Evaluating Gaussian Mixture model using a score metric? - python-3.x

I have 1D data (on column data). I used Gaussian Mixture Model (GMM) as a density estimation, using this implementation in Python: https://scikit-learn.org/stable/modules/generated/sklearn.mixture.GaussianMixture.html. By relying on AIC/BIC criteron i was able to determine number of components. After i fit the GMM, i plotted kernel density estimation of original observation + that of sampled data drawn from GMM. the plot of original and sampled desnities are quiet similar( that is good). But, i would like some metrics to report how good is the fitted model.
g = GaussianMixture(n_components = 35)
data= df['x'].values.reshape(-1,1) # data taken from data frame (10,000 data pints)
clf= g.fit(data)# fit model
samples= clf.sample(10000)[0] # generate sample data points (same # as original data points)
I found score in the implementation, but not sure how to implememnt. Am i doing it wrong? or is there any better way to show how accuracy is the fitted model, apart from histogram or kernel densities plots?.
print(clf.score(data))
print(clf.score(samples))

You can use normalized_mutual_info_score, adjusted_rand_score or silhouette score to evaluate your clusters. All of these metrics are implemented under sklearn.metrics section.
EDIT: You can check this link for more detail explanations.
In a summary:
Adjusted Rand Index: measures the similarity of the two assignments.
Normalized Mutual Information: measures the agreement of the two assignments.
Silhouette Coefficient: measures how well-assigned each individual point is.
gmm.fit(x_vec)
pred = gmm.predict(x_vec)
print ("gmm: silhouttte: ", silhouette_score(x_vec, pred))

I would better use cross-validation and try to see the accuracy of the trained model.
Use the predict method of the fitted model to predict the labels of unseen data (use cross-validation and report the acurracy): https://scikit-learn.org/stable/modules/generated/sklearn.mixture.GaussianMixture.html#sklearn.mixture.GaussianMixture.predict
Toy example:
g = GaussianMixture(n_components = 35)
g.fit(train_data)# fit model
y_pred = g.predict(test_data)
EDIT:
There are several options to measure the performance of your unsupervised case. For GMM, which base on real probabilities, the most common are BIC and AIC. They are immediatly included in the scikit GMM class.

Related

What steps should I take next to improve my accuracy? Can data be the problem?

I built various ML models using sklearn for a binary classification problem. The data-set is provided to me by my professor for this comparative study.
my jupyter notebook and dataset can be found here
As I am getting very low accuracy, I fear that I must be doing something wrong while building the model. So I tested my decision tree on the inbuilt data-set in sklearn (breast cancer data-set) which is very similar to my data-set as both are binary classifications. Here I get an mean accuracy of 95 %. So I think right now that the problem might be my data-set. Can I get some help on how do I pre-process my data or any other steps that I might look into to improve accuracy.
Encode labels
Categorical data are variables that contain label values rather than numeric values.The number of possible values is often limited to a fixed set.
For example, users are typically described by country, gender, age group etc. We will use Label Encoder to label the categorical data. Label Encoder is the part of SciKit Learn library in Python and used to convert categorical data, or text data, into numbers, which our predictive models can better understand.
#Encoding categorical data values
from sklearn.preprocessing import LabelEncoder
labelencoder_Y = LabelEncoder()
Y = labelencoder_Y.fit_transform(Y)
Feature scaling
Most of the times, your dataset will contain features highly varying in magnitudes, units and range. But since, most of the machine learning algorithms use Eucledian distance between two data points in their computations. We need to bring all features to the same level of magnitudes. This can be achieved by scaling. This means that you’re transforming your data so that it fits within a specific scale, like 0–100 or 0–1. We will use StandardScaler method from SciKit-Learn library.
#Feature Scalingfrom sklearn.preprocessing import StandardScaler
sc = StandardScaler()
X_train = sc.fit_transform(X_train)
X_test = sc.transform(X_test)
Choosing Right model
You kight also want to vhoose the appropriate model. You can't just use neural nets or so for all problems it's the no free luch theorem. For this you could use K-fold cross validation, AIC and BIC

