This notebook was put together by [Jake Vanderplas](http://www.vanderplas.com) for PyCon 2015. Source and license info is on [GitHub](https://github.com/jakevdp/sklearn_pycon2015/).
Here we'll dive into the basic principles of machine learning, and how to utilize them via the Scikit-Learn API.
After briefly introducing scikit-learn's Estimator object, we'll cover supervised learning, including classification and regression problems, and unsupervised learning, including dimensinoality reduction and clustering problems.
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%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
# use seaborn for plot defaults
# this can be safely commented out
import seaborn; seaborn.set()
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from sklearn.linear_model import LinearRegression
Estimator parameters: All the parameters of an estimator can be set when it is instantiated, and have suitable default values:
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model = LinearRegression(normalize=True)
print(model.normalize)
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print(model)
Estimated Model parameters: When data is fit with an estimator, parameters are estimated from the data at hand. All the estimated parameters are attributes of the estimator object ending by an underscore:
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x = np.arange(10)
y = 2 * x + 1
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print(x)
print(y)
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plt.plot(x, y, 'o');
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# The input data for sklearn is 2D: (samples == 3 x features == 1)
X = x[:, np.newaxis]
print(X)
print(y)
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# fit the model on our data
model.fit(X, y)
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# underscore at the end indicates a fit parameter
print(model.coef_)
print(model.intercept_)
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# residual error around fit
model.residues_
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The model found a line with a slope 2 and intercept 1, as we'd expect.
In Supervised Learning, we have a dataset consisting of both features and labels. The task is to construct an estimator which is able to predict the label of an object given the set of features. A relatively simple example is predicting the species of iris given a set of measurements of its flower. This is a relatively simple task. Some more complicated examples are:
What these tasks have in common is that there is one or more unknown quantities associated with the object which needs to be determined from other observed quantities.
Supervised learning is further broken down into two categories, classification and regression. In classification, the label is discrete, while in regression, the label is continuous. For example, in astronomy, the task of determining whether an object is a star, a galaxy, or a quasar is a classification problem: the label is from three distinct categories. On the other hand, we might wish to estimate the age of an object based on such observations: this would be a regression problem, because the label (age) is a continuous quantity.
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from sklearn import neighbors, datasets
iris = datasets.load_iris()
X, y = iris.data, iris.target
# create the model
knn = neighbors.KNeighborsClassifier(n_neighbors=5)
# fit the model
knn.fit(X, y)
# What kind of iris has 3cm x 5cm sepal and 4cm x 2cm petal?
# call the "predict" method:
result = knn.predict([[3, 5, 4, 2],])
print(iris.target_names[result])
You can also do probabilistic predictions:
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knn.predict_proba([[3, 5, 4, 2],])
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from fig_code import plot_iris_knn
plot_iris_knn()
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from sklearn.svm import SVC
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# Create some simple data
import numpy as np
np.random.seed(0)
X = np.random.random(size=(20, 1))
y = 3 * X.squeeze() + 2 + np.random.randn(20)
plt.plot(X.squeeze(), y, 'o');
As above, we can plot a line of best fit:
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model = LinearRegression()
model.fit(X, y)
# Plot the data and the model prediction
X_fit = np.linspace(0, 1, 100)[:, np.newaxis]
y_fit = model.predict(X_fit)
plt.plot(X.squeeze(), y, 'o')
plt.plot(X_fit.squeeze(), y_fit);
Scikit-learn also has some more sophisticated models, which can respond to finer features in the data:
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# Fit a Random Forest
from sklearn.ensemble import RandomForestRegressor
model = RandomForestRegressor()
model.fit(X, y)
# Plot the data and the model prediction
X_fit = np.linspace(0, 1, 100)[:, np.newaxis]
y_fit = model.predict(X_fit)
plt.plot(X.squeeze(), y, 'o')
plt.plot(X_fit.squeeze(), y_fit);
Whether either of these is a "good" fit or not depends on a number of things; we'll discuss details of how to choose a model later in the tutorial.
Explore the RandomForestRegressor object using IPython's help features (i.e. put a question mark after the object).
What arguments are available to RandomForestRegressor?
How does the above plot change if you change these arguments?
These class-level arguments are known as hyperparameters, and we will discuss later how you to select hyperparameters in the model validation section.
