Discussion of "A Tuning-Free Robust and Efficient Approach to High-Dimensional Regression".

Suppose we want to infer the conditional independence relationships among components of a random vector Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>X</mi><mo> </mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>p</mi></msup></mrow></math> ht . Then Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo stretchy="false">(</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo stretchy="false">)</mo><mo> </mo><mover accent="true"><mi>E</mi><mo> </mo></mover></mrow></math> ht if either Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mover accent="true"><mi> </mi><mo> </mo></mover></mrow><mrow><mi>j</mi><mi>k</mi></mrow></msub></mrow></math> ht or Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mover accent="true"><mi> </mi><mo> </mo></mover></mrow><mrow><mi>k</mi><mi>j</mi></mrow></msub></mrow></math> ht is nonzero. Alternatively, one may choose to include an edge only when both Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mover accent="true"><mi> </mi><mo> </mo></mover></mrow><mrow><mi>j</mi><mi>k</mi></mrow></msub></mrow></math> ht and Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mover accent="true"><mi> </mi><mo> </mo></mover></mrow><mrow><mi>k</mi><mi>j</mi></mrow></msub></mrow></math> ht are nonzero. [Extracted from the article]