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Evaluating Lasso's Unique Solution and its consequences in applications?

I've grasped from a paper (https://www.stat.cmu.edu/%7Eryantibs/papers/lassounique.pdf) that Lasso may not yield a unique solution when the number of variables (p) exceeds the number of observations (...
george1994's user avatar
3 votes
1 answer
172 views

Explanation of the proof that SCAD penalty has the oracle property

I am trying to understand the proof that the SCAD has the oracle property. Could you help me with an explanation and a full break down of the steps, so that I can understand it? I'm unclear on how ...
mike's user avatar
  • 31
1 vote
0 answers
32 views

The importance of stationarity for the oracle property of Elastic Net Regression?

I've been on the lookout for a while, but unfortunately, I'm still coming up empty-handed in my search for papers or books that dive into the theoretical derivation or simulation of the impact of non-...
Joe94's user avatar
  • 85
4 votes
1 answer
74 views

How could an oracle that knows the true distribution of things would still incur some errors?

The ideal model is an oracle that simply knows the true probability distribution that generates the data. Even such a model will still incur some error on many problems, because there may still be ...
Revolucion for Monica's user avatar
3 votes
0 answers
180 views

Why does it matter if we use an oracle estimator?

I read this question while studying adaptive LASSO, and while I think I have a decent understanding of the oracle property in theory, I am confused about what it means to use an oracle vs. non-oracle ...
wzbillings's user avatar
3 votes
1 answer
193 views

Word for the compliment of an ablation study: replacing estimated feature with perfect information

I need a word. We have ablation testing (or an ablation study, or ablation analysis) to quantify what happens if you remove a feature / component from a ML system. So one removes that feature/...
Frames Catherine White's user avatar
1 vote
1 answer
325 views

Why are oracle inequalities called that way?

The oracle property is an asymptotic property of an estimator, and is about variable selection: An estimator $\hat \beta_n$ satisfies the oracle property if in the limit of $n\to \infty$, the ...
user56834's user avatar
  • 2,877
4 votes
1 answer
352 views

Parameter estimation and model selection consistencies

In a highly cited paper by Zhao (2006) it is stated that (Section 2) An estimate which is consistent in terms of parameter estimation does not necessarily consistently selects the correct model (or ...
tosik's user avatar
  • 1,179
17 votes
1 answer
5k views

Oracle Inequality : In basic terms

I'm going through a paper that uses oracle inequality to prove something but I'm unable to understand what it is even trying to do. When I searched online about 'Oracle Inequality', some sources ...
Wolcott's user avatar
  • 171
2 votes
0 answers
48 views

What is the relation between coefficients selected by an Oracle-procedure and significant coefficients?

As proved by Zou (2006), the adaptive LASSO enjoys the Oracle Property in the sense that it does variable selection as if it knew the true (sparse) model. However, in the early days, the standard ...
adam's user avatar
  • 115
1 vote
0 answers
167 views

Trade-off between explanation and prediction (adaptive lasso)

The adaptive lasso penalises each coefficient differently by employing a weighted vector. Becuase of this modification from the original lasso, if combine with the additional conditions such as, $\...
MZ75's user avatar
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7 votes
0 answers
797 views

Is lasso always outperformed by adaptive lasso?

I have been reading some papers and I understood that adaptive lasso has the Oracle properties which lasso lacks. Does that mean adaptive lasso always better than lasso (let's focus on the simple ...
MZ75's user avatar
  • 81
2 votes
0 answers
1k views

Lasso variable selection consistency: "irrepresentable condition" explained in a non-technical way?

I am currently using the lasso for variable selection. Based on random subsamples of my data, the selections differ a lot, i.e. the selection consistency is bad. Literature such as Meinshausen & ...
Joachim Schork's user avatar
24 votes
3 answers
25k views

Lasso vs. adaptive Lasso

LASSO and adaptive LASSO are two different things, right? (To me, the penalties look different, but I'm just checking whether I miss something.) When you generally speak about elastic net, is the ...
Mr Validation's user avatar
31 votes
2 answers
19k views

What is the oracle property of an estimator?

What is the oracle property of an estimator? What modelling goals is the oracle property relevant for (predictive, explanatory, ...)? Both theoretically rigorous and (especially) intuitive ...
Richard Hardy's user avatar