Comment: Reflections on the Deconfounder.

To avoid measure-theoretic considerations when writing conditioning statements, I will consider the treatments Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>A</mi></mrow><mrow><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mrow></msup></mrow></math> ht to be discrete. I will write observed outcomes as Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>Y</mi></mrow><mrow><mtext>obs</mtext></mrow></msup></mrow></math> ht , where, under the stable unit treatment value assumption (SUTVA), Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>Y</mi></mrow><mrow><mtext>obs</mtext></mrow></msup><mo>=</mo><mi>Y</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow></math> ht . Throughout, I will consider models of the joint distribution Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><msup><mrow><mi>Y</mi></mrow><mrow><mtext>obs</mtext></mrow></msup><mo>,</mo><mi>Z</mi><mo stretchy="false">)</mo></mrow></math> ht , which I will refer to as latent variable models. For example, the setting of Theorem 7 can be framed as a problem where the unobserved confounder I Z i is measured with proxies Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo>:</mo><mi>m</mi></mrow></msub></mrow></math> ht . [Extracted from the article]