Model ensembling

Winning a Kaggle Competition in Python

Yauhen Babakhin

Kaggle Grandmaster

Model ensembling

Model blending

• Regression problem
• Train two different models: A and B
• Make predictions on the test data:

Test ID	Model A prediction	Model B prediction
1	1.2	1.5
2	0.1	0.4
3	5.4	7.2

Model blending

 

Test ID	Model A prediction	Model B prediction	Arithmetic mean
1	1.2	1.5	1.35
2	0.1	0.4	0.25
3	5.4	7.2	6.30

Model blending

 

Arithmetic mean

$$arithmetic = \frac{1}{n}\sum_{i=1}^{n}{x_i}$$

Geometric mean

$$geometric = \Bigg({\prod_{i=1}^{n}{x_i}}\Bigg)^{\frac{1}{n}}$$

Model stacking

 

1. Split train data into two parts
2. Train multiple models on Part 1
3. Make predictions on Part 2
4. Make predictions on the test data
5. Train a new model on Part 2 using predictions as features
6. Make predictions on the test data using the 2nd level model

Stacking example

Train ID	feature_1	...	feature_N	Target
1	0.55	...	1.37	1
2	0.12	...	-2.50	0
3	0.65	...	3.14	0
4	0.10	...	2.87	1
5	0.54	...	-0.10	0

Test IDs	feature_1	...	feature_N	Target
11	0.49	...	-2.32	?
12	0.32	...	1.15	?
13	0.91	...	0.81	?

Stacking example

Train ID	feature_1	...	feature_N	Target
1	0.55	...	1.37	1
2	0.12	...	-2.50	0
3	0.65	...	3.14	0

 

Train ID	feature_1	...	feature_N	Target
4	0.10	...	2.87	1
5	0.54	...	-0.10	0

Stacking example

Train ID	feature_1	...	feature_N	Target
1	0.55	...	1.37	1
2	0.12	...	-2.50	0
3	0.65	...	3.14	0

 

Train ID	feature_1	...	feature_N	Target
4	0.10	...	2.87	1
5	0.54	...	-0.10	0

Train models A, B, C on Part 1

Stacking example

Train ID	feature_1	...	feature_N	Target	A_pred	B_pred	C_pred
4	0.10	...	2.87	1	0.71	0.52	0.98
5	0.54	...	-0.10	0	0.45	0.32	0.24

 

Test IDs	feature_1	...	feature_N	Target	A_pred	B_pred	C_pred
11	0.49	...	-2.32	?	0.62	0.45	0.81
12	0.32	...	1.15	?	0.31	0.52	0.41
13	0.91	...	0.81	?	0.74	0.55	0.92

Stacking example

Train ID	Target	A_pred	B_pred	C_pred
4	1	0.71	0.52	0.98
5	0	0.45	0.32	0.24

 

Test IDs	Target	A_pred	B_pred	C_pred
11	?	0.62	0.45	0.81
12	?	0.31	0.52	0.41
13	?	0.74	0.55	0.92

Stacking example

Train ID	Target	A_pred	B_pred	C_pred
4	1	0.71	0.52	0.98
5	0	0.45	0.32	0.24

 

Test IDs	Target	A_pred	B_pred	C_pred
11	?	0.62	0.45	0.81
12	?	0.31	0.52	0.41
13	?	0.74	0.55	0.92

Train 2nd level model on Part 2

Stacking example

Train ID	Target	A_pred	B_pred	C_pred
4	1	0.71	0.52	0.98
5	0	0.45	0.32	0.24

 

Test IDs	Target	A_pred	B_pred	C_pred	Stacking prediction
11	?	0.62	0.45	0.81	0.73
12	?	0.31	0.52	0.41	0.35
13	?	0.74	0.55	0.92	0.88

Let's practice!

Winning a Kaggle Competition in Python