load ArxModel from given path

Creates a ARX model by training on the given frame. Fit an autoregressive model with additional exogenous variables.

1. Dataset being trained must be small enough to be worked with on a single node.
2. If the specified set of exogenous variables is not invertible, an exception is thrown stating that the "matrix is singular". This happens when there are certain patterns in the dataset or columns of all zeros. In order to work around the singular matrix issue, try selecting a different set of columns for exogenous variables, or use a different time window for training.

A trained ARX model.

Consider the following model trained and tested on the sample data set in frame 'frame'. The frame has a snippet of air quality data from:

https://archive.ics.uci.edu/ml/datasets/Air+Quality.

Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.

>>> frame.inspect()
[#]  Date        Time      CO_GT  PT08_S1_CO  NMHC_GT  C6H6_GT  PT08_S2_NMHC
============================================================================
[0]  10/03/2004  18.00.00    2.6        1360      150     11.9          1046
[1]  10/03/2004  19.00.00    2.0        1292      112      9.4           955
[2]  10/03/2004  20.00.00    2.2        1402       88      9.0           939
[3]  10/03/2004  21.00.00    2.2        1376       80      9.2           948
[4]  10/03/2004  22.00.00    1.6        1272       51      6.5           836
[5]  10/03/2004  23.00.00    1.2        1197       38      4.7           750
[6]  11/03/2004  00.00.00    1.2        1185       31      3.6           690
[7]  11/03/2004  01.00.00    1.0        1136       31      3.3           672
[8]  11/03/2004  02.00.00    0.9        1094       24      2.3           609
[9]  11/03/2004  03.00.00    0.6        1010       19      1.7           561
<BLANKLINE>
[#]  NOx_GT  PT08_S3_NOx  NO2_GT  PT08_S4_NO2  PT08_S5_O3_  T     RH    AH
==============================================================================
[0]     166         1056     113         1692         1268  13.6  48.9  0.7578
[1]     103         1174      92         1559          972  13.3  47.7  0.7255
[2]     131         1140     114         1555         1074  11.9  54.0  0.7502
[3]     172         1092     122         1584         1203  11.0  60.0  0.7867
[4]     131         1205     116         1490         1110  11.2  59.6  0.7888
[5]      89         1337      96         1393          949  11.2  59.2  0.7848
[6]      62         1462      77         1333          733  11.3  56.8  0.7603
[7]      62         1453      76         1333          730  10.7  60.0  0.7702
[8]      45         1579      60         1276          620  10.7  59.7  0.7648
[9]    -200         1705    -200         1235          501  10.3  60.2  0.7517

We will be using the column "T" (temperature) as our time series value:

>>> y = "T"

The sensor values will be used as our exogenous variables:

>>> x = ['CO_GT','PT08_S1_CO','NMHC_GT','C6H6_GT','PT08_S2_NMHC','NOx_GT','PT08_S3_NOx','NO2_GT','PT08_S4_NO2','PT08_S5_O3_']

Train the model and then take a look at the model properties and coefficients:

>>> model = tc.models.timeseries.arx.train(frame, y, x, 0, 0, True)
[===Job Progress===]

>>> model
c            = 0.0
coefficients = [0.005567992923907625, -0.010969068059453009, 0.012556586798371176, -0.39792503380811506, 0.04289162879826746, -0.012253952164677924, 0.01192148525581035, 0.014100699808650077, -0.021091473795935345, 0.007622676727420039]
no_intercept = True
x_max_lag    = 0
y_max_lag    = 0

In this example, we will call predict using the same frame that was used for training, again specifying the name of the time series column and the names of the columns that contain exogenous regressors.

>>> predicted_frame = model.predict(frame, y, x)
[===Job Progress===]

The predicted_frame that's return has a new column called predicted_y. This column contains the predicted time series values.

>>> predicted_frame.column_names
[u'Date',
 u'Time',
 u'CO_GT',
 u'PT08_S1_CO',
 u'NMHC_GT',
 u'C6H6_GT',
 u'PT08_S2_NMHC',
 u'NOx_GT',
 u'PT08_S3_NOx',
 u'NO2_GT',
 u'PT08_S4_NO2',
 u'PT08_S5_O3_',
 u'T',
 u'RH',
 u'AH',
 u'predicted_y']

>>> predicted_frame.inspect(n=15, columns=["T","predicted_y"])
[##]  T     predicted_y
=========================
[0]   13.6   13.236459938
[1]   13.3  13.0250130899
[2]   11.9  11.4147282294
[3]   11.0  11.3157457822
[4]   11.2  11.3982074883
[5]   11.2  11.7079198051
[6]   11.3  10.7879916472
[7]   10.7   10.527428478
[8]   10.7  10.4439615476
[9]   10.3   10.276662138
[10]  10.1  10.0999996581
[11]  11.0  11.2849327784
[12]  10.5  10.5726885589
[13]  10.2  10.1984619512
[14]  10.8  11.0063774234

The trained model can be saved to be used later:

>>> model_path = "sandbox/savedArxModel"
>>> model.save(model_path)

The saved model can be loaded through the tk context and then used for forecasting values the same way that the original model was used.

>>> loaded_model = tc.load(model_path)

>>> predicted_frame = loaded_model.predict(frame, y, x)

>>> predicted_frame.inspect(n=15,columns=["T","predicted_y"])
[##]  T     predicted_y
=========================
[0]   13.6   13.236459938
[1]   13.3  13.0250130899
[2]   11.9  11.4147282294
[3]   11.0  11.3157457822
[4]   11.2  11.3982074883
[5]   11.2  11.7079198051
[6]   11.3  10.7879916472
[7]   10.7   10.527428478
[8]   10.7  10.4439615476
[9]   10.3   10.276662138
[10]  10.1  10.0999996581
[11]  11.0  11.2849327784
[12]  10.5  10.5726885589
[13]  10.2  10.1984619512
[14]  10.8  11.0063774234

The trained model can also be exported to a .mar file, to be used with the scoring engine:

>>> canonical_path = model.export_to_mar("sandbox/arx.mar")