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dev/_downloads/face_recognition.py

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Expected results for the top 5 most represented people in the dataset::
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================== ============ ======= ========== =======
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precision recall f1-score support
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================== ============ ======= ========== =======
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Ariel Sharon 0.67 0.92 0.77 13
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Colin Powell 0.75 0.78 0.76 60
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Donald Rumsfeld 0.78 0.67 0.72 27
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Tony Blair 0.81 0.69 0.75 36
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avg / total 0.80 0.80 0.80 322
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================== ============ ======= ========== =======
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"""
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from __future__ import print_function

dev/_downloads/plot_gpr_co2.py

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The kernel is composed of several terms that are responsible for explaining
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different properties of the signal:
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- a long term, smooth rising trend is to be explained by an RBF kernel. The
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RBF kernel with a large length-scale enforces this component to be smooth;
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it is not enforced that the trend is rising which leaves this choice to the
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GP. The specific length-scale and the amplitude are free hyperparameters.
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- a seasonal component, which is to be explained by the periodic
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ExpSineSquared kernel with a fixed periodicity of 1 year. The length-scale
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of this periodic component, controlling its smoothness, is a free parameter.
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In order to allow decaying away from exact periodicity, the product with an
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RBF kernel is taken. The length-scale of this RBF component controls the
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decay time and is a further free parameter.
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- smaller, medium term irregularities are to be explained by a
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RationalQuadratic kernel component, whose length-scale and alpha parameter,
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which determines the diffuseness of the length-scales, are to be determined.
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According to [RW2006], these irregularities can better be explained by
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a RationalQuadratic than an RBF kernel component, probably because it can
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accommodate several length-scales.
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- a "noise" term, consisting of an RBF kernel contribution, which shall
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explain the correlated noise components such as local weather phenomena,
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and a WhiteKernel contribution for the white noise. The relative amplitudes
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and the RBF's length scale are further free parameters.
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- a long term, smooth rising trend is to be explained by an RBF kernel. The
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RBF kernel with a large length-scale enforces this component to be smooth;
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it is not enforced that the trend is rising which leaves this choice to the
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GP. The specific length-scale and the amplitude are free hyperparameters.
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- a seasonal component, which is to be explained by the periodic
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ExpSineSquared kernel with a fixed periodicity of 1 year. The length-scale
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of this periodic component, controlling its smoothness, is a free parameter.
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In order to allow decaying away from exact periodicity, the product with an
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RBF kernel is taken. The length-scale of this RBF component controls the
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decay time and is a further free parameter.
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- smaller, medium term irregularities are to be explained by a
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RationalQuadratic kernel component, whose length-scale and alpha parameter,
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which determines the diffuseness of the length-scales, are to be determined.
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According to [RW2006], these irregularities can better be explained by
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a RationalQuadratic than an RBF kernel component, probably because it can
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accommodate several length-scales.
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- a "noise" term, consisting of an RBF kernel contribution, which shall
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explain the correlated noise components such as local weather phenomena,
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and a WhiteKernel contribution for the white noise. The relative amplitudes
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and the RBF's length scale are further free parameters.
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Maximizing the log-marginal-likelihood after subtracting the target's mean
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yields the following kernel with an LML of -83.214:
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yields the following kernel with an LML of -83.214::
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34.4**2 * RBF(length_scale=41.8)
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+ 3.27**2 * RBF(length_scale=180) * ExpSineSquared(length_scale=1.44,
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periodicity=1)
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+ 0.446**2 * RationalQuadratic(alpha=17.7, length_scale=0.957)
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+ 0.197**2 * RBF(length_scale=0.138) + WhiteKernel(noise_level=0.0336)
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Thus, most of the target signal (34.4ppm) is explained by a long-term rising
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trend (length-scale 41.8 years). The periodic component has an amplitude of
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3.27ppm, a decay time of 180 years and a length-scale of 1.44. The long decay

dev/_sources/auto_examples/applications/face_recognition.txt

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@@ -16,8 +16,9 @@ The dataset used in this example is a preprocessed excerpt of the
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Expected results for the top 5 most represented people in the dataset::
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================== ============ ======= ========== =======
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precision recall f1-score support
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================== ============ ======= ========== =======
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Ariel Sharon 0.67 0.92 0.77 13
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Colin Powell 0.75 0.78 0.76 60
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Donald Rumsfeld 0.78 0.67 0.72 27
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Tony Blair 0.81 0.69 0.75 36
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avg / total 0.80 0.80 0.80 322
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================== ============ ======= ========== =======
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**Python source code:** :download:`face_recognition.py <face_recognition.py>`
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.. literalinclude:: face_recognition.py
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:lines: 28-
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:lines: 30-
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dev/_sources/auto_examples/gaussian_process/plot_gpr_co2.txt

