QATS is a new polylog-time approximate decoding procedure for HMMs that builds admissible state sequences by locally maximizing likelihoods over paths with at most three segments via adaptive ternary segmentation and cumulative sum storage.
Four transformations on the Catalan triangle
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abstract
In this paper, we define four transformations on the classical Catalan triangle $\mathcal{C}=(C_{n,k})_{n\geq k\geq 0}$ with $C_{n,k}=\frac{k+1}{n+1}\binom{2n-k}{n}$. The first three ones are based on the determinant and the forth is utilizing the permanent of a square matrix. It not only produces many known and new identities involving Catalan numbers, but also provides a new viewpoint on combinatorial triangles.
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Quick Adaptive Ternary Segmentation: An Efficient Decoding Procedure For Hidden Markov Models
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