Is it true that currently we cannot compute p-values or confidence intervals for the coefficients from a Lasso regression problem? I found a textbook online that had the following to say regarding the Lasso,

"Computing the p-values or confidence intervals for the coefficients of a model fitted with lasso, remains an open problem."

Why is it that currently inference on the coefficients is not possible? Is it that structurally the variance of the coefficient estimators have no closed form? Or is it something else?


Why is it that currently inference on the coefficients is not possible? Is it that structurally the variance of the coefficient estimators have no closed form? Or is it something else?

Prior to some work in the area of selective inference, the bias in the estimates of the coefficients complicated the theory for testing coefficients.  What's more, there may (or may not have, I can't recall) been some theory for fixed regularization strength, but we almost always estimate the regularization strength from the data, which further added to the complexity.
Around 2014/2015, work started to come out on selective inference which provided some theoretical grounding on how to do inference on penalized models such as LASSO. I'm not sure if it is very mainstream as of yet, I haven't seen it be used often, but it is an active area of research.
