Difference between coefficients of Linear Regression and weights in Linear SVM? Does they interpret same meaning. like impact of one variable on dependent variable keeping other variable constant.
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I could not find where the Manhattan distance of weights is calculated and multiplied with alpha (L1 reg. coefficient) in the Lasso Regression and the Quantile Regression source code of scikit-learn.
I was trying to implement Lasso Regression and Quantile Regression w/ NumPy and compare results w/ scikit-learn models.
I don't believe the loss function (including the regularization penalty) is ever explicitly calculated, no.
Instead, the loss function is optimized by coordinate descent, and so we only ever need to actually calculate derivatives of the loss function. That happens in the enet_coordinate_descent function (or relatives), and I think the relevant bit is here.
I am confused by this example here: https://scikit-learn.org/stable/visualizations.html
If we plot the ROC curve for a Logistic Regression Classifier the ROC curve is parametrized by the threshold parameter. But a usual SVM spits out binary values instead of probabilities.
Consequently there should not be a threshold which can be varied to obtain an ROC curve.
But which parameter is then varied in the example above?
SVMs have a measure of confidence in their predictions using the distance from the separating hyperplane (before the kernel, if you're not doing a linear SVM). These are obviously not probabilities, but they do rank-order the data points, and so you can get an ROC curve. In sklearn, this is done via the decision_function method. (You can also set probability=True in the SVC to calibrate the decision function values into probability estimates.)
See this section of the User Guide for some of the details on the decision function.
For example when executing the following logistic regression model on my data in Python . . .
### Logistic regression with ridge penalty (L2) ###
from sklearn.linear_model import LogisticRegression
log_reg_l2_sag = LogisticRegression(penalty='l2', solver='sag', n_jobs=-1)
log_reg_l2_sag.fit(xtrain, ytrain)
I have not specified a range of ridge penalty values. Is the optimum ridge penalty explicitly calculated with a formula (as is done with the ordinary least squares ridge regression), or is the optimum penalty chosen from a default range of penalty values? The documentation isn't clear on this.
As far as I understood your question. You want to know how the 'L2' regularization works in case of logistic regression. Like how the optimum value is found out.
We don't give a grid here like [0.0001, 0.01 ] because the optimum values are found out using the 'solver' paramter of the LogisticRegression.
The solver in your case is Stochastic Average Gradient Descent which finds out the optimum values for the L2 regularization.
The L2 regularization will keep all the columns, keeping the coefficients of the least important paramters close to 0.
So I am trying to explain my strictly bounded variable (percentage) with some predictors - categorical as well as numerical. I have read quite a bit about the topic, but I am still confused about some of the arguments. The purpose of my regression is explaining, not predicting.
What are the consequences of running a linear regression on a strictly bounded outcome variable?
A linear regression does not have a bounded output. It's a linear transformation of the input, so if the input is twice as large, the output will be twice as large. That way, it will always be possible to find an input that exceeds the boundaries of the output.
You can apply a sigmoid function to the output of the linear regression (this is called "logistic regression"), but this will model a binary variable and give you the probability of the variable being 1. In your case, your variable isn't binary, it can have any value between 0 and 1. For that problem, you need to apply a beta regression, which will give you a bounded output between 0 and 1.
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 .