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3404be75 · Florent Chatelain · ff39108a · 3404be75 · 3404be75 · 3404be75
Commit 3404be75 authored Sep 12, 2021 by Florent Chatelain
--- a/notebooks/1_introduction/N1_Linear_Classification.ipynb
+++ b/notebooks/1_introduction/N1_Linear_Classification.ipynb
@@ -163,14 +163,10 @@
   "metadata": {},
   "outputs": [
    {
-     "ename": "AttributeError",
-     "evalue": "'RidgeClassifier' object has no attribute 'scoef_'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-6-23b595ae4fed>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# What are the parameter values of the linear boundary equation x_2=a x_1 + b?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscoef_\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoef_\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintercept_\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoef_\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'boudary equation x_2={} x_1 + {}'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mAttributeError\u001b[0m: 'RidgeClassifier' object has no attribute 'scoef_'"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "boudary equation x_2=-0.5596406428840415 x_1 + 0.6410047882764905\n"
     ]
    }
   ],
@@ -191,9 +187,158 @@
  },
  {
   "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
   "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\u001b[0;31mInit signature:\u001b[0m\n",
+       "\u001b[0mlinear_model\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mRidgeClassifier\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0;34m*\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0mfit_intercept\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0mnormalize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0mcopy_X\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0mmax_iter\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0mtol\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.001\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0mclass_weight\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0msolver\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'auto'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m    \u001b[0mrandom_state\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
+       "\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+       "\u001b[0;31mDocstring:\u001b[0m     \n",
+       "Classifier using Ridge regression.\n",
+       "\n",
+       "This classifier first converts the target values into ``{-1, 1}`` and\n",
+       "then treats the problem as a regression task (multi-output regression in\n",
+       "the multiclass case).\n",
+       "\n",
+       "Read more in the :ref:`User Guide <ridge_regression>`.\n",
+       "\n",
+       "Parameters\n",
+       "----------\n",
+       "alpha : float, default=1.0\n",
+       "    Regularization strength; must be a positive float. Regularization\n",
+       "    improves the conditioning of the problem and reduces the variance of\n",
+       "    the estimates. Larger values specify stronger regularization.\n",
+       "    Alpha corresponds to ``1 / (2C)`` in other linear models such as\n",
+       "    :class:`~sklearn.linear_model.LogisticRegression` or\n",
+       "    :class:`sklearn.svm.LinearSVC`.\n",
+       "\n",
+       "fit_intercept : bool, default=True\n",
+       "    Whether to calculate the intercept for this model. If set to false, no\n",
+       "    intercept will be used in calculations (e.g. data is expected to be\n",
+       "    already centered).\n",
+       "\n",
+       "normalize : bool, default=False\n",
+       "    This parameter is ignored when ``fit_intercept`` is set to False.\n",
+       "    If True, the regressors X will be normalized before regression by\n",
+       "    subtracting the mean and dividing by the l2-norm.\n",
+       "    If you wish to standardize, please use\n",
+       "    :class:`sklearn.preprocessing.StandardScaler` before calling ``fit``\n",
+       "    on an estimator with ``normalize=False``.\n",
+       "\n",
+       "copy_X : bool, default=True\n",
+       "    If True, X will be copied; else, it may be overwritten.\n",
+       "\n",
+       "max_iter : int, default=None\n",
+       "    Maximum number of iterations for conjugate gradient solver.\n",
+       "    The default value is determined by scipy.sparse.linalg.\n",
+       "\n",
+       "tol : float, default=1e-3\n",
+       "    Precision of the solution.\n",
+       "\n",
+       "class_weight : dict or 'balanced', default=None\n",
