Robot - Feature engineering on sensor data¶

The purpose of this notebook is to illustrate how we can overcome the feature explosion problem based on an example dataset involving sensor data.

Summary:

Prediction type: Regression
Domain: Robotics
Prediction target: The force vector on the robot's arm
Population size: 15001

Author: Dr. Patrick Urbanke

The data set¶

To illustrate the problem, we use a data set related to robotics. When robots interact with humans, the most important think is that they don't hurt people. In order to prevent such accidents, the force vector on the robot's arm is measured. However, measuring the force vector is expensive.

Therefore, we want consider an alternative approach. We would like to predict the force vector based on other sensor data that are less costly to measure. To do so, we use machine learning.

However, the data set contains measurements from almost 100 different sensors and we do not know which and how many sensors are relevant for predicting the force vector.

The data set has been generously provided by Erik Berger who originally collected it for his dissertation:

Berger, E. (2018). Behavior-Specific Proprioception Models for Robotic Force Estimation: A Machine Learning Approach. Freiberg, Germany: Technische Universitaet Bergakademie Freiberg.

Analysis¶

1. Loading data¶

We begin by importing the libraries and setting the project.

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%pip install -q "getml==1.5.0" "matplotlib~=3.9"

import getml
import matplotlib.pyplot as plt
%matplotlib inline  
 
getml.engine.launch()
getml.engine.set_project('robot')
%pip install -q "getml==1.5.0" "matplotlib~=3.9" import getml import matplotlib.pyplot as plt %matplotlib inline getml.engine.launch() getml.engine.set_project('robot')

Note: you may need to restart the kernel to use updated packages.
Launching ./getML --allow-push-notifications=true --allow-remote-ips=false --home-directory=/home/user --in-memory=true --install=false --launch-browser=true --log=false in /home/user/.getML/getml-1.5.0-x64-community-edition-linux...
Launched the getML Engine. The log output will be stored in /home/user/.getML/logs/20240912151657.log.
  Loading pipelines... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:00

Connected to project 'robot'.

1.1 Download from source¶

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data_all = getml.data.DataFrame.from_csv(
    "https://static.getml.com/datasets/robotarm/robot-demo.csv", 
    "data_all"
)
data_all = getml.data.DataFrame.from_csv( "https://static.getml.com/datasets/robotarm/robot-demo.csv", "data_all" )

Downloading https://static.getml.com/datasets/robotarm/robot-demo.csv to 
/tmp/getml/static.getml.com/datasets/robotarm/robot-demo.csv...

  Downloading robot-demo.csv... ━━━━━━━━━━━━━━━━━━━━ 100% • 14.7/14.7 MB • 00:00

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data_all
data_all

Out[3]:

