  Distinguishing causal connections from correlations is important in many
scenarios. However, the presence of unobserved variables, such as the latent
confounder, can introduce bias in conditional independence testing commonly
employed in constraint-based causal discovery for identifying causal relations.
To address this issue, existing methods introduced proxy variables to adjust
for the bias caused by unobserveness. However, these methods were either
limited to categorical variables or relied on strong parametric assumptions for
identification. In this paper, we propose a novel hypothesis-testing procedure
that can effectively examine the existence of the causal relationship over
continuous variables, without any parametric constraint. Our procedure is based
on discretization, which under completeness conditions, is able to
asymptotically establish a linear equation whose coefficient vector is
identifiable under the causal null hypothesis. Based on this, we introduce our
test statistic and demonstrate its asymptotic level and power. We validate the
effectiveness of our procedure using both synthetic and real-world data.
