val_loss: 0.0063 - val_mae: 0.0510
Epoch 198/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0013 - mae: 0.0277 - val_loss: 0.0059 - val_mae: 0.0479
Epoch 199/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0012 - mae: 0.0257 - val_loss: 0.0065 - val_mae: 0.0513
Epoch 200/200
12/12 [==============================] - 0s 2ms/step - loss: 0.0014 - mae: 0.0272 - val_loss: 0.0066 - val_mae: 0.0507

print(results.history.keys())

dict_keys(['loss', 'mae', 'val_loss', 'val_mae'])

loss : 학습 데이터 비용
mae : 학습 데이터 오차
val_loss : 테스트 데이터 비용
val_mae : 테스트 데이터 오차

# 학습 수에 따른 loss 변화
plt.figure(figsize=(10,5))
plt.plot(results.history['loss']) 
plt.plot(results.history['val_loss'])
plt.title('loss')
plt.xlabel('epoch')
plt.ylabel('loss')
plt.legend(['train','test'],loc='upper right')
plt.show()

# 학습 수에 따른 정확도(mae) 변화
plt.figure(figsize=(10,5))
plt.plot(results.history['mae']) 
plt.plot(results.history['val_loss'])
plt.title('accuracy(MAE)')
plt.xlabel('epoch')
plt.ylabel('accuracy')
plt.legend(['train','test'],loc='upper right')
plt.show()

7. 예측

# 테스트 데이터 예측
y_pred=model.predict(X_test_norm).flatten()

# 예측 값의 역변환
y_pred_inverse=scalerY.inverse_transform(y_pred.reshape(-1,1))
print(y_pred_inverse[0:10])

5/5 [==============================] - 0s 540us/step
[[50.411358 ]
 [13.942274 ]
 [ 6.1426053]
 [10.471625 ]
 [30.684546 ]
 [44.55355  ]
 [26.434183 ]
 [31.944752 ]
 [32.296173 ]
 [23.545477 ]]

# 오차측정(MAE)
print('MAE:%.2f' %mean_absolute_error(y_test, y_pred_inverse))

MAE:2.28

# 실제 값 대비 예측 값의 산포도
plt.figure(figsize=(7,7))
plt.scatter(y_test_norm,y_pred,c='r')
plt.xlabel('TrueValues')
plt.ylabel('Predictions')
plt.axis('equal')
plt.xlim(0,1)
plt.ylim(0,1)
plt.plot([0,1],[0,1])
plt.show()

8. 드랍아웃 모형 추가

from keras.layers import Dropout

model=Sequential() # 순차모형
model.add(Dense(60,activation='relu', input_shape=(12,))) # 제 1은닉충과 입력층
model.add(Dropout(0.5)) # 제 1은닉충과 2은닉충 사이의 드롭 아웃 50%
model.add(Dense(60,activation='relu')) # 제 2은닉충
model.add(Dense(30,activation='relu')) # 제 3은닉충
model.add(Dropout(0.2)) # 제 3은닉충과 출력층 사이의 드롭 아웃 20%
model.add(Dense(1)) # 출력층 (선형 활섬화함수)

model.summary()

Model: "sequential_5"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 dense_20 (Dense)            (None, 60)                780       
                                                                 
 dropout_2 (Dropout)         (None, 60)                0         
                                                                 
 dense_21 (Dense)            (None, 60)                3660      
                                                                 
 dense_22 (Dense)            (None, 30)                1830      
                                                                 
 dropout_3 (Dropout)         (None, 30)                0         
                                                                 
 dense_23 (Dense)            (None, 1)                 31        
                                                                 
=================================================================
Total params: 6,301
Trainable params: 6,301
Non-trainable params: 0
_________________________________________________________________

model.compile(optimizer='adam',
              loss='mse',
              metrics=['mae'])

# results=model.fit(X_train_norm, y_train_norm,
#                   validation_data=(X_test_norm, y_test_norm),
#                   epochs=1000, batch_size=20)

print(results.history.keys())

dict_keys(['loss', 'mae', 'val_loss', 'val_mae'])

# 학습 수에 따른 loss 변화
plt.figure(figsize=(10,5))
plt.plot(results.history['loss']) 
plt.plot(results.history['val_loss'])
plt.title('loss')
plt.xlabel('epoch')
plt.ylabel('loss')
plt.legend(['train','test'],loc='upper right')
plt.show()

# 학습 수에 따른 정확도(mae) 변화
plt.figure(figsize=(10,5))
plt.plot(results.history['mae']) 
plt.plot(results.history['val_loss'])
plt.title('accuracy(MAE)')
plt.xlabel('epoch')
plt.ylabel('accuracy')
plt.legend(['train','test'],loc='upper right')
plt.show()

# 테스트 데이터 예측
y_pred=model.predict(X_test_norm).flatten()

# 예측 값의 역변환
y_pred_inverse=scalerY.inverse_transform(y_pred.reshape(-1,1))
print(y_pred_inverse[0:10])

5/5 [==============================] - 0s 517us/step
[[36.150234]
 [15.184836]
 [ 8.98333 ]
 [12.427422]
 [26.98419 ]
 [34.612114]
 [20.946304]
 [27.669504]
 [28.082466]
 [23.544407]]

# 오차측정(MAE)
print('MAE:%.2f' %mean_absolute_error(y_test, y_pred_inverse))

MAE:3.00

# 실제 값 대비 예측 값의 산포도
plt.figure(figsize=(7,7))
plt.scatter(y_test_norm,y_pred,c='r')
plt.xlabel('TrueValues')
plt.ylabel('Predictions')
plt.axis('equal')
plt.xlim(0,1)
plt.ylim(0,1)
plt.plot([0,1],[0,1])
plt.show()

9. 입력 노드의 드랍 아웃

model=Sequential() # 순차모형
model.add(Dropout(0.2, input_shape=(12,))) # 입력 노드에 대한 드랍아웃 비율 0.2
model.add(Dense(60,activation='relu', input_shape=(12,))) # 제 1은닉충과 입력층
model.add(Dense(60,activation='relu')) # 제 2은닉충
model.add(Dense(30,activation='relu')) # 제 3은닉충
model.add(Dense(1)) # 출력층 (선형 활섬화함수)