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<p>Asymptotically valid inference is obtained for graphical model edge parameters after selection using the same data set as the one used for inference. We consider Gaussian and (trans)elliptical graphical models, where the edge selection and consequent sparse estimation is operated by applying the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11222_2025_10564_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>, elastic net, smoothly clipped absolute deviation, or minimax concave penalty to an appropriately regular loss function. The polyhedral lemma is used to carry out conditional inference which is asymptotically valid in the (possibly wrong) selected graphical model. Simulation studies show how the method yields valid inference in a variety of finite-sample settings.</p>

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Asymptotic post-selection inference for regularized graphical models

  • 期刊论文

  • 发表日期：

    2025年1月25日

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  • Sofia Guglielmini,
  • Gerda Claeskens

摘要

Asymptotically valid inference is obtained for graphical model edge parameters after selection using the same data set as the one used for inference. We consider Gaussian and (trans)elliptical graphical models, where the edge selection and consequent sparse estimation is operated by applying the \(\ell _1\) ℓ 1 , elastic net, smoothly clipped absolute deviation, or minimax concave penalty to an appropriately regular loss function. The polyhedral lemma is used to carry out conditional inference which is asymptotically valid in the (possibly wrong) selected graphical model. Simulation studies show how the method yields valid inference in a variety of finite-sample settings.