Partial Identification with Proxy of Latent Confoundings via Sum-of-ratios Fractional Programming

Zhiheng Zhang, Xinyan Su

Keywords: causal effect;

TL;DR: Partial Identification with Proxy of Latent Confoundings via Sum-of-ratios Fractional Programming

Abstract:

Causal effect estimation is a crucial theoretical tool
in uncertainty analysis. The challenge of unobservable confoundings has raised concerns regarding
quantitative causality computation. To address this
issue, proxy control has become popular, employing auxiliary variables W as proxies for the confounding variables U. However, proximal methods
rely on strong assumptions, such as reversibility
and completeness, that are challenging to interpret
empirically and verify. Consequently, their applicability in real-world scenarios is limited, particularly when the proxies lack informativeness. In
our paper, we have developed a novel optimization
method named Partial Identification with Proxy of
Latent Confoundings via Sum-of-Ratios Fractional
Programming (PI-SFP). This method does not impose any additional restrictions upon proxies and
only assumes the mild partial observability of the
transition matrix P(W | U). We have theoretically proven the global convergence of PI-SFP to
the valid bound of the causal effect and analyzed
the conditions under which the bounds could be
tight. Our synthetic and real-world experiments
validate our theoretical framework.

List Of Authors: Zhang, Zhiheng and Su, Xinyan

Submission Number: 40