CarpeDiem: optimizing the Viterbi algorithm and applications to supervised sequential learning. The growth of information available to learning systems and the increasing complexity of learning tasks determine the need for devising algorithms that scale well with respect to all learning parameters. In the context of supervised sequential learning, the Viterbi algorithm plays a fundamental role, by allowing the evaluation of the best (most probable) sequence of labels with a time complexity linear in the number of time events, and quadratic in the number of labels. In this paper we propose CarpeDiem, a novel algorithm allowing the evaluation of the best possible sequence of labels with a sub-quadratic time complexity. We provide theoretical grounding together with solid empirical results supporting two chief facts. CarpeDiem always finds the optimal solution requiring, in most cases, only a small fraction of the time taken by the Viterbi algorithm; meantime, CarpeDiem is never asymptotically worse than the Viterbi algorithm, thus confirming it as a sound replacement.

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