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Coordinates of the lasso estimator

First of all, you should write $$ \widehat{\beta}\in\text{argmin}_{\beta}||Y-X\beta||_2^2+r||\beta||_1, $$ because the lasso estimator is not necessarily unique. Second, you can get intuition about ...
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5 votes

what is the idea behind SHRINKAGE (regularization) METHOD (e.g LASSO), and how to interpret it?

Why omit some variables is an excellent question. Many analysts do not realize that the data seldom contain sufficient information to correctly decide on which predictors to omit, thus variable ...
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When predicting case status, what is the appropriate way to examine differences in proteomics by gender (/the interaction between protein and gender)?

Approach 3: instead of modeling case/control against proteins and gender, model the set of protein expression levels against case/control and gender. That's been a standard approach dating back to the ...
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What if zero mean assumption is relased in graphical LASSO?

In practice I think one should always demean the data before applying the graphical lasso algorithm. I.e. just run with $X_i - \bar{X}$ where $\bar{X} = \tfrac{1}{n} \sum_{i=1}^n X_i$. This might be ...
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1 vote

Graphical lasso numerical problem (not SPD matrix result)

I also have run into this SPD problem. I was unable to avoid it by rescaling my data because I was interested in conducting simulations in a particular (strange) statistical regime. I then found the ...
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1 vote

Graphical LASSO Interpretation

Structure estimation in graphical models is a big field of statistics in it's own right. Two common methods are Neighbourhood Selection, Meinhausen and Buhlmann, 2006 Graphical Lasso, originally ...
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3 votes

Lasso regression Mathematical intuition

The other answer here covers the specific transformation issues you have asked about, so I'll focus solely on the intuition of the LASSO regression. One useful way to look at LASSO regression is that ...
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How to perform a fair simulation study?

Unless you think that computational time is a validation metric itself, you shouldn't be worrying about that initially. You might consider that in an evaluation of the tradeoffs among modeling ...
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Resources for learning about lasso

I think the suggestions in the comments above will all be good references: Introduction to Statistical Learning (ISL or ISLR, see statlearning.com) gives a "broad and less technical treatment of ...
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Lasso regression Mathematical intuition

You have three different questions. Let's tackle them in a somewhat different order. I'll refer to ISLR 2nd edition. First off, here are the two different formulations of the lasso: $$ \text{minimize }...
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