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.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/gaussian_process/plot_gpr_on_structured_data.py"
.. LINE NUMBERS ARE GIVEN BELOW.
.. only:: html
.. note::
:class: sphx-glr-download-link-note
:ref:`Go to the end <sphx_glr_download_auto_examples_gaussian_process_plot_gpr_on_structured_data.py>`
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.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_gaussian_process_plot_gpr_on_structured_data.py:
==========================================================================
Gaussian processes on discrete data structures
==========================================================================
This example illustrates the use of Gaussian processes for regression and
classification tasks on data that are not in fixed-length feature vector form.
This is achieved through the use of kernel functions that operates directly
on discrete structures such as variable-length sequences, trees, and graphs.
Specifically, here the input variables are some gene sequences stored as
variable-length strings consisting of letters 'A', 'T', 'C', and 'G',
while the output variables are floating point numbers and True/False labels
in the regression and classification tasks, respectively.
A kernel between the gene sequences is defined using R-convolution [1]_ by
integrating a binary letter-wise kernel over all pairs of letters among a pair
of strings.
This example will generate three figures.
In the first figure, we visualize the value of the kernel, i.e. the similarity
of the sequences, using a colormap. Brighter color here indicates higher
similarity.
In the second figure, we show some regression result on a dataset of 6
sequences. Here we use the 1st, 2nd, 4th, and 5th sequences as the training set
to make predictions on the 3rd and 6th sequences.
In the third figure, we demonstrate a classification model by training on 6
sequences and make predictions on another 5 sequences. The ground truth here is
simply whether there is at least one 'A' in the sequence. Here the model makes
four correct classifications and fails on one.
.. [1] Haussler, D. (1999). Convolution kernels on discrete structures
(Vol. 646). Technical report, Department of Computer Science, University
of California at Santa Cruz.
.. GENERATED FROM PYTHON SOURCE LINES 42-104
.. code-block:: default
import numpy as np
from sklearn.base import clone
from sklearn.gaussian_process import GaussianProcessClassifier, GaussianProcessRegressor
from sklearn.gaussian_process.kernels import GenericKernelMixin, Hyperparameter, Kernel
class SequenceKernel(GenericKernelMixin, Kernel):
"""
A minimal (but valid) convolutional kernel for sequences of variable
lengths."""
def __init__(self, baseline_similarity=0.5, baseline_similarity_bounds=(1e-5, 1)):
self.baseline_similarity = baseline_similarity
self.baseline_similarity_bounds = baseline_similarity_bounds
@property
def hyperparameter_baseline_similarity(self):
return Hyperparameter(
"baseline_similarity", "numeric", self.baseline_similarity_bounds
)
def _f(self, s1, s2):
"""
kernel value between a pair of sequences
"""
return sum(
[1.0 if c1 == c2 else self.baseline_similarity for c1 in s1 for c2 in s2]
)
def _g(self, s1, s2):
"""
kernel derivative between a pair of sequences
"""
return sum([0.0 if c1 == c2 else 1.0 for c1 in s1 for c2 in s2])
def __call__(self, X, Y=None, eval_gradient=False):
if Y is None:
Y = X
if eval_gradient:
return (
np.array([[self._f(x, y) for y in Y] for x in X]),
np.array([[[self._g(x, y)] for y in Y] for x in X]),
)
else:
return np.array([[self._f(x, y) for y in Y] for x in X])
def diag(self, X):
return np.array([self._f(x, x) for x in X])
def is_stationary(self):
return False
