This paper studies the problem of designing a quantizer (encoder) for the task of distributed detection of independence subject to one-side communication (limited bits) constraints. By exploiting the asymptotic performance limits as an objective to train a quantization scheme, we propose an algorithm that addresses an info-max problem for this lossy compression task. Tools from machine learning are incorporated to facilitate our data-driven optimization. Experiments on synthetic data support our design principle and approximations, expressing that the devised solutions are effective in compressing data while preserving the relevant information for the underlying task of testing against independence.