Unsupervised Learning addresses a different sort of problem. Here the data has no labels, and we are interested in finding similarities between the objects in question. In a sense, you can think of unsupervised learning as a means of discovering labels from the data itself. Unsupervised learning comprises tasks such as dimensionality reduction, clustering, and density estimation. For example, in the iris data discussed above, we can used unsupervised methods to determine combinations of the measurements which best display the structure of the data. As we'll see below, such a projection of the data can be used to visualize the four-dimensional dataset in two dimensions. Some more involved unsupervised learning problems are:
Sometimes the two may even be combined: e.g. Unsupervised learning can be used to find useful features in heterogeneous data, and then these features can be used within a supervised framework.
Principle Component Analysis (PCA) is a dimension reduction technique that can find the combinations of variables that explain the most variance.
Consider the iris dataset. It cannot be visualized in a single 2D plot, as it has 4 features. We are going to extract 2 combinations of sepal and petal dimensions to visualize it:
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X, y = iris.data, iris.target
from sklearn.decomposition import PCA
pca = PCA(n_components=2)
pca.fit(X)
X_reduced = pca.transform(X)
print("Reduced dataset shape:", X_reduced.shape)
import pylab as pl
pl.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y,
cmap='RdYlBu')
print("Meaning of the 2 components:")
for component in pca.components_:
print(" + ".join("%.3f x %s" % (value, name)
for value, name in zip(component,
iris.feature_names)))
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from sklearn.cluster import KMeans
k_means = KMeans(n_clusters=3, random_state=0) # Fixing the RNG in kmeans
k_means.fit(X)
y_pred = k_means.predict(X)
pl.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y_pred,
cmap='RdYlBu');
Scikit-learn strives to have a uniform interface across all methods,
and we'll see examples of these below. Given a scikit-learn estimator
object named model, the following methods are available:
model.fit() : fit training data. For supervised learning applications,
this accepts two arguments: the data X and the labels y (e.g. model.fit(X, y)).
For unsupervised learning applications, this accepts only a single argument,
the data X (e.g. model.fit(X)).model.predict() : given a trained model, predict the label of a new set of data.
This method accepts one argument, the new data X_new (e.g. model.predict(X_new)),
and returns the learned label for each object in the array.model.predict_proba() : For classification problems, some estimators also provide
this method, which returns the probability that a new observation has each categorical label.
In this case, the label with the highest probability is returned by model.predict().model.score() : for classification or regression problems, most (all?) estimators implement
a score method. Scores are between 0 and 1, with a larger score indicating a better fit.model.predict() : predict labels in clustering algorithms.model.transform() : given an unsupervised model, transform new data into the new basis.
This also accepts one argument X_new, and returns the new representation of the data based
on the unsupervised model.model.fit_transform() : some estimators implement this method,
which more efficiently performs a fit and a transform on the same input data.An important piece of machine learning is model validation: that is, determining how well your model will generalize from the training data to future unlabeled data. Let's look at an example using the nearest neighbor classifier. This is a very simple classifier: it simply stores all training data, and for any unknown quantity, simply returns the label of the closest training point.
With the iris data, it very easily returns the correct prediction for each of the input points:
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from sklearn.neighbors import KNeighborsClassifier
X, y = iris.data, iris.target
clf = KNeighborsClassifier(n_neighbors=1)
clf.fit(X, y)
y_pred = clf.predict(X)
print(np.all(y == y_pred))
A more useful way to look at the results is to view the confusion matrix, or the matrix showing the frequency of inputs and outputs:
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from sklearn.metrics import confusion_matrix
print(confusion_matrix(y, y_pred))
For each class, all 50 training samples are correctly identified. But this does not mean that our model is perfect! In particular, such a model generalizes extremely poorly to new data. We can simulate this by splitting our data into a training set and a testing set. Scikit-learn contains some convenient routines to do this:
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from sklearn.cross_validation import train_test_split
Xtrain, Xtest, ytrain, ytest = train_test_split(X, y)
clf.fit(Xtrain, ytrain)
ypred = clf.predict(Xtest)
print(confusion_matrix(ytest, ypred))
This paints a better picture of the true performance of our classifier: apparently there is some confusion between the second and third species, which we might anticipate given what we've seen of the data above.