def clone_with_theta(self, theta):
cloned = clone(self)
cloned.theta = theta
return cloned
kernel = SequenceKernel()
.. GENERATED FROM PYTHON SOURCE LINES 105-107
Sequence similarity matrix under the kernel
===========================================
.. GENERATED FROM PYTHON SOURCE LINES 107-122
.. code-block:: default
import matplotlib.pyplot as plt
X = np.array(["AGCT", "AGC", "AACT", "TAA", "AAA", "GAACA"])
K = kernel(X)
D = kernel.diag(X)
plt.figure(figsize=(8, 5))
plt.imshow(np.diag(D**-0.5).dot(K).dot(np.diag(D**-0.5)))
plt.xticks(np.arange(len(X)), X)
plt.yticks(np.arange(len(X)), X)
plt.title("Sequence similarity under the kernel")
plt.show()
.. image-sg:: /auto_examples/gaussian_process/images/sphx_glr_plot_gpr_on_structured_data_001.png
:alt: Sequence similarity under the kernel
:srcset: /auto_examples/gaussian_process/images/sphx_glr_plot_gpr_on_structured_data_001.png
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 123-125
Regression
==========
.. GENERATED FROM PYTHON SOURCE LINES 125-141
.. code-block:: default
X = np.array(["AGCT", "AGC", "AACT", "TAA", "AAA", "GAACA"])
Y = np.array([1.0, 1.0, 2.0, 2.0, 3.0, 3.0])
training_idx = [0, 1, 3, 4]
gp = GaussianProcessRegressor(kernel=kernel)
gp.fit(X[training_idx], Y[training_idx])
plt.figure(figsize=(8, 5))
plt.bar(np.arange(len(X)), gp.predict(X), color="b", label="prediction")
plt.bar(training_idx, Y[training_idx], width=0.2, color="r", alpha=1, label="training")
plt.xticks(np.arange(len(X)), X)
plt.title("Regression on sequences")
plt.legend()
plt.show()
.. image-sg:: /auto_examples/gaussian_process/images/sphx_glr_plot_gpr_on_structured_data_002.png
:alt: Regression on sequences
:srcset: /auto_examples/gaussian_process/images/sphx_glr_plot_gpr_on_structured_data_002.png
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 142-144
Classification
==============
.. GENERATED FROM PYTHON SOURCE LINES 144-188
.. code-block:: default
X_train = np.array(["AGCT", "CGA", "TAAC", "TCG", "CTTT", "TGCT"])
# whether there are 'A's in the sequence
Y_train = np.array([True, True, True, False, False, False])
gp = GaussianProcessClassifier(kernel)
gp.fit(X_train, Y_train)
X_test = ["AAA", "ATAG", "CTC", "CT", "C"]
Y_test = [True, True, False, False, False]
plt.figure(figsize=(8, 5))
plt.scatter(
np.arange(len(X_train)),
[1.0 if c else -1.0 for c in Y_train],
s=100,
marker="o",
edgecolor="none",
facecolor=(1, 0.75, 0),
label="training",
)
plt.scatter(
len(X_train) + np.arange(len(X_test)),
[1.0 if c else -1.0 for c in Y_test],
s=100,
marker="o",
edgecolor="none",
facecolor="r",
label="truth",
)
plt.scatter(
len(X_train) + np.arange(len(X_test)),
[1.0 if c else -1.0 for c in gp.predict(X_test)],
s=100,
marker="x",
facecolor="b",
linewidth=2,
label="prediction",
)
plt.xticks(np.arange(len(X_train) + len(X_test)), np.concatenate((X_train, X_test)))
plt.yticks([-1, 1], [False, True])
plt.title("Classification on sequences")
plt.legend()
plt.show()
.. image-sg:: /auto_examples/gaussian_process/images/sphx_glr_plot_gpr_on_structured_data_003.png
:alt: Classification on sequences
:srcset: /auto_examples/gaussian_process/images/sphx_glr_plot_gpr_on_structured_data_003.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
.. code-block:: none
/home/circleci/project/sklearn/gaussian_process/kernels.py:419: ConvergenceWarning:
The optimal value found for dimension 0 of parameter baseline_similarity is close to the specified lower bound 1e-05. Decreasing the bound and calling fit again may find a better value.
.. rst-class:: sphx-glr-timing
**Total running time of the script:** (0 minutes 0.336 seconds)
.. _sphx_glr_download_auto_examples_gaussian_process_plot_gpr_on_structured_data.py:
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