name	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79	80	81	82	83	84	85	86	98	99	100	101	102	103	104	105	106	f_x	f_y	f_z
role	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float	unused_float
0	3.4098	-0.3274	0.9604	-3.7436	-1.0191	-6.0205	0	0	0	0	0	0	0	0	0	0	0	0	8.38e-17	-4.8116	-1.4033	-0.1369	0.002472	0	9.803e-16	-55.642	-16.312	-1.2042	0.02167	0	3.4098	-0.3274	0.9605	-3.7437	-1.0191	-6.0205	0	0	0	0	0	0	0.1233	-6.5483	-2.8045	-0.8296	0.07625	-0.1906	0.1211	-6.5483	-2.8157	-0.8281	0.07015	-0.1983	0.7699	0.41	0.08279	-1.4094	0.786	-0.3682	0	0	0	0	0	0	-22.654	-11.503	-18.673	-3.5155	5.8354	-2.05	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	48.069	48.009	0.9668	47.834	47.925	47.818	47.834	47.955	47.971	-11.03	6.9	-7.33
1	3.4098	-0.3274	0.9604	-3.7436	-1.0191	-6.0205	0	0	0	0	0	0	0	0	0	0	0	0	8.38e-17	-4.8116	-1.4033	-0.1369	0.002472	0	9.803e-16	-55.642	-16.312	-1.2042	0.02167	0	3.4098	-0.3274	0.9604	-3.7437	-1.0191	-6.0205	0	0	0	0	0	0	0.1188	-6.5506	-2.8404	-0.8281	0.06405	-0.1998	0.1211	-6.5483	-2.8157	-0.8281	0.07015	-0.1983	0.7699	0.41	0.0828	-1.4094	0.7859	-0.3682	0	0	0	0	0	0	-21.627	-11.046	-18.66	-3.5395	5.7577	-1.9805	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	48.009	48.009	0.8594	47.834	47.925	47.818	47.834	47.955	47.971	-10.848	6.7218	-7.4427
2	3.4098	-0.3274	0.9604	-3.7436	-1.0191	-6.0205	0	0	0	0	0	0	0	0	0	0	0	0	8.38e-17	-4.8116	-1.4033	-0.1369	0.002472	0	9.803e-16	-55.642	-16.312	-1.2042	0.02167	0	3.4098	-0.3274	0.9605	-3.7437	-1.0191	-6.0205	0	0	0	0	0	0	0.1099	-6.5438	-2.8	-0.8205	0.07473	-0.183	0.1211	-6.5483	-2.8157	-0.8281	0.07015	-0.1922	0.7699	0.41	0.08279	-1.4094	0.7859	-0.3682	0	0	0	0	0	0	-23.843	-12.127	-18.393	-3.6453	5.978	-1.9978	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	48.009	48.069	0.931	47.879	47.925	47.818	47.834	47.955	47.971	-10.666	6.5436	-7.5555
3	3.4098	-0.3274	0.9604	-3.7436	-1.0191	-6.0205	0	0	0	0	0	0	0	0	0	0	0	0	8.38e-17	-4.8116	-1.4033	-0.1369	0.002472	0	9.803e-16	-55.642	-16.312	-1.2042	0.02167	0	3.4098	-0.3273	0.9604	-3.7437	-1.0191	-6.0205	0	0	0	0	0	0	0.1233	-6.5483	-2.8224	-0.8266	0.07168	-0.1998	0.1211	-6.5483	-2.8157	-0.8281	0.07015	-0.1967	0.7699	0.41	0.08275	-1.4094	0.786	-0.3681	0	0	0	0	0	0	-21.772	-10.872	-18.691	-3.5512	5.6648	-1.9976	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	48.069	48.069	0.931	47.879	47.925	47.818	47.834	47.955	47.971	-10.507	6.4533	-7.65
4	3.4098	-0.3274	0.9604	-3.7436	-1.0191	-6.0205	0	0	0	0	0	0	0	0	0	0	0	0	8.38e-17	-4.8116	-1.4033	-0.1369	0.002472	0	9.803e-16	-55.642	-16.312	-1.2042	0.02167	0	3.4098	-0.3274	0.9604	-3.7437	-1.0191	-6.0205	0	0	0	0	0	0	0.1255	-6.5394	-2.8	-0.8327	0.07473	-0.1952	0.1211	-6.5483	-2.8157	-0.8327	0.07015	-0.1922	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	-22.823	-11.645	-18.524	-3.5305	5.8712	-2.0096	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	48.069	48.069	0.8952	47.879	47.925	47.818	47.834	47.955	47.971	-10.413	6.6267	-7.69
	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
