The eye diagram is one of the most common tools used for quality assessment in high-speed links. This paper proposes a method of predicting the shape of the inner-eye for a link subject to uncertainties. The approach relies on machine learning regression and is tested on the very challenging example of flexible link for smart-textiles. Several sources of uncertainties are taken into account related to both manufacturing tolerances and physical deformation. The resulting model is fast and accurate. It is also extremely versatile: rather than focusing on a specific metric derived from the eye-diagram, its aim is to fully reconstruct the inner eye and enable designers to use it as they see fit. The paper investigates the features and convergence of three alternative machine learning algorithms, including the singleoutput support vector machine regression, together with its least squares variant, and the vector-valued kernel ridge regression. The latter method is arguably the most promising, resulting in an accurate, fast and robust tool enabling a complete parametric stochastic map of the eye.