Rephrase coherently and logically the following text about the autoregressive formalism:
The AR formalism expresses the input data distribution as the product of conditional probabilities.
The product of conditionals is a possible decomposition of the joint probability given by the chain rule for random variables.
The product that preserves the temporal order is the AR representation, i.e., it predicts only from the past. Provide two versions of response separated with exactly 6 asterisk symbols: ******.
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