.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_tutorial/plot_ebegin_float_double.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_tutorial_plot_ebegin_float_double.py: .. _l-example-discrepencies-float-double: Issues when switching to float ============================== .. index:: float, double, discrepencies Most models in :epkg:`scikit-learn` do computation with double, not float. Most models in deep learning use float because that's the most common situation with GPU. ONNX was initially created to facilitate the deployment of deep learning models and that explains why many converters assume the converted models should use float. That assumption does not usually harm the predictions, the conversion to float introduce small discrepencies compare to double predictions. That assumption is usually true if the prediction function is continuous, :math:`y = f(x)`, then :math:`dy = f'(x) dx`. We can determine an upper bound to the discrepencies : :math:`\Delta(y) \leqslant \sup_x \left\Vert f'(x)\right\Vert dx`. *dx* is the discrepency introduced by a float conversion, ``dx = x - numpy.float32(x)``. However, that's not the case for every model. A decision tree trained for a regression is not a continuous function. Therefore, even a small *dx* may introduce a huge discrepency. Let's look into an example which always produces discrepencies and some ways to overcome this situation. More into the issue +++++++++++++++++++ The below example is built to fail. It contains integer features with different order of magnitude rounded to integer. A decision tree compares features to thresholds. In most cases, float and double comparison gives the same result. We denote :math:`[x]_{f32}` the conversion (or cast) ``numpy.float32(x)``. .. math:: x \leqslant y = [x]_{f32} \leqslant [y]_{f32} However, the probability that both comparisons give different results is not null. The following graph shows the discord areas. .. GENERATED FROM PYTHON SOURCE LINES 52-105 .. code-block:: default from skl2onnx.sklapi import CastTransformer from skl2onnx import to_onnx from onnxruntime import InferenceSession from sklearn.model_selection import train_test_split from sklearn.tree import DecisionTreeRegressor from sklearn.preprocessing import StandardScaler from sklearn.pipeline import Pipeline from sklearn.datasets import make_regression import numpy import matplotlib.pyplot as plt def area_mismatch_rule(N, delta, factor, rule=None): if rule is None: def rule(t): return numpy.float32(t) xst = [] yst = [] xsf = [] ysf = [] for x in range(-N, N): for y in range(-N, N): dx = (1.0 + x * delta) * factor dy = (1.0 + y * delta) * factor c1 = 1 if numpy.float64(dx) <= numpy.float64(dy) else 0 c2 = 1 if numpy.float32(dx) <= rule(dy) else 0 key = abs(c1 - c2) if key == 1: xsf.append(dx) ysf.append(dy) else: xst.append(dx) yst.append(dy) return xst, yst, xsf, ysf delta = 36e-10 factor = 1 xst, yst, xsf, ysf = area_mismatch_rule(100, delta, factor) fig, ax = plt.subplots(1, 1, figsize=(5, 5)) ax.plot(xst, yst, ".", label="agree") ax.plot(xsf, ysf, ".", label="disagree") ax.set_title("Region where x <= y and (float)x <= (float)y agree") ax.set_xlabel("x") ax.set_ylabel("y") ax.plot([min(xst), max(xst)], [min(yst), max(yst)], "k--") ax.legend() .. image-sg:: /auto_tutorial/images/sphx_glr_plot_ebegin_float_double_001.png :alt: Region where x <= y and (float)x <= (float)y agree :srcset: /auto_tutorial/images/sphx_glr_plot_ebegin_float_double_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 106-113 The pipeline and the data +++++++++++++++++++++++++ We can now build an example where the learned decision tree does many comparisons in this discord area. This is done by rounding features to integers, a frequent case happening when dealing with categorical features. .. GENERATED FROM PYTHON SOURCE LINES 113-132 .. code-block:: default X, y = make_regression(10000, 10) X_train, X_test, y_train, y_test = train_test_split(X, y) Xi_train, yi_train = X_train.copy(), y_train.copy() Xi_test, yi_test = X_test.copy(), y_test.copy() for i in range(X.shape[1]): Xi_train[:, i] = (Xi_train[:, i] * 2**i).astype(numpy.int64) Xi_test[:, i] = (Xi_test[:, i] * 2**i).astype(numpy.int64) max_depth = 10 model = Pipeline( [("scaler", StandardScaler()), ("dt", DecisionTreeRegressor(max_depth=max_depth))] ) model.fit(Xi_train, yi_train) .. raw:: html 
