.. DO NOT EDIT. .. 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 ` to download the full example code or to run this example in your browser via JupyterLite or Binder .. 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:: Python 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:: Python 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:: Python 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:: Python 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:445: 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 0.232 seconds) .. _sphx_glr_download_auto_examples_gaussian_process_plot_gpr_on_structured_data.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/gaussian_process/plot_gpr_on_structured_data.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/?path=auto_examples/gaussian_process/plot_gpr_on_structured_data.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_gpr_on_structured_data.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_gpr_on_structured_data.py ` .. include:: plot_gpr_on_structured_data.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_