14996	3.0837	-0.8836	1.4501	-2.2102	-1.559	-5.3265	-0.03151	-0.05375	0.04732	0.1482	-0.05218	0.06706	0.2969	0.5065	-0.4459	-1.3963	0.4916	-0.6319	-0.3694	-4.1879	-1.1847	-0.09441	-0.1568	0.1898	1.1605	-42.951	-19.023	-2.6343	0.1551	-0.1338	3.0836	-0.8836	1.4503	-2.2101	-1.5591	-5.3263	-0.03347	-0.05585	0.04805	0.151	-0.05513	0.07114	-0.3564	-6.0394	-2.3001	-0.2181	-0.1159	0.09608	-0.3632	-6.0394	-2.3023	-0.212	-0.125	0.1113	0.7116	0.06957	0.06036	-0.8506	2.9515	-0.03352	-0.03558	-0.03029	0.002444	-0.04208	0.1458	-0.1098	-0.8784	-0.07291	-37.584	0.0001132	-2.1031	0.03318	0.7117	0.0697	0.06044	-0.8511	2.951	-0.03356	-0.03508	-0.02849	0.001571	-0.03951	0.1442	-0.1036	48.069	48.009	0.8952	47.818	47.834	47.818	47.803	47.94	47.94	10.84	-1.41	16.14
14997	3.0835	-0.884	1.4505	-2.2091	-1.5594	-5.326	-0.02913	-0.0497	0.04376	0.137	-0.04825	0.062	0.2969	0.5065	-0.4459	-1.3963	0.4916	-0.6319	-0.3677	-4.1837	-1.1874	-0.09682	-0.1562	0.189	1.1592	-42.937	-19.023	-2.6331	0.1545	-0.1338	3.0833	-0.8841	1.4507	-2.209	-1.5596	-5.3258	-0.02909	-0.04989	0.04198	0.1481	-0.05465	0.06249	-0.3161	-6.1179	-2.253	-0.3752	-0.03965	0.08693	-0.3273	-6.1022	-2.2597	-0.366	-0.05033	0.0915	0.7114	0.06932	0.06039	-0.8497	2.953	-0.03359	-0.0335	-0.02723	0.001208	-0.04242	0.1428	-0.0967	-2.7137	0.8552	-38.514	-0.6088	-3.2383	-0.9666	0.7114	0.06948	0.06045	-0.8503	2.9525	-0.03359	-0.03246	-0.02633	0.001469	-0.03657	0.1333	-0.09571	48.009	48.009	0.8594	47.818	47.834	47.818	47.803	47.94	47.94	10.857	-1.52	15.943
14998	3.0833	-0.8844	1.4508	-2.208	-1.5598	-5.3256	-0.02676	-0.04565	0.04019	0.1258	-0.04431	0.05695	0.2969	0.5065	-0.4459	-1.3963	0.4916	-0.6319	-0.3659	-4.1797	-1.1901	-0.09922	-0.1555	0.1881	1.1579	-42.924	-19.023	-2.6321	0.154	-0.1338	3.0831	-0.8844	1.451	-2.2078	-1.56	-5.3253	-0.02776	-0.04382	0.03652	0.1295	-0.05064	0.04818	-0.343	-6.2569	-2.1566	-0.3035	0.00305	0.1434	-0.3385	-6.2322	-2.1589	-0.302	-0.00915	0.1571	0.7111	0.06912	0.06039	-0.849	2.9544	-0.0337	-0.02911	-0.02589	0.001292	-0.04046	0.1246	-0.08058	4.2749	1.0128	-36.412	-1.2811	-0.4296	-1.1013	0.7112	0.06928	0.06046	-0.8495	2.9538	-0.03362	-0.02984	-0.02417	0.001364	-0.03362	0.1224	-0.08786	48.009	48.009	0.931	47.818	47.834	47.818	47.803	47.94	47.94	10.89	-1.74	15.55
14999	3.0831	-0.8847	1.4511	-2.2071	-1.5602	-5.3251	-0.02438	-0.0416	0.03662	0.1147	-0.04038	0.0519	0.2969	0.5065	-0.4459	-1.3963	0.4916	-0.6319	-0.3642	-4.1758	-1.1928	-0.1016	-0.1548	0.1873	1.1568	-42.912	-19.023	-2.6311	0.1535	-0.1338	3.0829	-0.8848	1.4513	-2.2068	-1.5604	-5.3249	-0.02149	-0.04059	0.03417	0.1202	-0.0395	0.04178	-0.4237	-6.2703	-2.0939	-0.302	-0.01372	0.1739	-0.4125	-6.2569	-2.0916	-0.2943	-0.02898	0.1891	0.7109	0.06894	0.06039	-0.8484	2.9557	-0.03384	-0.02738	-0.01982	0.001031	-0.03028	0.1157	-0.06702	11.518	1.5002	-39.314	-1.8671	-0.3734	-0.5733	0.7109	0.06909	0.06047	-0.8488	2.955	-0.03364	-0.02721	-0.02201	0.001255	-0.03067	0.1115	-0.08003	48.009	48.009	0.931	47.818	47.834	47.818	47.803	47.94	47.94	11.29	-1.4601	15.743
15000	3.0829	-0.885	1.4514	-2.2062	-1.5605	-5.3247	-0.02201	-0.03755	0.03305	0.1035	-0.03645	0.04684	0.2969	0.5065	-0.4459	-1.3963	0.4916	-0.6319	-0.3624	-4.172	-1.1955	-0.1041	-0.1542	0.1864	1.1558	-42.901	-19.023	-2.6302	0.1531	-0.1338	3.0827	-0.8851	1.4516	-2.2059	-1.5607	-5.3246	-0.02096	-0.03808	0.02958	0.1171	-0.03289	0.03883	-0.417	-6.2434	-2.058	-0.4102	-0.04728	0.1967	-0.4237	-6.2367	-2.0714	-0.4163	-0.0671	0.2059	0.7107	0.06878	0.06041	-0.8478	2.9567	-0.03382	-0.02535	-0.01854	0.001614	-0.02421	0.11	-0.06304	15.099	2.936	-39.068	-1.9402	0.139	-0.2674	0.7107	0.06893	0.06048	-0.8482	2.9561	-0.03367	-0.02458	-0.01986	0.001142	-0.0277	0.1007	-0.07221	48.009	48.069	0.8952	47.818	47.834	47.818	47.803	47.94	47.955	11.69	-1.1801	15.937

