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We propose DenseHMM - a modification of Hidden Markov Models (HMMs) thatallows to learn dense representations of both the hidden states and theobservables. Compared to the standard HMM, transition probabilities are notatomic but composed of these representations via kernelization. Our approachenables constraint-free and gradient-based optimization. We propose twooptimization schemes that make use of this: a modification of the Baum-Welchalgorithm and a direct co-occurrence optimization. The latter one is highlyscalable and comes empirically without loss of performance compared to standardHMMs. We show that the non-linearity of the kernelization is crucial for theexpressiveness of the representations. The properties of the DenseHMM likelearned co-occurrences and log-likelihoods are studied empirically on syntheticand biomedical datasets.

DenseHMM: Learning Hidden Markov Models by Learning Dense Representations