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Regularisation by convolution in probability density estimation is equivalent to jittering

We demonstrate that regularisation by convolution, a smoothing technique based on the convolution of Gaussian kernels with Gaussian mixture models (Molina and Niranjan, 1997), is equivalent to jittering (the addition of noise to the input data of the mixture model) (Bishop, 1995) in the case of probability density estimation. We also demonstrate that regularisation by convolution is consistent with linear transformations of the input space when used with full covariance matrix Gaussian components. Regularisation by convolution is illustrated on the probability density estimation of ink in ancient manuscript letters (British library Beowulf manuscript).