15001 rows x 96 columns
memory usage: 11.52 MB
name: data_all
type: getml.DataFrame

1.2 Prepare data for getML¶

The force vector consists of three component (f_x, f_y and f_z), meaning that we have three targets.

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data_all.set_role(["f_x", "f_y", "f_z"], getml.data.roles.target)
data_all.set_role(data_all.roles.unused, getml.data.roles.numerical)
data_all.set_role(["f_x", "f_y", "f_z"], getml.data.roles.target) data_all.set_role(data_all.roles.unused, getml.data.roles.numerical)

This is what the data set looks like:

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data_all
data_all

Out[5]:

name	f_x	f_y	f_z	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79	80	81	82	83	84	85	86	98	99	100	101	102	103	104	105	106
role	target	target	target	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical	numerical
0	-11.03	6.9	-7.33	3.4098	-0.3274	0.9604	-3.7436	-1.0191	-6.0205	0	0	0	0	0	0	0	0	0	0	0	0	8.38e-17	-4.8116	-1.4033	-0.1369	0.002472	0	9.803e-16	-55.642	-16.312	-1.2042	0.02167	0	3.4098	-0.3274	0.9605	-3.7437	-1.0191	-6.0205	0	0	0	0	0	0	0.1233	-6.5483	-2.8045	-0.8296	0.07625	-0.1906	0.1211	-6.5483	-2.8157	-0.8281	0.07015	-0.1983	0.7699	0.41	0.08279	-1.4094	0.786	-0.3682	0	0	0	0	0	0	-22.654	-11.503	-18.673	-3.5155	5.8354	-2.05	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	48.069	48.009	0.9668	47.834	47.925	47.818	47.834	47.955	47.971
1	-10.848	6.7218	-7.4427	3.4098	-0.3274	0.9604	-3.7436	-1.0191	-6.0205	0	0	0	0	0	0	0	0	0	0	0	0	8.38e-17	-4.8116	-1.4033	-0.1369	0.002472	0	9.803e-16	-55.642	-16.312	-1.2042	0.02167	0	3.4098	-0.3274	0.9604	-3.7437	-1.0191	-6.0205	0	0	0	0	0	0	0.1188	-6.5506	-2.8404	-0.8281	0.06405	-0.1998	0.1211	-6.5483	-2.8157	-0.8281	0.07015	-0.1983	0.7699	0.41	0.0828	-1.4094	0.7859	-0.3682	0	0	0	0	0	0	-21.627	-11.046	-18.66	-3.5395	5.7577	-1.9805	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	48.009	48.009	0.8594	47.834	47.925	47.818	47.834	47.955	47.971
2	-10.666	6.5436	-7.5555	3.4098	-0.3274	0.9604	-3.7436	-1.0191	-6.0205	0	0	0	0	0	0	0	0	0	0	0	0	8.38e-17	-4.8116	-1.4033	-0.1369	0.002472	0	9.803e-16	-55.642	-16.312	-1.2042	0.02167	0	3.4098	-0.3274	0.9605	-3.7437	-1.0191	-6.0205	0	0	0	0	0	0	0.1099	-6.5438	-2.8	-0.8205	0.07473	-0.183	0.1211	-6.5483	-2.8157	-0.8281	0.07015	-0.1922	0.7699	0.41	0.08279	-1.4094	0.7859	-0.3682	0	0	0	0	0	0	-23.843	-12.127	-18.393	-3.6453	5.978	-1.9978	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	48.009	48.069	0.931	47.879	47.925	47.818	47.834	47.955	47.971
