Hidden Markov Model (HMM) combined with Gaussian Process (GP) emission can be effectively used to estimate the hidden state with a sequence of complex input-output relational observations. Especially when the spectral mixture (SM) kernel is used for GP emission, we call this model as a hybrid HMM-GPSM. This model can effectively model the sequence of time-series data. However, because of a large number of parameters for the SM kernel, this model can not effectively be trained with a large volume of data having (1) long sequence for state transition and 2) a large number of time-series dataset in each sequence. This paper proposes a scalable learning method for HMM-GPSM. To effectively train the model with a long sequence, the proposed method employs a Stochastic Variational Inference (SVI) approach. Also, to effectively process a large number of data point each time-series data, we approximate the SM kernel using Reparametrized Random Fourier Feature (R-RFF). The combination of these two techniques significantly reduces the training time. We validate the proposed learning method in terms of its hidden-sate estimation accuracy and computation time using large-scale synthetic and real data sets with missing values.
Motivated by high-throughput single-cell cytometry data with applications to vaccine development and immunological research, we consider statistical clustering in large-scale data that contain multiple rare clusters. We propose a new hierarchical mixture model, namely Hidden Markov Model on Variable Blocks (HMM-VB), and a new mode search algorithm called Modal Baum-Welch (MBW) for efficient clustering. Exploiting the widely accepted chain-like dependence among groups of variables in the cytometry data, we propose to treat the hierarchy of variable groups as a figurative time line and employ a …
University of Warwick（华威大学）；The Alan Turing Institute（艾伦·图灵研究所）
We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification. In particular, we leverage the loss-theoretic perspective of Generalized Bayesian Inference (GBI) to define generalised filtering recursions in HMMs, that can tackle the problem of inference under model misspecification. In doing so, we arrive at principled procedures for robust inference against observation contamination by utilising the $β$-divergence. Operationalising the proposed framework is made possible via sequential Monte Carlo methods (SMC), where most standard…
We test the robustness of a maximum-likelihood (ML) based classifier where sequential data as observation is corrupted by noise. The hypothesis is that a generative model, that combines the state transitions of a hidden Markov model (HMM) and the neural network based probability distributions for the hidden states of the HMM, can provide a robust classification performance. The combined model is called normalizing-flow mixture model based HMM (NMM-HMM). It can be trained using a combination of expectation-maximization (EM) and backpropagation. We verify the improved robustness of NMM-HMM class…
Speaker clustering is the task of differentiating speakers in a recording. In a way, the aim is to answer "who spoke when" in audio recordings. A common method used in industry is feature extraction directly from the recording thanks to MFCC features, and by using well-known techniques such as Gaussian Mixture Models (GMM) and Hidden Markov Models (HMM). In this paper, we studied neural networks (especially CNN) followed by clustering and audio processing in the quest to reach similar accuracy to state-of-the-art methods.
In this paper, we explore the class of the Hidden Semi-Markov Model (HSMM), a flexible extension of the popular Hidden Markov Model (HMM) that allows the underlying stochastic process to be a semi-Markov chain. HSMMs are typically used less frequently than their basic HMM counterpart due to the increased computational challenges when evaluating the likelihood function. Moreover, while both models are sequential in nature, parameter estimation is mainly conducted via batch estimation methods. Thus, a major motivation of this paper is to provide methods to estimate HSMMs (1) in a computationally…
State University of New York at Buffalo（纽约州立大学布法罗分校）；University of California, Irvine（加州大学欧文分校）
Current state-of-the-art nonparametric Bayesian text clustering methods model documents through multinomial distribution on bags of words. Although these methods can effectively utilize the word burstiness representation of documents and achieve decent performance, they do not explore the sequential information of text and relationships among synonyms. In this paper, the documents are modeled as the joint of bags of words, sequential features and word embeddings. We proposed Sequential Embedding induced Dirichlet Process Mixture Model (SiDPMM) to effectively exploit this joint document represe…
Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models (HMMs) can be simulated on a quantum circuit, (2) we reformulate HQMMs by relaxing the constraints for modeling HMMs on quantum circuits, and (3) we present a learning algorithm to estimate the parameters of an HQMM from data. While our algorithm requires further optimization to handle larger datasets, we are able to evaluate our algorithm using several synthetic…
Posterior Regimes and Latent Deception: Variational Bayesian Inference in Hidden Markov Models for Sequential Fraud Detection in Financial Transactions
