101: Linear Regression and export to ONNX

scikit-learn and torch to train a linear regression.

data

import numpy as np
from sklearn.datasets import make_regression
from sklearn.linear_model import LinearRegression, SGDRegressor
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.model_selection import train_test_split
import torch
from onnxruntime import InferenceSession
from experimental_experiment.helpers import pretty_onnx
from onnx_array_api.plotting.graphviz_helper import plot_dot
from experimental_experiment.torch_interpreter import to_onnx


X, y = make_regression(1000, n_features=5, noise=10.0, n_informative=2)
print(X.shape, y.shape)

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

(1000, 5) (1000,)

scikit-learn: the simple regression

clr = LinearRegression()
clr.fit(X_train, y_train)

print(f"coefficients: {clr.coef_}, {clr.intercept_}")

coefficients: [-0.4156729  68.16768474 -0.14817797 -0.13074446 79.68740891], -0.26352200022452266

Evaluation

y_pred = clr.predict(X_test)
l2 = mean_squared_error(y_test, y_pred)
r2 = r2_score(y_test, y_pred)
print(f"LinearRegression: l2={l2}, r2={r2}")

LinearRegression: l2=94.01302744583698, r2=0.9917297757770004

scikit-learn: SGD algorithm

SGD = Stochastic Gradient Descent

clr = SGDRegressor(max_iter=5, verbose=1)
clr.fit(X_train, y_train)

print(f"coefficients: {clr.coef_}, {clr.intercept_}")

-- Epoch 1
Norm: 88.27, NNZs: 5, Bias: 0.844179, T: 750, Avg. loss: 1130.952914
Total training time: 0.00 seconds.
-- Epoch 2
Norm: 100.02, NNZs: 5, Bias: 0.239097, T: 1500, Avg. loss: 104.278971
Total training time: 0.00 seconds.
-- Epoch 3
Norm: 103.16, NNZs: 5, Bias: -0.042557, T: 2250, Avg. loss: 59.880112
Total training time: 0.00 seconds.
-- Epoch 4
Norm: 104.22, NNZs: 5, Bias: -0.102363, T: 3000, Avg. loss: 55.392890
Total training time: 0.00 seconds.
-- Epoch 5
Norm: 104.58, NNZs: 5, Bias: -0.137567, T: 3750, Avg. loss: 54.760405
Total training time: 0.00 seconds.
/home/xadupre/vv/this/lib/python3.10/site-packages/sklearn/linear_model/_stochastic_gradient.py:1616: ConvergenceWarning: Maximum number of iteration reached before convergence. Consider increasing max_iter to improve the fit.
  warnings.warn(
coefficients: [-6.13996456e-01  6.78142089e+01 -7.22902356e-02 -1.09481207e-01
  7.96098393e+01], [-0.13756652]

Evaluation

y_pred = clr.predict(X_test)
sl2 = mean_squared_error(y_test, y_pred)
sr2 = r2_score(y_test, y_pred)
print(f"SGDRegressor: sl2={sl2}, sr2={sr2}")

SGDRegressor: sl2=96.61863163474834, sr2=0.9915005635979639

torch

class TorchLinearRegression(torch.nn.Module):
    def __init__(self, n_dims: int, n_targets: int):
        super().__init__()
        self.linear = torch.nn.Linear(n_dims, n_targets)

    def forward(self, x):
        return self.linear(x)


def train_loop(dataloader, model, loss_fn, optimizer):
    total_loss = 0.0

    # Set the model to training mode - important for batch normalization and dropout layers
    # Unnecessary in this situation but added for best practices
    model.train()
    for X, y in dataloader:
        # Compute prediction and loss
        pred = model(X)
        loss = loss_fn(pred.ravel(), y)

        # Backpropagation
        loss.backward()
        optimizer.step()
        optimizer.zero_grad()

        # training loss
        total_loss += loss

    return total_loss


model = TorchLinearRegression(X_train.shape[1], 1)
optimizer = torch.optim.SGD(model.parameters(), lr=1e-3)
loss_fn = torch.nn.MSELoss()

device = "cpu"
model = model.to(device)
dataset = torch.utils.data.TensorDataset(
    torch.Tensor(X_train).to(device), torch.Tensor(y_train).to(device)
)
dataloader = torch.utils.data.DataLoader(dataset, batch_size=1)


for i in range(5):
    loss = train_loop(dataloader, model, loss_fn, optimizer)
    print(f"iteration {i}, loss={loss}")

iteration 0, loss=2694195.5
iteration 1, loss=228070.96875
iteration 2, loss=90632.5
iteration 3, loss=82579.359375
iteration 4, loss=82213.4140625

Let’s check the error

y_pred = model(torch.Tensor(X_test)).detach().numpy()
tl2 = mean_squared_error(y_test, y_pred)
tr2 = r2_score(y_test, y_pred)
print(f"TorchLinearRegression: tl2={tl2}, tr2={tr2}")

TorchLinearRegression: tl2=94.02586960430797, tr2=0.9917286460662258

And the coefficients.

print("coefficients:")
for p in model.parameters():
    print(p)

coefficients:
Parameter containing:
tensor([[-0.5584, 68.3682, -0.1259,  0.1630, 79.7769]], requires_grad=True)
Parameter containing:
tensor([-0.2713], requires_grad=True)

Conversion to ONNX

Let’s convert it to ONNX.

onx = to_onnx(model, (torch.Tensor(X_test[:2]),), input_names=["x"])

Let’s check it is work.

sess = InferenceSession(onx.SerializeToString(), providers=["CPUExecutionProvider"])
res = sess.run(None, {"x": X_test.astype(np.float32)[:2]})
print(res)

[array([[ 99.81213 ],
       [-20.478058]], dtype=float32)]

And the model.

plot_dot(onx)

<Axes: >

With dynamic shapes

onx = to_onnx(
    model,
    (torch.Tensor(X_test[:2]),),
    input_names=["x"],
    dynamic_shapes={"x": {0: torch.export.Dim("batch")}},
)

print(pretty_onnx(onx))

opset: domain='' version=18
doc_string: large_model=False, inline=False, external_threshold=102...
input: name='x' type=dtype('float32') shape=['batch', 5]
init: name='p_linear_weight' type=dtype('float32') shape=(1, 5)
init: name='p_linear_bias' type=dtype('float32') shape=(1,) -- array([-0.27127013], dtype=float32)
Transpose(p_linear_weight, perm=[1,0]) -> _onx_transpose0
  Transpose(_onx_transpose0, perm=[1,0]) -> GemmTransposePattern--_onx_transpose0
    Gemm(x, GemmTransposePattern--_onx_transpose0, p_linear_bias, transB=1) -> output_0
output: name='output_0' type=dtype('float32') shape=['batch', 1]