This is why it's extremely important to use a train/test split when evaluating your models. We'll go into more depth on model evaluation later in this tutorial.
This is a flow chart created by scikit-learn super-contributor Andreas Mueller which gives a nice summary of which algorithms to choose in various situations. Keep it around as a handy reference!
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from IPython.display import Image
Image("http://scikit-learn.org/dev/_static/ml_map.png")
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Original source on the scikit-learn website
To demonstrate the above principles on a more interesting problem, let's consider OCR (Optical Character Recognition) – that is, recognizing hand-written digits. In the wild, this problem involves both locating and identifying characters in an image. Here we'll take a shortcut and use scikit-learn's set of pre-formatted digits, which is built-in to the library.
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from sklearn import datasets
digits = datasets.load_digits()
digits.images.shape
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Let's plot a few of these:
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fig, axes = plt.subplots(10, 10, figsize=(8, 8))
fig.subplots_adjust(hspace=0.1, wspace=0.1)
for i, ax in enumerate(axes.flat):
ax.imshow(digits.images[i], cmap='binary')
ax.text(0.05, 0.05, str(digits.target[i]),
transform=ax.transAxes, color='green')
ax.set_xticks([])
ax.set_yticks([])
Here the data is simply each pixel value within an 8x8 grid:
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# The images themselves
print(digits.images.shape)
print(digits.images[0])
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# The data for use in our algorithms
print(digits.data.shape)
print(digits.data[0])
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# The target label
print(digits.target)
So our data have 1797 samples in 64 dimensions.
We'd like to visualize our points within the 64-dimensional parameter space, but it's difficult to plot points in 64 dimensions! Instead we'll reduce the dimensions to 2, using an unsupervised method. Here, we'll make use of a manifold learning algorithm called Isomap, and transform the data to two dimensions.
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from sklearn.manifold import Isomap
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iso = Isomap(n_components=2)
data_projected = iso.fit_transform(digits.data)
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data_projected.shape
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plt.scatter(data_projected[:, 0], data_projected[:, 1], c=digits.target,
edgecolor='none', alpha=0.5, cmap=plt.cm.get_cmap('nipy_spectral', 10));
plt.colorbar(label='digit label', ticks=range(10))
plt.clim(-0.5, 9.5)
We see here that the digits are fairly well-separated in the parameter space; this tells us that a supervised classification algorithm should perform fairly well. Let's give it a try.
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from sklearn.cross_validation import train_test_split
Xtrain, Xtest, ytrain, ytest = train_test_split(digits.data, digits.target,
random_state=2)
print(Xtrain.shape, Xtest.shape)
Let's use a simple logistic regression which (despite its confusing name) is a classification algorithm:
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from sklearn.linear_model import LogisticRegression
clf = LogisticRegression(penalty='l2')
clf.fit(Xtrain, ytrain)
ypred = clf.predict(Xtest)
We can check our classification accuracy by comparing the true values of the test set to the predictions:
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from sklearn.metrics import accuracy_score
accuracy_score(ytest, ypred)
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This single number doesn't tell us where we've gone wrong: one nice way to do this is to use the confusion matrix
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from sklearn.metrics import confusion_matrix
print(confusion_matrix(ytest, ypred))
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plt.imshow(np.log(confusion_matrix(ytest, ypred)),
cmap='Blues', interpolation='nearest')
plt.grid(False)
plt.ylabel('true')
plt.xlabel('predicted');
We might also take a look at some of the outputs along with their predicted labels. We'll make the bad labels red:
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fig, axes = plt.subplots(10, 10, figsize=(8, 8))
fig.subplots_adjust(hspace=0.1, wspace=0.1)
for i, ax in enumerate(axes.flat):
ax.imshow(Xtest[i].reshape(8, 8), cmap='binary')
ax.text(0.05, 0.05, str(ypred[i]),
transform=ax.transAxes,
color='green' if (ytest[i] == ypred[i]) else 'red')
ax.set_xticks([])
ax.set_yticks([])
The interesting thing is that even with this simple logistic regression algorithm, many of the mislabeled cases are ones that we ourselves might get wrong!
There are many ways to improve this classifier, but we're out of time here. To go further, we could use a more sophisticated model, use cross validation, or apply other techniques. We'll cover some of these topics later in the tutorial.