3	-10.507	6.4533	-7.65	3.4098	-0.3274	0.9604	-3.7436	-1.0191	-6.0205	0	0	0	0	0	0	0	0	0	0	0	0	8.38e-17	-4.8116	-1.4033	-0.1369	0.002472	0	9.803e-16	-55.642	-16.312	-1.2042	0.02167	0	3.4098	-0.3273	0.9604	-3.7437	-1.0191	-6.0205	0	0	0	0	0	0	0.1233	-6.5483	-2.8224	-0.8266	0.07168	-0.1998	0.1211	-6.5483	-2.8157	-0.8281	0.07015	-0.1967	0.7699	0.41	0.08275	-1.4094	0.786	-0.3681	0	0	0	0	0	0	-21.772	-10.872	-18.691	-3.5512	5.6648	-1.9976	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	48.069	48.069	0.931	47.879	47.925	47.818	47.834	47.955	47.971
4	-10.413	6.6267	-7.69	3.4098	-0.3274	0.9604	-3.7436	-1.0191	-6.0205	0	0	0	0	0	0	0	0	0	0	0	0	8.38e-17	-4.8116	-1.4033	-0.1369	0.002472	0	9.803e-16	-55.642	-16.312	-1.2042	0.02167	0	3.4098	-0.3274	0.9604	-3.7437	-1.0191	-6.0205	0	0	0	0	0	0	0.1255	-6.5394	-2.8	-0.8327	0.07473	-0.1952	0.1211	-6.5483	-2.8157	-0.8327	0.07015	-0.1922	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	-22.823	-11.645	-18.524	-3.5305	5.8712	-2.0096	0.7699	0.41	0.08278	-1.4094	0.786	-0.3681	0	0	0	0	0	0	48.069	48.069	0.8952	47.879	47.925	47.818	47.834	47.955	47.971
	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
14996	10.84	-1.41	16.14	3.0837	-0.8836	1.4501	-2.2102	-1.559	-5.3265	-0.03151	-0.05375	0.04732	0.1482	-0.05218	0.06706	0.2969	0.5065	-0.4459	-1.3963	0.4916	-0.6319	-0.3694	-4.1879	-1.1847	-0.09441	-0.1568	0.1898	1.1605	-42.951	-19.023	-2.6343	0.1551	-0.1338	3.0836	-0.8836	1.4503	-2.2101	-1.5591	-5.3263	-0.03347	-0.05585	0.04805	0.151	-0.05513	0.07114	-0.3564	-6.0394	-2.3001	-0.2181	-0.1159	0.09608	-0.3632	-6.0394	-2.3023	-0.212	-0.125	0.1113	0.7116	0.06957	0.06036	-0.8506	2.9515	-0.03352	-0.03558	-0.03029	0.002444	-0.04208	0.1458	-0.1098	-0.8784	-0.07291	-37.584	0.0001132	-2.1031	0.03318	0.7117	0.0697	0.06044	-0.8511	2.951	-0.03356	-0.03508	-0.02849	0.001571	-0.03951	0.1442	-0.1036	48.069	48.009	0.8952	47.818	47.834	47.818	47.803	47.94	47.94
14997	10.857	-1.52	15.943	3.0835	-0.884	1.4505	-2.2091	-1.5594	-5.326	-0.02913	-0.0497	0.04376	0.137	-0.04825	0.062	0.2969	0.5065	-0.4459	-1.3963	0.4916	-0.6319	-0.3677	-4.1837	-1.1874	-0.09682	-0.1562	0.189	1.1592	-42.937	-19.023	-2.6331	0.1545	-0.1338	3.0833	-0.8841	1.4507	-2.209	-1.5596	-5.3258	-0.02909	-0.04989	0.04198	0.1481	-0.05465	0.06249	-0.3161	-6.1179	-2.253	-0.3752	-0.03965	0.08693	-0.3273	-6.1022	-2.2597	-0.366	-0.05033	0.0915	0.7114	0.06932	0.06039	-0.8497	2.953	-0.03359	-0.0335	-0.02723	0.001208	-0.04242	0.1428	-0.0967	-2.7137	0.8552	-38.514	-0.6088	-3.2383	-0.9666	0.7114	0.06948	0.06045	-0.8503	2.9525	-0.03359	-0.03246	-0.02633	0.001469	-0.03657	0.1333	-0.09571	48.009	48.009	0.8594	47.818	47.834	47.818	47.803	47.94	47.94