+       "    Weights associated with classes in the form ``{class_label: weight}``.\n",
+       "    If not given, all classes are supposed to have weight one.\n",
+       "\n",
+       "    The \"balanced\" mode uses the values of y to automatically adjust\n",
+       "    weights inversely proportional to class frequencies in the input data\n",
+       "    as ``n_samples / (n_classes * np.bincount(y))``.\n",
+       "\n",
+       "solver : {'auto', 'svd', 'cholesky', 'lsqr', 'sparse_cg', 'sag', 'saga'},         default='auto'\n",
+       "    Solver to use in the computational routines:\n",
+       "\n",
+       "    - 'auto' chooses the solver automatically based on the type of data.\n",
+       "\n",
+       "    - 'svd' uses a Singular Value Decomposition of X to compute the Ridge\n",
+       "      coefficients. More stable for singular matrices than 'cholesky'.\n",
+       "\n",
+       "    - 'cholesky' uses the standard scipy.linalg.solve function to\n",
+       "      obtain a closed-form solution.\n",
+       "\n",
+       "    - 'sparse_cg' uses the conjugate gradient solver as found in\n",
+       "      scipy.sparse.linalg.cg. As an iterative algorithm, this solver is\n",
+       "      more appropriate than 'cholesky' for large-scale data\n",
+       "      (possibility to set `tol` and `max_iter`).\n",
+       "\n",
+       "    - 'lsqr' uses the dedicated regularized least-squares routine\n",
+       "      scipy.sparse.linalg.lsqr. It is the fastest and uses an iterative\n",
+       "      procedure.\n",
+       "\n",
+       "    - 'sag' uses a Stochastic Average Gradient descent, and 'saga' uses\n",
+       "      its unbiased and more flexible version named SAGA. Both methods\n",
+       "      use an iterative procedure, and are often faster than other solvers\n",
+       "      when both n_samples and n_features are large. Note that 'sag' and\n",
+       "      'saga' fast convergence is only guaranteed on features with\n",
+       "      approximately the same scale. You can preprocess the data with a\n",
+       "      scaler from sklearn.preprocessing.\n",
+       "\n",
+       "      .. versionadded:: 0.17\n",
+       "         Stochastic Average Gradient descent solver.\n",
+       "      .. versionadded:: 0.19\n",
+       "       SAGA solver.\n",
+       "\n",
+       "random_state : int, RandomState instance, default=None\n",
+       "    Used when ``solver`` == 'sag' or 'saga' to shuffle the data.\n",
+       "    See :term:`Glossary <random_state>` for details.\n",
+       "\n",
+       "Attributes\n",
+       "----------\n",
+       "coef_ : ndarray of shape (1, n_features) or (n_classes, n_features)\n",
+       "    Coefficient of the features in the decision function.\n",
+       "\n",
+       "    ``coef_`` is of shape (1, n_features) when the given problem is binary.\n",
+       "\n",
+       "intercept_ : float or ndarray of shape (n_targets,)\n",
+       "    Independent term in decision function. Set to 0.0 if\n",
+       "    ``fit_intercept = False``.\n",
+       "\n",
+       "n_iter_ : None or ndarray of shape (n_targets,)\n",
+       "    Actual number of iterations for each target. Available only for\n",
+       "    sag and lsqr solvers. Other solvers will return None.\n",
+       "\n",
+       "classes_ : ndarray of shape (n_classes,)\n",
+       "    The classes labels.\n",
+       "\n",
+       "See Also\n",
+       "--------\n",
+       "Ridge : Ridge regression.\n",
+       "RidgeClassifierCV :  Ridge classifier with built-in cross validation.\n",
+       "\n",
+       "Notes\n",
+       "-----\n",
+       "For multi-class classification, n_class classifiers are trained in\n",
+       "a one-versus-all approach. Concretely, this is implemented by taking\n",
+       "advantage of the multi-variate response support in Ridge.\n",
+       "\n",
+       "Examples\n",
+       "--------\n",
+       ">>> from sklearn.datasets import load_breast_cancer\n",
+       ">>> from sklearn.linear_model import RidgeClassifier\n",
+       ">>> X, y = load_breast_cancer(return_X_y=True)\n",
+       ">>> clf = RidgeClassifier().fit(X, y)\n",
+       ">>> clf.score(X, y)\n",
+       "0.9595...\n",
+       "\u001b[0;31mFile:\u001b[0m           ~/miniconda3/envs/calc/lib/python3.7/site-packages/sklearn/linear_model/_ridge.py\n",
+       "\u001b[0;31mType:\u001b[0m           ABCMeta\n",
+       "\u001b[0;31mSubclasses:\u001b[0m     \n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
   "source": [
    "#get the documentation for sklearn RidgeClassification object\n",
    "linear_model.RidgeClassifier?"

