Questions tagged [oracle]

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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 ...
3
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1answer
169 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 ...
14
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1answer
1k 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 ...
2
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0answers
30 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 ...
1
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0answers
110 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, $\...
5
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0answers
309 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 ...
1
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0answers
722 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 & ...
12
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3answers
9k 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 ...
22
votes
2answers
9k 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 ...