14998	10.89	-1.74	15.55	3.0833	-0.8844	1.4508	-2.208	-1.5598	-5.3256	-0.02676	-0.04565	0.04019	0.1258	-0.04431	0.05695	0.2969	0.5065	-0.4459	-1.3963	0.4916	-0.6319	-0.3659	-4.1797	-1.1901	-0.09922	-0.1555	0.1881	1.1579	-42.924	-19.023	-2.6321	0.154	-0.1338	3.0831	-0.8844	1.451	-2.2078	-1.56	-5.3253	-0.02776	-0.04382	0.03652	0.1295	-0.05064	0.04818	-0.343	-6.2569	-2.1566	-0.3035	0.00305	0.1434	-0.3385	-6.2322	-2.1589	-0.302	-0.00915	0.1571	0.7111	0.06912	0.06039	-0.849	2.9544	-0.0337	-0.02911	-0.02589	0.001292	-0.04046	0.1246	-0.08058	4.2749	1.0128	-36.412	-1.2811	-0.4296	-1.1013	0.7112	0.06928	0.06046	-0.8495	2.9538	-0.03362	-0.02984	-0.02417	0.001364	-0.03362	0.1224	-0.08786	48.009	48.009	0.931	47.818	47.834	47.818	47.803	47.94	47.94
14999	11.29	-1.4601	15.743	3.0831	-0.8847	1.4511	-2.2071	-1.5602	-5.3251	-0.02438	-0.0416	0.03662	0.1147	-0.04038	0.0519	0.2969	0.5065	-0.4459	-1.3963	0.4916	-0.6319	-0.3642	-4.1758	-1.1928	-0.1016	-0.1548	0.1873	1.1568	-42.912	-19.023	-2.6311	0.1535	-0.1338	3.0829	-0.8848	1.4513	-2.2068	-1.5604	-5.3249	-0.02149	-0.04059	0.03417	0.1202	-0.0395	0.04178	-0.4237	-6.2703	-2.0939	-0.302	-0.01372	0.1739	-0.4125	-6.2569	-2.0916	-0.2943	-0.02898	0.1891	0.7109	0.06894	0.06039	-0.8484	2.9557	-0.03384	-0.02738	-0.01982	0.001031	-0.03028	0.1157	-0.06702	11.518	1.5002	-39.314	-1.8671	-0.3734	-0.5733	0.7109	0.06909	0.06047	-0.8488	2.955	-0.03364	-0.02721	-0.02201	0.001255	-0.03067	0.1115	-0.08003	48.009	48.009	0.931	47.818	47.834	47.818	47.803	47.94	47.94
15000	11.69	-1.1801	15.937	3.0829	-0.885	1.4514	-2.2062	-1.5605	-5.3247	-0.02201	-0.03755	0.03305	0.1035	-0.03645	0.04684	0.2969	0.5065	-0.4459	-1.3963	0.4916	-0.6319	-0.3624	-4.172	-1.1955	-0.1041	-0.1542	0.1864	1.1558	-42.901	-19.023	-2.6302	0.1531	-0.1338	3.0827	-0.8851	1.4516	-2.2059	-1.5607	-5.3246	-0.02096	-0.03808	0.02958	0.1171	-0.03289	0.03883	-0.417	-6.2434	-2.058	-0.4102	-0.04728	0.1967	-0.4237	-6.2367	-2.0714	-0.4163	-0.0671	0.2059	0.7107	0.06878	0.06041	-0.8478	2.9567	-0.03382	-0.02535	-0.01854	0.001614	-0.02421	0.11	-0.06304	15.099	2.936	-39.068	-1.9402	0.139	-0.2674	0.7107	0.06893	0.06048	-0.8482	2.9561	-0.03367	-0.02458	-0.01986	0.001142	-0.0277	0.1007	-0.07221	48.009	48.069	0.8952	47.818	47.834	47.818	47.803	47.94	47.955

