Three-dimensional computer avatars are often implemented as a parametric model, where the parameters control the facial expression. Commonly, the parameterization is in terms of independent muscle actions, which prevents automatic methods such as principal component analysis from being used, since the corresponding deformations are approximately but not strictly orthogonal. As a result, high-quality avatar models are often constructed by laborious manual sculpting. In this paper, we adopt the perspective of blind source separation and independent component analysis, and seek a set of statistically independent parameters that can be linearly combined to produce the facial motion. While blind source separation and independent component analysis have rigorous information theoretic foundations, some of the associated algorithms have well-known limitations associated with the practical difficulties of computing entropy. Instead, we explore the use of the Hilbert-Schmidt Independence Criterion (HSIC)for solving our problem. We demonstrate the difference between a standard ICA-like criterion and our proposed method using HSIC regularization. Our method discovers more varied, unique, and asymmetric basis shapes compared to the standard ICA-like optimization.