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The paper presents a general method for non-conjugate variational inference based on proximal method and linearisation of the non-conjugate model. This is shown to reduce to natural gradient optimisation for conjugate exponential models. The method is shown to lead to slightly better predictive accuracy than standard approximate inference methods in a few selected problems and data sets. Quality The method relies on linearisation to handle non-conjugate models. The seems potentially problematic, as previous works have found linearisation to be unreliable in variational inference with non-conjugate models (see e.g.