15001 rows x 96 columns
memory usage: 11.52 MB
name: data_all
type: getml.DataFrame

1.3 Separate data into a training and testing set¶

We also want to separate the data set into a training and testing set. We do so by using the first 10,500 measurements for training and then using the remainder for testing.

In [6]:

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split = getml.data.split.time(data_all, "rowid", test=10500)
split
split = getml.data.split.time(data_all, "rowid", test=10500) split

Out[6]:


0	train
1	train
2	train
3	train
4	train
	...

unknown number of rows
type: StringColumnView

In [7]:

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time_series = getml.data.TimeSeries(
    population=data_all,
    split=split,
    time_stamps="rowid",
    lagged_targets=False,
    memory=30,
)

time_series
time_series = getml.data.TimeSeries( population=data_all, split=split, time_stamps="rowid", lagged_targets=False, memory=30, ) time_series

Out[7]:

data model

diagram

staging

	data frames	staging table
0	population	POPULATION__STAGING_TABLE_1
1	data_all	DATA_ALL__STAGING_TABLE_2

container

population

	subset	name	rows	type
0	test	data_all	unknown	View
1	train	data_all	unknown	View

peripheral

	name	rows	type
0	data_all	15001	View

2. Predictive modeling¶

2.1 Building the pipeline¶

We then build a pipeline based on the relboost algorithm with xgboost as our predictor.

In [8]:

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fast_prop = getml.feature_learning.FastProp(
    loss_function=getml.feature_learning.loss_functions.SquareLoss,
    num_features=10,
)

xgboost = getml.predictors.XGBoostRegressor()

pipe1 = getml.pipeline.Pipeline(
    data_model=time_series.data_model,
    feature_learners=[fast_prop],
    predictors=xgboost
)
fast_prop = getml.feature_learning.FastProp( loss_function=getml.feature_learning.loss_functions.SquareLoss, num_features=10, ) xgboost = getml.predictors.XGBoostRegressor() pipe1 = getml.pipeline.Pipeline( data_model=time_series.data_model, feature_learners=[fast_prop], predictors=xgboost )

It is always a good idea to check the pipeline for any potential issues.

