Based on a probabilistic method, the data regularization framework known as stochastic interpolation (SI) recovers well-behaved functional representations of input data. SI splits the interpolation operator into a discrete deconvolution that is followed by a discrete convolution of the data. At the heart of the process is a row stochastic matrix which represents the approximation of the data by a probabilistic weighting of the data values. It allows the direct inclusion of statistical models into data regularization. We examine connections to radial basisfunctions and posit that SI is a general framework providing a unique mechanism for linking statistical data analysis with conventional interpolation and approximation methods that are built on non-negative operators. SI can be implemented with flexibility to yield data approximation, interpolation, peak sharpening, non-linear smoothing, and all manner of hybrid schemes in a principled way by a deliberate choice of different generators of the row space of the convolution matrix.