University of Stirling（斯特灵大学）；University of Nottingham（诺丁汉大学）
Variable order sequence modeling is an important problem in artificial and natural intelligence. While overcomplete Hidden Markov Models (HMMs), in theory, have the capacity to represent long-term temporal structure, they often fail to learn and converge to local minima. We show that by constraining HMMs with a simple sparsity structure inspired by biology, we can make it learn variable order sequences efficiently. We call this model cloned HMM (CHMM) because the sparsity structure enforces that many hidden states map deterministically to the same emission state. CHMMs with over 1 billion para…
Suppose that we are given a time series where consecutive samples are believed to come from a probabilistic source, that the source changes from time to time and that the total number of sources is fixed. Our objective is to estimate the distributions of the sources. A standard approach to this problem is to model the data as a hidden Markov model (HMM). However, since the data often lacks the Markov or the stationarity properties of an HMM, one can ask whether this approach is still suitable or perhaps another approach is required. In this paper we show that a maximum likelihood HMM estimator…
This paper describes a new method, HMM gauge likelihood analysis, or GLA, of detecting anomalies in discrete time series using Hidden Markov Models and clustering. At the center of the method lies the comparison of subsequences. To achieve this, they first get assigned to their Hidden Markov Models using the Baum-Welch algorithm. Next, those models are described by an approximating representation of the probability distributions they define. Finally, this representation is then analyzed with the help of some clustering technique or other outlier detection tool and anomalies are detected. Clear…
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi-Markovianity, which has been developed mainly in the parametric frequentist setting, to allow construction of highly interp…
University of California, San Diego（加利福尼亚大学圣迭戈分校）；City University of Hong Kong（香港城市大学）
The hidden Markov model (HMM) is a widely-used generative model that copes with sequential data, assuming that each observation is conditioned on the state of a hidden Markov chain. In this paper, we derive a novel algorithm to cluster HMMs based on the hierarchical EM (HEM) algorithm. The proposed algorithm i) clusters a given collection of HMMs into groups of HMMs that are similar, in terms of the distributions they represent, and ii) characterizes each group by a "cluster center", i.e., a novel HMM that is representative for the group, in a manner that is consistent with the underlying gene…
In the recent years, the desire and need to understand sequential data has been increasing, with particular interest in sequential contexts such as patient monitoring, understanding daily activities, video surveillance, stock market and the like. Along with the constant flow of data, it is critical to classify and segment the observations on-the-fly, without being limited to a rigid number of classes. In addition, the model needs to be capable of updating its parameters to comply with possible evolutions. This interesting problem, however, is not adequately addressed in the literature since ma…
Labeling of sequential data is a prevalent meta-problem for a wide range of real world applications. While the first-order Hidden Markov Models (HMM) provides a fundamental approach for unsupervised sequential labeling, the basic model does not show satisfying performance when it is directly applied to real world problems, such as part-of-speech tagging (PoS tagging) and optical character recognition (OCR). Aiming at improving performance, important extensions of HMM have been proposed in the literatures. One of the common key features in these extensions is the incorporation of proper prior i…
The Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) has been used widely as a natural Bayesian nonparametric extension of the classical Hidden Markov Model for learning from sequential and time-series data. A sticky extension of the HDP-HMM has been proposed to strengthen the self-persistence probability in the HDP-HMM. However, the sticky HDP-HMM entangles the strength of the self-persistence prior and transition prior together, limiting its expressiveness. Here, we propose a more general model: the disentangled sticky HDP-HMM (DS-HDP-HMM). We develop novel Gibbs sampling algorit…
Flow cytometry is a high-throughput technology used to quantify multiple surface and intracellular markers at the level of a single cell. This enables to identify cell sub-types, and to determine their relative proportions. Improvements of this technology allow to describe millions of individual cells from a blood sample using multiple markers. This results in high-dimensional datasets, whose manual analysis is highly time-consuming and poorly reproducible. While several methods have been developed to perform automatic recognition of cell populations, most of them treat and analyze each sample…
