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Summary: A method for jointly training all parameters (decision splits and posterior probabilities) of decision trees is proposed. This is an important topic since current methods train trees in a greedy manner, layer by layer. The task is phrased as a single optimization problem which is then upper-bounded and approximated to obtain a tractable formulation. Quality - The paper is well written but there might be flaws in the reasoning. Clarity - The derivation is clean but experiments and their presentation could be improved.