Dataset Information

Quantile hidden semi-Markov models for multivariate time series.

ABSTRACT: This paper develops a quantile hidden semi-Markov regression to jointly estimate multiple quantiles for the analysis of multivariate time series. The approach is based upon the Multivariate Asymmetric Laplace (MAL) distribution, which allows to model the quantiles of all univariate conditional distributions of a multivariate response simultaneously, incorporating the correlation structure among the outcomes. Unobserved serial heterogeneity across observations is modeled by introducing regime-dependent parameters that evolve according to a latent finite-state semi-Markov chain. Exploiting the hierarchical representation of the MAL, inference is carried out using an efficient Expectation-Maximization algorithm based on closed form updates for all model parameters, without parametric assumptions about the states' sojourn distributions. The validity of the proposed methodology is analyzed both by a simulation study and through the empirical analysis of air pollutant concentrations in a small Italian city.

Supplementary information

The online version contains supplementary material available at 10.1007/s11222-022-10130-1.

SUBMITTER: Merlo L

PROVIDER: S-EPMC9360757 | biostudies-literature | 2022

REPOSITORIES: biostudies-literature

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Quantile hidden semi-Markov models for multivariate time series.

Merlo Luca L Maruotti Antonello A Petrella Lea L Punzo Antonio A

Statistics and computing 20220809 4

This paper develops a quantile hidden semi-Markov regression to jointly estimate multiple quantiles for the analysis of multivariate time series. The approach is based upon the Multivariate Asymmetric Laplace (MAL) distribution, which allows to model the quantiles of all univariate conditional distributions of a multivariate response simultaneously, incorporating the correlation structure among the outcomes. Unobserved serial heterogeneity across observations is modeled by introducing regime-dep ...[more]

PMID: 35968041

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Project description:BackgroundThe accuracy of protein secondary structure prediction has been improving steadily towards the 88% estimated theoretical limit. There are two types of prediction algorithms: Single-sequence prediction algorithms imply that information about other (homologous) proteins is not available, while algorithms of the second type imply that information about homologous proteins is available, and use it intensively. The single-sequence algorithms could make an important contribution to studies of proteins with no detected homologs, however the accuracy of protein secondary structure prediction from a single-sequence is not as high as when the additional evolutionary information is present.ResultsIn this paper, we further refine and extend the hidden semi-Markov model (HSMM) initially considered in the BSPSS algorithm. We introduce an improved residue dependency model by considering the patterns of statistically significant amino acid correlation at structural segment borders. We also derive models that specialize on different sections of the dependency structure and incorporate them into HSMM. In addition, we implement an iterative training method to refine estimates of HSMM parameters. The three-state-per-residue accuracy and other accuracy measures of the new method, IPSSP, are shown to be comparable or better than ones for BSPSS as well as for PSIPRED, tested under the single-sequence condition.ConclusionsWe have shown that new dependency models and training methods bring further improvements to single-sequence protein secondary structure prediction. The results are obtained under cross-validation conditions using a dataset with no pair of sequences having significant sequence similarity. As new sequences are added to the database it is possible to augment the dependency structure and obtain even higher accuracy. Current and future advances should contribute to the improvement of function prediction for orphan proteins inscrutable to current similarity search methods.

Dataset Information

Quantile hidden semi-Markov models for multivariate time series.

Supplementary information

Publications

Quantile hidden semi-Markov models for multivariate time series.

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