I am making a machine learning program which classifies words in one of the following categories: Hardware, Software, None_of_these. I make use of the Multinomial Naive Bayes classifier from sklearn.
The function predict() gives me the prediction of every word, however, I can't see the actual probability (float ranging for 0 to 1.0) that the word matches with the predicted categorie. I didn't find this on sklearn's site either.
Is there a function which gives me the probability of every sample?
Nevermind, I found the solution.:
predict_proba(X) Returns probability estimates for the test vector X.
Related
I am using sklearn.linear_model.LogisticRegression for a text classification project. With the features I have extracted, the samples mostly receive a low probability score. Therefore, when I use the predict() those samples always classified to class 0. But what I want to do is get the actual probabilities for samples and choose the top 25%-30% based on the probability score. How do I get the probability score for a sample? In linear regression, the predict() provides the actual output. But it is not the case for logistic regression. I am not restricted to sklearn. A different package also works.
To make it more clear, what I want from the predict function is to return actual probability value (output of the sigmoid function) instead of the class label like linear regression predict function.
Can anyone explain how to interpret coefficientMatrix, interceptVector , Confusion matrix
of a multinomial logistic regression.
According to Spark documentation:
Multiclass classification is supported via multinomial logistic (softmax) regression. In multinomial logistic regression, the algorithm produces K sets of coefficients, or a matrix of dimension K×J where K is the number of outcome classes and J is the number of features. If the algorithm is fit with an intercept term then a length K vector of intercepts is available.
I turned an example using spark ml 2.3.0 and I got this result.
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If I analyse what I get :
The coefficientMatrix has dimension of 5 * 11
The interceptVector has dimension of 5
If so,why the Confusion matrix has a dimension of 4 * 4 ?
Also, can anyone give an interpretation of coefficientMatrix, interceptVector ?
Why I get negative coefficients ?
If 5 is the number of classes after classification, why I get 4 rows in the confusion matrix ?
EDIT
I forgot to mention that I am still beginner in machine learning and that my search in google didn't help, so maybe I get an Up Vote :)
Regarding the 4x4 confusion matrix: I imagine that when you split your data into test and train, there were 5 classes present in your training set and only 4 classes present in your test set. This can easily happen if the distribution of your response variable is imbalanced.
You'll want to try to perform some stratified split between test and train prior to modeling. If you are working with pyspark, you may find this library helpful: https://github.com/databricks/spark-sklearn
Now regarding negative coefficients for a multi-class Logistic Regression: As you mentioned, your returned coefficientMatrix shape is 5x11.
Spark generated five models via one-vs-all approach. The 1st model corresponds to the model where the positive class is the 1st label and the negative class is composed of all other labels. Lets say the 1st coefficient for this model is -2.23. In order to interpret this coefficient we take the exponential of -2.23 which is (approx) 0.10. Interpretation here: 'With one unit increase of 1st feature we expect a reduced odds of the positive label by 90%'
Is it possible to get a Z-score from sklearn's svm implementation?
So, if it classifies inputs X as [0,1,0,1,1,1,0,0,0], could you get it to output: [0.5,0.78,0.95,0.11,0.34,...], where these are the estimated confidences the learner has in its predictions?
If I implemented it myself, would I be able to extract this info, or would it turn into a huge project?
As far as I know SVM's don't have a closed-form Z-score, however if you create your SVC with the parameter probability=True, it will include a probability model constructed using cross-validation which you can access using predict_proba, to get an estimate of the confidence of the predictions.
I would like to fit a regression model to probabilities. I am aware that linear regression is often used for this purpose, but I have several probabilities at or near 0.0 and 1.0 and would like to fit a regression model where the output is constrained to lie between 0.0 and 1.0. I want to be able to specify a regularization norm and strength for the model and ideally do this in python (but an R implementation would be helpful as well). All the logistic regression packages I've found seem to be only suited for classification whereas this is a regression problem (albeit one where I want to use the logit link function). I use scikits-learn for my classification and regression needs so if this regression model can be implemented in scikits-learn, that would be fantastic (it seemed to me that this is not possible), but I'd be happy about any solution in python and/or R.
The question has two issues, penalized estimation and fractional or proportions data as dependent variable. I worked on each separately but never tried the combination.
Penalization
Statsmodels has had L1 regularized Logit and other discrete models like Poisson for some time. In recent months there has been a lot of effort to support more penalization but it is not in statsmodels yet. Elastic net for linear and Generalized Linear Model (GLM) is in a pull request and will be merged soon. More penalized GLM like L2 penalization for GAM and splines or SCAD penalization will follow over the next months based on pull requests that still need work.
Two examples for the current L1 fit_regularized for Logit are here
Difference in SGD classifier results and statsmodels results for logistic with l1 and https://github.com/statsmodels/statsmodels/blob/master/statsmodels/examples/l1_demo/short_demo.py
Note, the penalization weight alpha can be a vector with zeros for coefficients like the constant if they should not be penalized.
http://www.statsmodels.org/dev/generated/statsmodels.discrete.discrete_model.Logit.fit_regularized.html
Fractional models
Binary and binomial models in statsmodels do not impose that the dependent variable is binary and work as long as the dependent variable is in the [0,1] interval.
Fractions or proportions can be estimated with Logit as Quasi-maximum likelihood estimator. The estimates are consistent if the mean function, logistic, cumulative normal or similar link function, is correctly specified but we should use robust sandwich covariance for proper inference. Robust standard errors can be obtained in statsmodels through a fit keyword cov_type='HC0'.
Best documentation is for Stata http://www.stata.com/manuals14/rfracreg.pdf and the references therein. I went through those references before Stata had fracreg, and it works correctly with at least Logit and Probit which were my test cases. (I don't find my scripts or test cases right now.)
The bad news for inference is that robust covariance matrices have not been added to fit_regularized, so the correct sandwich covariance is not directly available. The standard covariance matrix and standard errors of the parameter estimates are derived under the assumption that the model, i.e. the likelihood function, is correctly specified, which will not be the case if the data are fractions and not binary.
Besides using Quasi-Maximum Likelihood with binary models, it is also possible to use a likelihood that is defined for fractional data in (0, 1). A popular model is Beta regression, which is also waiting in a pull request for statsmodels and is expected to be merged within the next months.
I am attempting 3 class classification by using SVM classifier. How do we interpret the probabililty estimates predicted by LIBSVM. Is it based on perpendicular distance of the instance from the maximal margin hyperplane?.
Kindly through some light on the interpretation of probability estimates predicted by LIBSVM classifier. Parameters C and gamma are first tuned and then probability estimates are outputted by using -b option with both training and testing.
Multiclass SVM is always decomposed into several binary classifiers (typically a set of one vs all classifiers). Any binary SVM classifier's decision function outputs a (signed) distance to the separating hyperplane. In short, an SVM maps the input domain to a one-dimensional real number (the decision value). The predicted label is determined by the sign of the decision value. The most common technique to obtain probabilistic output from SVM models is through so-called Platt scaling (paper of LIBSVM authors).
Is it based on perpendicular distance of the instance from the maximal margin hyperplane?
Yes. Any classifier that outputs such a one-dimensional real value can be post-processed to yield probabilities, by calibrating a logistic function on the decision values of the classifier. This is the exact same approach as in standard logistic regression.
SVM performs binary classification. In order to achieve multiclass classification libsvm performs what it's called one vs all. What you get when you invoke -bis the probability related to this technique that you can found explained here .