In [9]:

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pipe1.check(time_series.train)
pipe1.check(time_series.train)

Checking data model...

  Staging... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:00
  Checking... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:00

OK.

2.2 Fitting the pipeline¶

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pipe1.fit(time_series.train)
pipe1.fit(time_series.train)

Checking data model...

  Staging... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:00

OK.

  Staging... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:00
  FastProp: Trying 1130 features... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:01
  FastProp: Building features... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:00
  XGBoost: Training as predictor... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:02
  XGBoost: Training as predictor... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:02
  XGBoost: Training as predictor... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:03

Trained pipeline.

Time taken: 0:00:11.060886.

Out[10]:

Pipeline(data_model='population',
         feature_learners=['FastProp'],
         feature_selectors=[],
         include_categorical=False,
         loss_function='SquareLoss',
         peripheral=['data_all'],
         predictors=['XGBoostRegressor'],
         preprocessors=[],
         share_selected_features=0.5,
         tags=['container-Y7lpuV'])

2.3 Evaluating the pipeline¶

In [11]:

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pipe1.score(time_series.test)
pipe1.score(time_series.test)

  Staging... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:00
  Preprocessing... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:00
  FastProp: Building features... ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100% • 00:00

Out[11]:

	date time	set used	target	mae	rmse	rsquared
0	2024-09-12 15:17:15	train	f_x	0.4403	0.58	0.9962
1	2024-09-12 15:17:15	train	f_y	0.5168	0.6813	0.9893
2	2024-09-12 15:17:15	train	f_z	0.2918	0.385	0.9986
3	2024-09-12 15:17:15	test	f_x	0.5605	0.7316	0.995
4	2024-09-12 15:17:15	test	f_y	0.5654	0.7533	0.9871
5	2024-09-12 15:17:15	test	f_z	0.3133	0.4074	0.9984

2.4 Feature importances¶

It is always a good idea to study the features the relational learning algorithm has extracted.

The feature importance is calculated by xgboost based on the improvement of the optimizing criterium at each split in the decision tree and is normalized to 100%.

Also note that we have three different target (f_x, f_y and f_z) and that different features are relevant for different targets.

In [12]:

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plt.subplots(figsize=(20, 10))

names, importances = pipe1.features.importances(target_num=0)

plt.bar(names[0:30], importances[0:30], color='#6829c2')

plt.title("feature importances for the x-component", size=20)
plt.grid(True)
plt.xlabel("features")
plt.ylabel("importance")
plt.xticks(rotation='vertical')

plt.show()
plt.subplots(figsize=(20, 10)) names, importances = pipe1.features.importances(target_num=0) plt.bar(names[0:30], importances[0:30], color='#6829c2') plt.title("feature importances for the x-component", size=20) plt.grid(True) plt.xlabel("features") plt.ylabel("importance") plt.xticks(rotation='vertical') plt.show()

No description has been provided for this image

In [13]:

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plt.subplots(figsize=(20, 10))

names, importances = pipe1.features.importances(target_num=1)

plt.bar(names[0:30], importances[0:30], color='#6829c2')

plt.title("feature importances for the y-component", size=20)
plt.grid(True)
plt.xlabel("features")
plt.ylabel("importance")
plt.xticks(rotation='vertical')

plt.show()
plt.subplots(figsize=(20, 10)) names, importances = pipe1.features.importances(target_num=1) plt.bar(names[0:30], importances[0:30], color='#6829c2') plt.title("feature importances for the y-component", size=20) plt.grid(True) plt.xlabel("features") plt.ylabel("importance") plt.xticks(rotation='vertical') plt.show()