SMOTE over sampling applied on text classification

I am working on text classification, where I am using Multinominal Naive Bayes Classifier to predict article titles into their respective subject categories. Both of these are stored in a pandas data frame and are text columns. However they're are two categories which contain 50,000 records and 30,000 records respectively. Hence I need to do oversampling of the data and then apply the algorithm. When I do oversampling it reduces the model accuracy score and give me 15%. Please tell me how I can improve it.
X_train, X_test, Y_train, Y_test=train_test_split(df['Title'],df['Subjects'], test_size=0.2,random_state=42)
count_vect = CountVectorizer()
X_train_counts = count_vect.fit_transform(X_train)
tfidf_transformer = TfidfTransformer()
X_train_tfidf = tfidf_transformer.fit_transform(X_train_counts)
sm = SMOTE(random_state=2)
X_train_res, y_train_res = sm.fit_sample(X_train_tfidf, Y_train)
print("Shape after smote is:",X_train_res.shape,y_train_res.shape)
nb = Pipeline([('clf', MultinomialNB())])
nb.fit(X_train_res, y_train_res)
y_pred = nb.predict(count_vect.transform(X_test))
print(accuracy_score(Y_test,y_pred))
I expect to increase model accuracy by doing so. Model accuracy without oversampling is 62% and after oversampling is 15%, when it should actually be higher.
Actually, using SMOTE for balancing/oversampling classes can be problematic in text classification tasks. There are nice explanations and suggestions for alternatives here:
https://datascience.stackexchange.com/a/27758
In short, the SMOTE output may not represent "meaningful" substitutes and due to the size of the feature space its nearest-neighbor based approach may yield poor results.
Some more ideas:
Instead of using accuracy, it is advisable to use F1 or similar.
Rather unlikely to help but did you try undersampling?
For the MultinomialNB classifier you might try setting class_prior explicitly.
Finally, other methods like Forests and Boosting approaches might be better suited for imbalanced datasets.

Model evaluation : model.score Vs. ROC curve (AUC indicator)

I want to evaluate a logistic regression model (binary event) using two measures:
1. model.score and confusion matrix which give me a 81% of classification accuracy
2. ROC Curve (using AUC) which gives back a 50% value
Are these two result in contradiction? Is that possible
I'missing something but still can't find it
y_pred = log_model.predict(X_test)
accuracy_score(y_test , y_pred)
cm = confusion_matrix( y_test,y_pred )
y_test.count()
print (cm)
tpr , fpr, _= roc_curve( y_test , y_pred, drop_intermediate=False)
roc = roc_auc_score( y_test ,y_pred)
enter image description here
The accuracy score is calculated based on the assumption that a class is selected if it has a prediction probability of more than 50%. This means that you are looking only at 1 case (one working point) out of many. Let's say you'd like to classify an instance as '0' even if it has a probability greater than 30% (this may happen if one of your classes is more important for you, and its a-priori probability is very low). In this case - you will have a very different confusion matrix with a different accuracy ([TP+TN]/[ALL]). The ROC auc score examines all of these working points and gives you an estimation of your overall model. A score of 50% means that the model is equal to a random selection of classes based on your a-priori probabilities of the classes. You would like the ROC to be much higher to say that you have a good model.
So in the above case - you can say that your model does not have a good prediction strength. As a matter of fact - a better prediction will be to predict everything as "1" - in your case it will lead to an accuracy of above 99%.

sklearn: AUC score for LinearSVC and OneSVM

One option of the SVM classifier (SVC) is probability which is false by default. The documentation does not say what it does. Looking at libsvm source code, it seems to do some sort of cross-validation.
This option does not exist for LinearSVC nor OneSVM.
I need to calculate AUC scores for several SVM models, including these last two. Should I calculate the AUC score using decision_function(X) as the thresholds?
Answering my own question.
Firstly, it is a common "myth" that you need probabilities to draw the ROC curve. No, you need some kind of threshold in your model that you can change. The ROC curve is then drawn by changing this threshold. The point of the ROC curve being, of course, to see how well your model is reproducing the hypothesis by seeing how well it is ordering the observations.
In the case of SVM, there are two ways I see people drawing ROC curves for them:
using distance to the decision bondary, as I mentioned in my own question
using the bias term as your threshold in the SVM: http://researchgate.net/post/How_can_I_plot_determine_ROC_AUC_for_SVM. In fact, if you use SVC(probabilities=True) then probabilities will be calculated for you in this manner, by using CV, which you can then use to draw the ROC curve. But as mentioned in the link I provide, it is much faster if you draw the ROC curve directly by varying the bias.
I think #2 is the same as #1 if we are using a linear kernel, as in my own case, because varying the bias is varying the distance in this particular case.
In order to calculate AUC, using sklearn, you need a predict_proba method on your classifier; this is what the probability parameter on SVC does (you are correct that it's calculated using cross-validation). From the docs:
probability : boolean, optional (default=False)
Whether to enable probability estimates. This must be enabled prior to calling fit, and will slow down that method.
You can't use the decision function directly to compute AUC, since it's not a probability. I suppose you could scale the decision function to take values in the range [0,1], and compute AUC, however I'm not sure what statistical properties this will have; you certainly won't be able to use it to compare with ROC calculated using probabilities.

Negative R2 on training data for linear regression

Using scikit-learn to fit a one dimensional model, without an intercept:
lm = sklearn.linear_models.LinearRegression(fit_intercept=False).
lm.fit(x, y)
When evaluating the score using the training data I get a negative .score().
lm.score(x, y)
-0.00256
Why? Does the R2 score compare the variance of my intercept-less model with a model with an intercept?
(Note that it is the same data that I used to fit the model.)
From Wikipedia article on R^2:
Important cases where the computational definition of R2 can yield
negative values, depending on the definition used, arise [...] where
linear regression is conducted without including an intercept.
(emphasis mine).

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