Tuesday, April 22, 2014

Parameters selection with Cross-Validation

Most of the pattern recognition techniques have one or more free parameters and choose them for a given classification problem is often not a trivial task. In real applications we only have access to a finite set of examples, usually smaller than we wanted, and we need to test our model on samples not seen during the training process. A model that would just classify the samples that it has seen would have a very good score, but would definitely fail to predict unseen data. This situation is called overfitting and to avoid it we need to apply an appropriate validation procedure to select the parameters. A tool that can help us solve this problem is the Cross-Validation (CV). The idea behind CV is simple: the data are split into train and test sets several consecutive times and the averaged value of the prediction scores obtained with the different sets is the evaluation of the classifier.
Let's see a simple example where a smoothing parameter for a Bayesian classifier is select using the capabilities of the Sklearn library.
To begin we load one of the test datasets provided by sklearn (the same used here) and we hold 33% of the samples for the final evaluation:
from sklearn.datasets import load_digits
data = load_digits()
from sklearn.cross_validation import train_test_split
X,X_test,y,y_test = train_test_split(data.data,data.target,
                                     test_size=.33,
                                     random_state=1899)
Now, we import the classifier we want to use (a Bernoullian Naive Bayes in this case), specify a set of values for the parameter we want to choose and run a grid search:
from sklearn.naive_bayes import BernoulliNB
# test the model for alpha = 0.1, 0.2, ..., 1.0
parameters = [{'alpha':np.linspace(0.1,1,10)}]

from sklearn.grid_search import GridSearchCV
clf = GridSearchCV(BernoulliNB(), parameters, cv=10, scoring='f1')
clf.fit(X,y) # running the grid search
The grid search has evaluated the classifier for each value specified for the parameter alpha using the CV. We can visualize the results as follows:
res = zip(*[(f1m, f1s.std(), p['alpha']) 
            for p, f1m, f1s in clf.grid_scores_])
subplot(2,1,1)
plot(res[2],res[0],'-o')
subplot(2,1,2)
plot(res[2],res[1],'-o')
show()

The plots above show the average score (top) and the standard deviation of the score (bottom) for each values of alpha used. Looking at the graphs it seems plausible that a small alpha could be a good choice.
We can also see using the alpha value that gave us the best results during the grid search on the the test set we selected at the beginning gives us results that are similar to the ones obtained during the CV stage:
from sklearn.metrics import f1_score
print 'Best alpha in CV = %0.01f' % clf.best_params_['alpha']
final = f1_score(y_test,clf.best_estimator_.predict(X_test))
print 'F1-score on the final testset: %0.5f' % final
Best alpha in CV = 0.1
F1-score on the final testset: 0.85861

Wednesday, February 26, 2014

Terms selection with chi-square

In Natural Language Processing, the identification the most relevant terms in a collection of documents is a common task. It can produce meaningful insights about the data and it can also be useful to improve classification performances and computational efficiency. A popular measure of relevance for terms is the χ2 statistic. To compute it we can convert the terms of our document collection and turn them into features of a vectorial model, then χ2 can be computed as follow:


Where f is a feature (a term in this case), t is a target variable that we, usually, want to predict, A is the number of times that f and t cooccur, B is the number of times that f occurs without t, C is the number of times that t occurs without f, D is the number of times neither t or f occur and N is the number of observations.

Let's see how χ2 can be used through a simple example. We load some posts from 4 different newsgroups categories using the sklearn interface:
from sklearn.datasets import fetch_20newsgroups
 # newsgroups categories
categories = ['alt.atheism','talk.religion.misc',
              'comp.graphics','sci.space']

posts = fetch_20newsgroups(subset='train', categories=categories,
                           shuffle=True, random_state=42,
                           remove=('headers','footers','quotes'))
From the posts loaded, we build a linear model using all the terms in the document collection but the stop words:
from sklearn.feature_extraction.text import CountVectorizer
vectorizer = CountVectorizer(lowercase=True,stop_words='english')
X = vectorizer.fit_transform(posts.data)
Now, X is a document-term matrix where the element Xi,j is the frequency of the term j in the document i. Then, the features are given by the columns of X and we want to compute χ2 between the categories of interest and each feature in order to figure out what are the most relevant terms. This can be done as follows
from sklearn.feature_selection import chi2
# compute chi2 for each feature
chi2score = chi2(X,posts.target)[0]
To have a visual insight, we can plot a bar chart where each bar shows the χ2 value computed above:
from pylab import barh,plot,yticks,show,grid,xlabel,figure
figure(figsize=(6,6))
wscores = zip(vectorizer.get_feature_names(),chi2score)
wchi2 = sorted(wscores,key=lambda x:x[1]) 
topchi2 = zip(*wchi2[-25:])
x = range(len(topchi2[1]))
labels = topchi2[0]
barh(x,topchi2[1],align='center',alpha=.2,color='g')
plot(topchi2[1],x,'-o',markersize=2,alpha=.8,color='g')
yticks(x,labels)
xlabel('$\chi^2$')
show()



We can observe that the terms with a high χ2 can be considered relevant for the newsgroup categories we are analyzing. For example, the terms space, nasa and launch can be considered relevant for the group sci.space. The terms god, jesus and atheism can be considered relevant for the groups alt.atheism and talk.religion.misc. And, the terms image, graphics and jpeg can be considered relevant in the category comp.graphics.

Tuesday, January 14, 2014

Review: Fundamentals of Data Analytics in Python

I massively use Python for data analysis and when I was offered to review the video tutorial with the title “Fundamentals of Data Analytics in Python LiveLessons”, I couldn't refuse.

The tutorial starts from the basics showing how to install Python and its data analysis libraries. Then it continues explaining the main uses that data scientists and engineers practice during their analysis: importing and cleaning data, vectorial computing, visualization and data summarization.




Most of the videos are commented sessions of IPython notebook sometimes supported by some slides. The authors go deep into the explanation of how to use the libraries for the manipulation of the data (Numpy, Scipy and Pandas), while they summarize the potential of the other complementary libraries. In particular, the last video is a survey of various visualization tools.

In conclusion, this video tutorial provides a solid introduction to the main tools for data analysis in Python and a clear view of the open source Python tools relevant to scientific and engineering programming. This tutorial seems perfect for people who need to learn the technical methodologies for data analysis and for people who already know Python but want to acquire skills about data analysis.