This notebook was put together by [Jake Vanderplas](http://www.vanderplas.com) for PyData Seattle 2015. Source and license info is on [GitHub](https://github.com/jakevdp/sklearn_pydata2015/).
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.
%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()
Every algorithm is exposed in scikit-learn via an ''Estimator'' object. For instance a linear regression is implemented as so:
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:
model = LinearRegression(normalize=True) print(model.normalize)
LinearRegression(copy_X=True, fit_intercept=True, normalize=True)
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:
x = np.arange(10) y = 2 * x + 1
[0 1 2 3 4 5 6 7 8 9] [ 1 3 5 7 9 11 13 15 17 19]
plt.plot(x, y, 'o');
# The input data for sklearn is 2D: (samples == 3 x features == 1) X = x[:, np.newaxis] print(X) print(y)
[         ] [ 1 3 5 7 9 11 13 15 17 19]
# fit the model on our data model.fit(X, y)
LinearRegression(copy_X=True, fit_intercept=True, normalize=True)
# underscore at the end indicates a fit parameter print(model.coef_) print(model.intercept_)
[ 2.] 1.0
# residual error around fit model.residues_
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.
K nearest neighbors (kNN) is one of the simplest learning strategies: given a new, unknown observation, look up in your reference database which ones have the closest features and assign the predominant class.
Let's try it out on our iris classification problem:
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:
knn.predict_proba([[3, 5, 4, 2],])
array([[ 0. , 0.8, 0.2]])
from fig_code import plot_iris_knn plot_iris_knn()
Use a different estimator on the same problem:
Note that you don't have to know what it is do use it. We're simply trying out the interface here
If you finish early, try to create a similar plot as above with the SVC estimator.
from sklearn.svm import SVC
One of the simplest regression problems is fitting a line to data, which we saw above. Scikit-learn also contains more sophisticated regression algorithms
# 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:
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:
# 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.
RandomForestRegressor object using IPython's help features (i.e. put a question mark after the object).
What arguments are available to
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:
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)))
Reduced dataset shape: (150, 2) Meaning of the 2 components: 0.362 x sepal length (cm) + -0.082 x sepal width (cm) + 0.857 x petal length (cm) + 0.359 x petal width (cm) -0.657 x sepal length (cm) + -0.730 x sepal width (cm) + 0.176 x petal length (cm) + 0.075 x petal width (cm)
Clustering groups together observations that are homogeneous with respect to a given criterion, finding ''clusters'' in the data.
Note that these clusters will uncover relevent hidden structure of the data only if the criterion used highlights it.
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
model, the following methods are available:
model.fit(): fit training data. For supervised learning applications, this accepts two arguments: the data
Xand the labels
model.fit(X, y)). For unsupervised learning applications, this accepts only a single argument, the data
model.predict(): given a trained model, predict the label of a new set of data. This method accepts one argument, the new data
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.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:
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:
from sklearn.metrics import confusion_matrix print(confusion_matrix(y, y_pred))
[[50 0 0] [ 0 50 0] [ 0 0 50]]
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:
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))
[[12 0 0] [ 0 6 0] [ 0 2 18]]
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.
from IPython.display import Image Image("http://scikit-learn.org/dev/_static/ml_map.png")