 %% Cell type:markdown id: tags:

 This notebook can be run on mybinder: [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/git/https%3A%2F%2Fgricad-gitlab.univ-grenoble-alpes.fr%2Fchatelaf%2Fml-sicom3a/master?filepath=notebooks%2F/1_introduction/N1_Linear_Classification.ipynb)

 %% Cell type:code id: tags:

 ``` python
 # Import modules
 %matplotlib inline
 import matplotlib
 import numpy as np
 import scipy as sp
 import matplotlib.pyplot as plt
 ```

 %% Cell type:code id: tags:

 ``` python
 # Select random seed
 random_state = 0
 ```

 %% Cell type:markdown id: tags:

 We use scikit-learn to generate a toy 2D data set (two features $x_1$ and $x_2$)  for binary classification  (two classes)
 - each sample $(x_1,x_2)$ in the dataset is plotted as a 2D point where the two features $x_1$ and $x_2$ are displayed along the abscissa and ordinate axes respectively
 - the corresponding class label $y$ is displayed as a color mark (e.g., yellow or purple)

 %% Cell type:code id: tags:

 ``` python
 from sklearn.datasets import make_classification
 #X are the features (aka inputs, ...), y the labels (aka responses, targets, output...)
 X,y = make_classification(n_features=2, n_redundant=0, n_informative=2, n_samples=150,
                          random_state=random_state, n_clusters_per_class=1)
 # make the class labels y_i as +1 or -1
 y[y==0]=-1
 # display the dataset
 plt.figure(figsize=(8,6))
 plt.scatter(X[:,0], X[:,1], c=y)
 plt.grid(True)
 plt.xlabel('$x_1$')
 plt.ylabel('$x_2$')
 #plt.savefig("2d_binary_classif.pdf")
 ```

 %% Output

    Text(0, 0.5, '$x_2$')



 %% Cell type:markdown id: tags:

 Then, a linear model is used to learn the classification function/rule.

 %% Cell type:code id: tags:

 ``` python
 from sklearn import linear_model
 # Train a linear model, namely  RidgeClassifier,
 # this includes standard linear regression as particular case (alpha=0)
 model = linear_model.RidgeClassifier(alpha=0)
 model.fit(X,y)
 ```

 %% Output

    RidgeClassifier(alpha=0)

 %% Cell type:code id: tags:

 ``` python
 # Plot the decision functions
 XX, YY = np.meshgrid(np.linspace(X[:,0].min(), X[:,0].max(),200),
                     np.linspace(X[:,1].min(), X[:,1].max(),200))
 XY = np.vstack([XX.flatten(), YY.flatten()]).T
 yp = model.predict(XY)
 plt.figure(figsize=(8,6))
 plt.contour(XX,YY,yp.reshape(XX.shape),[0])
 plt.scatter(X[:,0], X[:,1], c=y)
 plt.grid("on")
 plt.xlabel('$x_1$')
 plt.ylabel('$x_2$')
 ```

 %% Output

    Text(0, 0.5, '$x_2$')



 %% Cell type:code id: tags:

 ``` python
 # What are the parameter values of the linear boundary equation x_2=a x_1 + b?
 a = -model.coef_[0][0]/model.coef_[0][1]
 b = -model.intercept_[0]/model.coef_[0][1]
 print('boudary equation x_2={} x_1 + {}'.format(a,b))
 ```

 %% Output

-    ---------------------------------------------------------------------------
-    AttributeError                            Traceback (most recent call last)
-    <ipython-input-6-23b595ae4fed> in <module>
-          1 # What are the parameter values of the linear boundary equation x_2=a x_1 + b?
-    ----> 2 a = -model.scoef_[0][0]/model.coef_[0][1]
-          3 b = -model.intercept_[0]/model.coef_[0][1]
-          4 print('boudary equation x_2={} x_1 + {}'.format(a,b))
-    AttributeError: 'RidgeClassifier' object has no attribute 'scoef_'
+    boudary equation x_2=-0.5596406428840415 x_1 + 0.6410047882764905

 %% Cell type:markdown id: tags:

 ### Exercise
 Change the number of informative features from  `n_informative=2̀` to `n_informative=1` in the `make_classification()` procedure, regenerate the data set and fit the classification rule. Interpret now the new decision boundary: are the two variables of equal importance in predicting the class of the data?

 %% Cell type:code id: tags:

 ``` python
 #get the documentation for sklearn RidgeClassification object
 linear_model.RidgeClassifier?
 ```

+%% Output
+
+
 %% Cell type:code id: tags:

 ``` python
 ```

--- a/notebooks/1_introduction/N2_Polynomial_Classification_Model_Complexity.ipynb
+++ b/notebooks/1_introduction/N2_Polynomial_Classification_Model_Complexity.ipynb
--- a/slides/1_introduction.pdf
+++ b/slides/1_introduction.pdf