# Train a linear regression with onnxruntime-training#

This example explores how onnxruntime-training can be used to train a simple linear regression using a gradient descent. It compares the results with those obtained by `sklearn.linear_model.SGDRegressor`

## A simple linear regression with scikit-learn#

```from pprint import pprint
import numpy
import onnx
from pandas import DataFrame
from onnxruntime import (
InferenceSession, get_device)
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.linear_model import SGDRegressor
from sklearn.neural_network import MLPRegressor
from mlprodict.onnx_conv import to_onnx
from onnxcustom.plotting.plotting_onnx import plot_onnxs
from onnxcustom.utils.orttraining_helper import (

X, y = make_regression(n_features=2, bias=2)
X = X.astype(numpy.float32)
y = y.astype(numpy.float32)
X_train, X_test, y_train, y_test = train_test_split(X, y)

lr = SGDRegressor(l1_ratio=0, max_iter=200, eta0=5e-2)
lr.fit(X, y)
print(lr.predict(X[:5]))
```
```[ 53.83746772   6.79334086  86.31569796  73.72210063 -79.5078181 ]
```

The trained coefficients are:

```print("trained coefficients:", lr.coef_, lr.intercept_)
```
```trained coefficients: [67.74134798  7.91162025] [2.00017697]
```

However this model does not show the training curve. We switch to a `sklearn.neural_network.MLPRegressor`.

```lr = MLPRegressor(hidden_layer_sizes=tuple(),
activation='identity', max_iter=200,
batch_size=10, solver='sgd',
alpha=0, learning_rate_init=1e-2,
n_iter_no_change=200,
momentum=0, nesterovs_momentum=False)
lr.fit(X, y)
print(lr.predict(X[:5]))
```
```somewhere/workspace/onnxcustom/onnxcustom_UT_39_std/_venv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:679: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.
warnings.warn(
[ 53.842594    6.7937374  86.3236     73.72894   -79.51577  ]
```

The trained coefficients are:

```print("trained coefficients:", lr.coefs_, lr.intercepts_)
```
```trained coefficients: [array([[67.74782 ],
[ 7.911858]], dtype=float32)] [array([2.0000002], dtype=float32)]
```

## ONNX graph#

Training with onnxruntime-training starts with an ONNX graph which defines the model to learn. It is obtained by simply converting the previous linear regression into ONNX.

```onx = to_onnx(lr, X_train[:1].astype(numpy.float32), target_opset=15,
black_op={'LinearRegressor'})
```

## Choosing a loss#

The training requires a loss function. By default, it is the square function but it could be the absolute error or include regularization. Function `add_loss_output` appends the loss function to the ONNX graph.

```onx_train = add_loss_output(onx)

plot_onnxs(onx, onx_train,
title=['Linear Regression',
'Linear Regression + Loss with ONNX'])
``` ```array([<AxesSubplot: title={'center': 'Linear Regression'}>,
<AxesSubplot: title={'center': 'Linear Regression + Loss with ONNX'}>],
dtype=object)
```

Let’s check inference is working.

```sess = InferenceSession(onx_train.SerializeToString(),
providers=['CPUExecutionProvider'])
res = sess.run(None, {'X': X_test, 'label': y_test.reshape((-1, 1))})
print(f"onnx loss={res[0, 0] / X_test.shape!r}")
```
```onnx loss=2.4012649646465434e-08
```

## Weights#

Every initializer is a set of weights which can be trained and a gradient will be computed for it. However an initializer used to modify a shape or to extract a subpart of a tensor does not need training. Let’s remove them from the list of initializer to train.

```inits = get_train_initializer(onx)
weights = {k: v for k, v in inits.items() if k != "shape_tensor"}
pprint(list((k, v.shape) for k, v in weights.items()))
```
```[('coefficient', (2, 1)), ('intercepts', (1, 1))]
```

## Train on CPU or GPU if available#

```device = "cuda" if get_device().upper() == 'GPU' else 'cpu'
print(f"device={device!r} get_device()={get_device()!r}")
```
```device='cpu' get_device()='CPU'
```

The training logic is hidden in class `OrtGradientOptimizer`. It follows scikit-learn API (see SGDRegressor. The gradient graph is not available at this stage.

```train_session = OrtGradientOptimizer(
onx_train, list(weights), device=device, verbose=1, learning_rate=1e-2,
warm_start=False, max_iter=200, batch_size=10,

train_session.fit(X, y)
```
```  0%|          | 0/200 [00:00<?, ?it/s]
16%|#5        | 31/200 [00:00<00:00, 309.89it/s]
34%|###4      | 68/200 [00:00<00:00, 343.63it/s]
52%|#####2    | 105/200 [00:00<00:00, 355.36it/s]
71%|#######1  | 142/200 [00:00<00:00, 360.51it/s]
90%|########9 | 179/200 [00:00<00:00, 363.87it/s]
100%|##########| 200/200 [00:00<00:00, 357.83it/s]

OrtGradientOptimizer(model_onnx='ir_version...', weights_to_train=['coefficient', 'intercepts'], loss_output_name='loss', max_iter=200, training_optimizer_name='SGDOptimizer', batch_size=10, learning_rate=LearningRateSGD(eta0=0.01, alpha=0.0001, power_t=0.25, learning_rate='invscaling'), value=0.0026591479484724943, device='cpu', warm_start=False, verbose=1, validation_every=20, saved_gradient='saved_gradient.onnx', sample_weight_name='weight')
```

And the trained coefficient are…

```state_tensors = train_session.get_state()
pprint(["trained coefficients:", state_tensors])
print("last_losses:", train_session.train_losses_[-5:])

min_length = min(len(train_session.train_losses_), len(lr.loss_curve_))
df = DataFrame({'ort losses': train_session.train_losses_[:min_length],
'skl losses': lr.loss_curve_[:min_length]})
df.plot(title="Train loss against iterations")
``` ```['trained coefficients:',
{'coefficient': array([[67.74761  ],
[ 7.9118924]], dtype=float32),
'intercepts': array([[1.9999774]], dtype=float32)}]
last_losses: [1.8183808e-07, 1.3479456e-07, 1.2890612e-07, 1.6501485e-07, 1.506005e-07]

<AxesSubplot: title={'center': 'Train loss against iterations'}>
```

the training graph looks like the following…

```with open("saved_gradient.onnx.training.onnx", "rb") as f:
for inode, node in enumerate(graph.graph.node):
if '' in node.output:
for i in range(len(node.output)):
if node.output[i] == "":
node.output[i] = "n%d-%d" % (inode, i)

plot_onnxs(graph, title='Training graph')
``` ```<AxesSubplot: title={'center': 'Training graph'}>
```

The convergence speed is not the same but both gradient descents do not update the gradient multiplier the same way. onnxruntime-training does not implement any gradient descent, it just computes the gradient. That’s the purpose of `OrtGradientOptimizer`. Next example digs into the implementation details.

```# import matplotlib.pyplot as plt
# plt.show()
```

Total running time of the script: ( 0 minutes 4.645 seconds)

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