I am trying to identify relevant features for a problem. The features are discrete and continuous in [0,1]. The target variable is [0,1]. I have tried linear regression by standardizing(subtract mean and divide by standard deviation) all the features. For example, 10,4,0.5,0.3 and the target is 0.6. I have two doubts: i) do I need to standardize the data for linear regression (I am getting p-value of 0 for most of the features) ii) Should I use beta regression, mixture model or mutual information regression. Do these methods need standardization.
The best method for your problem is Logistic Regression, also called Logit Regression. This is a variation of OLS Regression that specifically caters to a binomial dependent variable (0,1). Logistic Regression is very flexbible. While the Y variable has to be (0, 1), the Xs variables can be pretty much anything you want: binomial (0, 1), discretionary, continuous.
When using Logistic Regression, I don't think you will get much benefit from standardizing variables. That's because it just does not make that much sense when using binomial variables (0, 1).
If you care to standardize variables in your model, I would only standardize the continuous ones, and not the binomial ones.