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@@ -17,34 +17,40 @@ model the CO2 concentration as a function of the time t.
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The kernel is composed of several terms that are responsible for explaining
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different properties of the signal:
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- a long term, smooth rising trend is to be explained by an RBF kernel. The
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RBF kernel with a large length-scale enforces this component to be smooth;
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it is not enforced that the trend is rising which leaves this choice to the
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GP. The specific length-scale and the amplitude are free hyperparameters.
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- a seasonal component, which is to be explained by the periodic
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ExpSineSquared kernel with a fixed periodicity of 1 year. The length-scale
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of this periodic component, controlling its smoothness, is a free parameter.
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In order to allow decaying away from exact periodicity, the product with an
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RBF kernel is taken. The length-scale of this RBF component controls the
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decay time and is a further free parameter.
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- smaller, medium term irregularities are to be explained by a
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RationalQuadratic kernel component, whose length-scale and alpha parameter,
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which determines the diffuseness of the length-scales, are to be determined.
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According to [RW2006], these irregularities can better be explained by
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a RationalQuadratic than an RBF kernel component, probably because it can
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accommodate several length-scales.
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- a "noise" term, consisting of an RBF kernel contribution, which shall
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explain the correlated noise components such as local weather phenomena,
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and a WhiteKernel contribution for the white noise. The relative amplitudes
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and the RBF's length scale are further free parameters.
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- a long term, smooth rising trend is to be explained by an RBF kernel. The
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RBF kernel with a large length-scale enforces this component to be smooth;
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it is not enforced that the trend is rising which leaves this choice to the
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GP. The specific length-scale and the amplitude are free hyperparameters.
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- a seasonal component, which is to be explained by the periodic
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ExpSineSquared kernel with a fixed periodicity of 1 year. The length-scale
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of this periodic component, controlling its smoothness, is a free parameter.
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In order to allow decaying away from exact periodicity, the product with an
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RBF kernel is taken. The length-scale of this RBF component controls the
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decay time and is a further free parameter.
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- smaller, medium term irregularities are to be explained by a
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RationalQuadratic kernel component, whose length-scale and alpha parameter,
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which determines the diffuseness of the length-scales, are to be determined.
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According to [RW2006], these irregularities can better be explained by
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a RationalQuadratic than an RBF kernel component, probably because it can
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accommodate several length-scales.
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- a "noise" term, consisting of an RBF kernel contribution, which shall
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explain the correlated noise components such as local weather phenomena,
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and a WhiteKernel contribution for the white noise. The relative amplitudes
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and the RBF's length scale are further free parameters.
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Maximizing the log-marginal-likelihood after subtracting the target's mean
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yields the following kernel with an LML of -83.214:
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yields the following kernel with an LML of -83.214::
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34.4**2 * RBF(length_scale=41.8)
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+ 3.27**2 * RBF(length_scale=180) * ExpSineSquared(length_scale=1.44,
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periodicity=1)
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+ 0.446**2 * RationalQuadratic(alpha=17.7, length_scale=0.957)
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+ 0.197**2 * RBF(length_scale=0.138) + WhiteKernel(noise_level=0.0336)
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Thus, most of the target signal (34.4ppm) is explained by a long-term rising
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trend (length-scale 41.8 years). The periodic component has an amplitude of
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3.27ppm, a decay time of 180 years and a length-scale of 1.44. The long decay
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**Python source code:** :download:`plot_gpr_co2.py <plot_gpr_co2.py>`
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.. literalinclude:: plot_gpr_co2.py
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:lines: 54-
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:lines: 60-
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**Total running time of the example:** 31.99 seconds
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( 0 minutes 31.99 seconds)
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**Total running time of the example:** 33.09 seconds
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( 0 minutes 33.09 seconds)
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dev/_sources/datasets/index.txt

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.. include:: rcv1.rst
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.. _boston_house_prices
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.. _boston_house_prices:
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.. include:: ../../sklearn/datasets/descr/boston_house_prices.rst
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.. _breast_cancer
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.. _breast_cancer:
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.. include:: ../../sklearn/datasets/descr/breast_cancer.rst
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.. _diabetes
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.. _diabetes:
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.. include:: ../../sklearn/datasets/descr/diabetes.rst
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.. _digits
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.. _digits:
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.. include:: ../../sklearn/datasets/descr/digits.rst
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.. _iris
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.. _iris:
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.. include:: ../../sklearn/datasets/descr/iris.rst
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.. _linnerud
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.. _linnerud:
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.. include:: ../../sklearn/datasets/descr/linnerud.rst

dev/_sources/datasets/rcv1.txt

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>>> rcv1.target_names[:3].tolist() # doctest: +SKIP
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['E11', 'ECAT', 'M11']
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The dataset will be downloaded from the `dataset's homepage`_ if necessary.
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The dataset will be downloaded from the `rcv1 homepage`_ if necessary.
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The compressed size is about 656 MB.
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.. _dataset's homepage: http://jmlr.csail.mit.edu/papers/volume5/lewis04a/
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.. _rcv1 homepage: http://jmlr.csail.mit.edu/papers/volume5/lewis04a/
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.. topic:: References

dev/_sources/modules/decomposition.txt

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2. For each document :math:`d`, draw :math:`\theta_d \sim Dirichlet(\alpha), \: d=1...D`
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3. For each word :math:`i` in document :math:`d`:
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a. Draw a topic index :math:`z_{di} \sim Multinomial(\theta_d)`
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b. Draw the observed word :math:`w_{ij} \sim Multinomial(beta_{z_{di}}.)`
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dev/_sources/modules/feature_selection.txt