An intrinsic problem of classifiers based on machine learning (ML) methods is that their learning time grows as the size and complexity of the training dataset increases. For this reason, it is important to have efficient computational methods and algorithms that can be applied on large datasets, such that it is still possible to complete the machine learning tasks in reasonable time. In this context, we present in this paper a more accurate simple process to speed up ML methods. An unsupervised clustering algorithm is combined with Expectation, Maximization (EM) algorithm to develop an effici…
In pursuit of explainability, we develop generative models for sequential data. The proposed models provide state-of-the-art classification results and robust performance for speech phone classification. We combine modern neural networks (normalizing flows) and traditional generative models (hidden Markov models - HMMs). Normalizing flow-based mixture models (NMMs) are used to model the conditional probability distribution given the hidden state in the HMMs. Model parameters are learned through judicious combinations of time-tested Bayesian learning methods and contemporary neural network lear…
Sequence analysis is being more and more widely used for the analysis of social sequences and other multivariate categorical time series data. However, it is often complex to describe, visualize, and compare large sequence data, especially when there are multiple parallel sequences per subject. Hidden (latent) Markov models (HMMs) are able to detect underlying latent structures and they can be used in various longitudinal settings: to account for measurement error, to detect unobservable states, or to compress information across several types of observations. Extending to mixture hidden Markov…
The recurrent neural networks (RNN) with richly distributed internal states and flexible non-linear transition functions, have overtaken the dynamic Bayesian networks such as the hidden Markov models (HMMs) in the task of modeling highly structured sequential data. These data, such as from speech and handwriting, often contain complex relationships between the underlaying variational factors and the observed data. The standard RNN model has very limited randomness or variability in its structure, coming from the output conditional probability model. This paper will present different ways of us…
Institut FEMTO-ST（FEMTO-ST研究所）；Université Bourgogne Franche-Comté（勃艮第-弗朗什-孔泰大学）；Université de technologie de Compiègne（贡比涅技术大学）；CNRS（法国国家科学研究中心）；Heudiasyc（Heudiasyc实验室）；Institut universitaire de France（法兰西大学研究院）
The interpretation of unlabeled acoustic emission (AE) data classically relies on general-purpose clustering methods. While several external criteria have been used in the past to select the hyperparameters of those algorithms, few studies have paid attention to the development of dedicated objective functions in clustering methods able to cope with the specificities of AE data. We investigate how to explicitly represent clusters onsets in mixture models in general, and in Gaussian Mixture Models (GMM) in particular. By modifying the internal criterion of such models, we propose the first clus…
We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman's coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottom-up agglomerative fashion. We show experimentally the superiority of our algorithms over others, and demonstrate our approach in document clustering and phylolinguistics.
University of Michigan（密歇根大学）；Duke University（杜克大学）
Analysis of heterogeneous patterns in complex spatio-temporal data finds usage across various domains in applied science and engineering, including training autonomous vehicles to navigate in complex traffic scenarios. Motivated by applications arising in the transportation domain, in this paper we develop a model for learning heterogeneous and dynamic patterns of velocity field data. We draw from basic nonparameric Bayesian modeling elements such as hierarchical Dirichlet process and infinite hidden Markov model, while the smoothness of each homogeneous velocity field element is captured with…
State University of New York (SUNY) at Buffalo（纽约州立大学布法罗分校）
Most existing approaches to clustering gene expression time course data treat the different time points as independent dimensions and are invariant to permutations, such as reversal, of the experimental time course. Approaches utilizing HMMs have been shown to be helpful in this regard, but are hampered by having to choose model architectures with appropriate complexities. Here we propose for a clustering application an HMM with a countably infinite state space; inference in this model is possible by recasting it in the hierarchical Dirichlet process (HDP) framework (Teh et al. 2006), and henc…
KTH Royal Institute of Technology（KTH皇家理工学院）；Karolinska Institute（卡罗林斯卡学院）
Hidden Markov model (HMM) has been successfully used for sequential data modeling problems. In this work, we propose to power the modeling capacity of HMM by bringing in neural network based generative models. The proposed model is termed as GenHMM. In the proposed GenHMM, each HMM hidden state is associated with a neural network based generative model that has tractability of exact likelihood and provides efficient likelihood computation. A generative model in GenHMM consists of mixture of generators that are realized by flow models. A learning algorithm for GenHMM is proposed in expectation-…