Pipeline(steps=[('scaler', StandardScaler()),
                    ('dt', DecisionTreeRegressor(max_depth=10))])
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.. GENERATED FROM PYTHON SOURCE LINES 133-139 The discrepencies +++++++++++++++++ Let's reuse the function implemented in the first example :ref:`l-diff-dicrepencies` and look into the conversion. .. GENERATED FROM PYTHON SOURCE LINES 139-159 .. code-block:: default def diff(p1, p2): p1 = p1.ravel() p2 = p2.ravel() d = numpy.abs(p2 - p1) return d.max(), (d / numpy.abs(p1)).max() onx = to_onnx(model, Xi_train[:1].astype(numpy.float32), target_opset=15) sess = InferenceSession(onx.SerializeToString(), providers=["CPUExecutionProvider"]) X32 = Xi_test.astype(numpy.float32) skl = model.predict(X32) ort = sess.run(None, {"X": X32})[0] print(diff(skl, ort)) .. rst-class:: sphx-glr-script-out .. code-block:: none (191.14468356708568, 4.322660335343007) .. GENERATED FROM PYTHON SOURCE LINES 160-193 The discrepencies are significant. The ONNX model keeps float at every step. .. blockdiag:: diagram { x_float32 -> normalizer -> y_float32 -> dtree -> z_float32 } In :epkg:`scikit-learn`: .. blockdiag:: diagram { x_float32 -> normalizer -> y_double -> dtree -> z_double } CastTransformer +++++++++++++++ We could try to use double everywhere. Unfortunately, :epkg:`ONNX ML Operators` only allows float coefficients for the operator *TreeEnsembleRegressor*. We may want to compromise by casting the output of the normalizer into float in the :epkg:`scikit-learn` pipeline. .. blockdiag:: diagram { x_float32 -> normalizer -> y_double -> cast -> y_float -> dtree -> z_float } .. GENERATED FROM PYTHON SOURCE LINES 193-205 .. code-block:: default model2 = Pipeline( [ ("scaler", StandardScaler()), ("cast", CastTransformer()), ("dt", DecisionTreeRegressor(max_depth=max_depth)), ] ) model2.fit(Xi_train, yi_train) .. raw:: html 
Pipeline(steps=[('scaler', StandardScaler()), ('cast', CastTransformer()),
                    ('dt', DecisionTreeRegressor(max_depth=10))])
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.. GENERATED FROM PYTHON SOURCE LINES 206-207 The discrepencies. .. GENERATED FROM PYTHON SOURCE LINES 207-217 .. code-block:: default onx2 = to_onnx(model2, Xi_train[:1].astype(numpy.float32), target_opset=15) sess2 = InferenceSession(onx2.SerializeToString(), providers=["CPUExecutionProvider"]) skl2 = model2.predict(X32) ort2 = sess2.run(None, {"X": X32})[0] print(diff(skl2, ort2)) .. rst-class:: sphx-glr-script-out .. code-block:: none (191.14468356708568, 4.322660335343007) .. GENERATED FROM PYTHON SOURCE LINES 218-223 That still fails because the normalizer in :epkg:`scikit-learn` and in :epkg:`ONNX` use different types. The cast still happens and the *dx* is still here. To remove it, we need to use double in ONNX normalizer. .. GENERATED FROM PYTHON SOURCE LINES 223-248 .. code-block:: default model3 = Pipeline( [ ("cast64", CastTransformer(dtype=numpy.float64)), ("scaler", StandardScaler()), ("cast", CastTransformer()), ("dt", DecisionTreeRegressor(max_depth=max_depth)), ] ) model3.fit(Xi_train, yi_train) onx3 = to_onnx( model3, Xi_train[:1].astype(numpy.float32), options={StandardScaler: {"div": "div_cast"}}, target_opset=15, ) sess3 = InferenceSession(onx3.SerializeToString(), providers=["CPUExecutionProvider"]) skl3 = model3.predict(X32) ort3 = sess3.run(None, {"X": X32})[0] print(diff(skl3, ort3)) .. rst-class:: sphx-glr-script-out .. code-block:: none (2.0221857994329184e-05, 5.733250169110544e-08) .. GENERATED FROM PYTHON SOURCE LINES 249-253 It works. That also means that it is difficult to change the computation type when a pipeline includes a discontinuous function. It is better to keep the same types all along before using a decision tree. .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.936 seconds) .. _sphx_glr_download_auto_tutorial_plot_ebegin_float_double.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_ebegin_float_double.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_ebegin_float_double.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_