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most important features from the Boston dataset without knowing the
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threshold beforehand.
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.. _l1_feature_selection:
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L1-based feature selection
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--------------------------
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dev/_sources/modules/gaussian_process.txt

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The implementation is based on Algorithm 2.1 of [RW2006]_. In addition to
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the API of standard sklearn estimators, GaussianProcessRegressor:
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* allows prediction without prior fitting (based on the GP prior)
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* provides an additional method ``sample_y(X)``, which evaluates samples
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drawn from the GPR (prior or posterior) at given inputs
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* exposes a method ``log_marginal_likelihood(theta)``, which can be used
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externally for other ways of selecting hyperparameters, e.g., via
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Markov chain Monte Carlo.
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* allows prediction without prior fitting (based on the GP prior)
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* provides an additional method ``sample_y(X)``, which evaluates samples
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drawn from the GPR (prior or posterior) at given inputs
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* exposes a method ``log_marginal_likelihood(theta)``, which can be used
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externally for other ways of selecting hyperparameters, e.g., via
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Markov chain Monte Carlo.
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GPR examples
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The kernel is composed of several terms that are responsible for explaining
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different properties of the signal:
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- a long term, smooth rising trend is to be explained by an RBF kernel. The
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RBF kernel with a large length-scale enforces this component to be smooth;
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it is not enforced that the trend is rising which leaves this choice to the
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GP. The specific length-scale and the amplitude are free hyperparameters.
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- a seasonal component, which is to be explained by the periodic
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ExpSineSquared kernel with a fixed periodicity of 1 year. The length-scale
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of this periodic component, controlling its smoothness, is a free parameter.
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In order to allow decaying away from exact periodicity, the product with an
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RBF kernel is taken. The length-scale of this RBF component controls the
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decay time and is a further free parameter.
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- smaller, medium term irregularities are to be explained by a
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RationalQuadratic kernel component, whose length-scale and alpha parameter,
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which determines the diffuseness of the length-scales, are to be determined.
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According to [RW2006]_, these irregularities can better be explained by
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a RationalQuadratic than an RBF kernel component, probably because it can
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accommodate several length-scales.
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- a "noise" term, consisting of an RBF kernel contribution, which shall
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explain the correlated noise components such as local weather phenomena,
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and a WhiteKernel contribution for the white noise. The relative amplitudes
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and the RBF's length scale are further free parameters.
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- a long term, smooth rising trend is to be explained by an RBF kernel. The
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RBF kernel with a large length-scale enforces this component to be smooth;
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it is not enforced that the trend is rising which leaves this choice to the
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GP. The specific length-scale and the amplitude are free hyperparameters.
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- a seasonal component, which is to be explained by the periodic
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ExpSineSquared kernel with a fixed periodicity of 1 year. The length-scale
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of this periodic component, controlling its smoothness, is a free parameter.
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In order to allow decaying away from exact periodicity, the product with an
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RBF kernel is taken. The length-scale of this RBF component controls the
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decay time and is a further free parameter.
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- smaller, medium term irregularities are to be explained by a
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RationalQuadratic kernel component, whose length-scale and alpha parameter,
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which determines the diffuseness of the length-scales, are to be determined.
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According to [RW2006]_, these irregularities can better be explained by
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a RationalQuadratic than an RBF kernel component, probably because it can
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accommodate several length-scales.
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197+
- a "noise" term, consisting of an RBF kernel contribution, which shall
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explain the correlated noise components such as local weather phenomena,
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and a WhiteKernel contribution for the white noise. The relative amplitudes
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and the RBF's length scale are further free parameters.
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Maximizing the log-marginal-likelihood after subtracting the target's mean
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yields the following kernel with an LML of -83.214:

dev/_sources/modules/multiclass.txt

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@@ -214,7 +214,7 @@ code book. The code size is the dimensionality of the aforementioned space.
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Intuitively, each class should be represented by a code as unique as
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possible and a good code book should be designed to optimize classification
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accuracy. In this implementation, we simply use a randomly-generated code
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book as advocated in [2]_ although more elaborate methods may be added in the
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book as advocated in [3]_ although more elaborate methods may be added in the
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future.
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At fitting time, one binary classifier per bit in the code book is fitted.
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.. topic:: References:
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.. [1] "Solving multiclass learning problems via error-correcting output codes",
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.. [2] "Solving multiclass learning problems via error-correcting output codes",
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Dietterich T., Bakiri G.,
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Journal of Artificial Intelligence Research 2,
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1995.
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.. [2] "The error coding method and PICTs",
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.. [3] "The error coding method and PICTs",
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James G., Hastie T.,
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Journal of Computational and Graphical statistics 7,
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1998.
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.. [3] "The Elements of Statistical Learning",
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.. [4] "The Elements of Statistical Learning",
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Hastie T., Tibshirani R., Friedman J., page 606 (second-edition)
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2008.

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