This paper proposes a new estimation algorithm for the parameters of an HMM as to best account for the observed data. In this model, in addition to the observation sequence, we have \emph{partial} and \emph{noisy} access to the hidden state sequence as side information. This access can be seen as "partial labeling" of the hidden states. Furthermore, we model possible mislabeling in the side information in a joint framework and derive the corresponding EM updates accordingly. In our simulations, we observe that using this side information, we considerably improve the state recognition performance, up to 70%, with respect to the "achievable margin" defined by the baseline algorithms. Moreover, our algorithm is shown to be robust to the training conditions.
Quick Adaptive Ternary Segmentation: An Efficient Decoding Procedure For Hidden Markov Models
Nonclinical Biostatistics, F. Hoffmann-La Roche, Switzerland（非临床生物统计学，霍夫曼拉罗奇公司，瑞士）；Institute for Mathematical Stochastics, Cluster of Excellence “Multiscale Bioimaging: from Molecular Machines to Networks of Excitable Cells”（数学概率研究所，卓越中心“多尺度生物成像：从分子机器到可兴奋细胞网络”）；Georg-August-Universität Göttingen, Germany（哥廷根大学，德国）
Optimization of Smooth Functions with Noisy Observations: Local Minimax Rates
Machine Learning Department, Carnegie Mellon University（卡内基梅隆大学机器学习系）；Department of Statistics and Data Science, Carnegie Mellon University（卡内基梅隆大学统计与数据科学系）
Needles in Needle Stacks: Meaningful Clinical Information Buried in Noisy Waveform Data
University of Toronto（多伦多大学）；SickKids（SickKids医院（多伦多儿童医院））；Vector Institute（向量研究所）；University of Sydney（悉尼大学）；University of Oxford（牛津大学）；Technion - Israel Institute of Technology（以色列理工学院）；Canadian Institute for Advanced Research（加拿大高级研究院）；Seattle Children’s Hospital（西雅图儿童医院）