ENSTA Bretagne（布列塔尼国立高等先进技术学校）；Université Européenne de Bretagne（布列塔尼欧洲大学）；Université Paris Descartes（巴黎笛卡尔大学）
Hidden Markov Models (HMMs) are a ubiquitous tool to model time series data, and have been widely used in two main tasks of Automatic Music Transcription (AMT): note segmentation, i.e. identifying the played notes after a multi-pitch estimation, and sequential post-processing, i.e. correcting note segmentation using training data. In this paper, we employ the multi-pitch estimation method called Probabilistic Latent Component Analysis (PLCA), and develop AMT systems by integrating different HMM-based modules in this framework. For note segmentation, we use two different twostate on/o? HMMs, in…
Bilkent University（比尔肯特大学）；DataBoss A. S.（DataBoss股份公司）
We investigate nonlinear regression for nonstationary sequential data. In most real-life applications such as business domains including finance, retail, energy and economy, timeseries data exhibits nonstationarity due to the temporally varying dynamics of the underlying system. We introduce a novel recurrent neural network (RNN) architecture, which adaptively switches between internal regimes in a Markovian way to model the nonstationary nature of the given data. Our model, Markovian RNN employs a hidden Markov model (HMM) for regime transitions, where each regime controls hidden state transi…
As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We focus on recurrent neural networks, state of the art models in speech recognition and translation. Our approach to increasing interpretability is by combining a long short-term memory (LSTM) model with a hidden Markov model (HMM), a simpler and more transparent model. We add the HMM state probabilities to the output layer of the LSTM, and then train the HMM…
Phoneme-based acoustic modeling of large vocabulary automatic speech recognition takes advantage of phoneme context. The large number of context-dependent (CD) phonemes and their highly varying statistics require tying or smoothing to enable robust training. Usually, classification and regression trees are used for phonetic clustering, which is standard in hidden Markov model (HMM)-based systems. However, this solution introduces a secondary training objective and does not allow for end-to-end training. In this work, we address a direct phonetic context modeling for the hybrid deep neural netw…
Engineering, KTH Royal Institute of Technology, Stockholm, Sweden Dept. Women's；Children's Health, Karolinska Institutet, Stockholm, Sweden
We explore the use of traditional and contemporary hidden Markov models (HMMs) for sequential physiological data analysis and sepsis prediction in preterm infants. We investigate the use of classical Gaussian mixture model based HMM, and a recently proposed neural network based HMM. To improve the neural network based HMM, we propose a discriminative training approach. Experimental results show the potential of HMMs over logistic regression, support vector machine and extreme learning machine.
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；UC Riverside（加州大学河滨分校）
This paper presents new parallel algorithms for generating Euclidean minimum spanning trees and spatial clustering hierarchies (known as HDBSCAN$^*$). Our approach is based on generating a well-separated pair decomposition followed by using Kruskal's minimum spanning tree algorithm and bichromatic closest pair computations. We introduce a new notion of well-separation to reduce the work and space of our algorithm for HDBSCAN$^*$. We also present a parallel approximate algorithm for OPTICS based on a recent sequential algorithm by Gan and Tao. Finally, we give a new parallel divide-and-conquer …
Discovery and recognition of Group Activities (GA) based on imagery data processing have significant applications in persistent surveillance systems, which play an important role in some Internet services. The process is involved with analysis of sequential imagery data with spatiotemporal associations. Discretion of video imagery requires a proper inference system capable of discriminating and differentiating cohesive observations and interlinking them to known ontologies. We propose an Ontology based GAR with a proper inference model that is capable of identifying and classifying a sequence …
Cyprus University of Technology（塞浦路斯理工大学）；National and Kapodistrian University of Athens（雅典大学）；Aalborg University（奥尔堡大学）
Hidden Markov Models (HMMs) comprise a powerful generative approach for modeling sequential data and time-series in general. However, the commonly employed assumption of the dependence of the current time frame to a single or multiple immediately preceding frames is unrealistic; more complicated dynamics potentially exist in real world scenarios. This paper revisits conventional sequential modeling approaches, aiming to address the problem of capturing time-varying temporal dependency patterns. To this end, we propose a different formulation of HMMs, whereby the dependence on past frames is dy…
Machine learning and data mining techniques have been used extensively in order to detect credit card frauds. However, most studies consider credit card transactions as isolated events and not as a sequence of transactions. In this article, we model a sequence of credit card transactions from three different perspectives, namely (i) does the sequence contain a Fraud? (ii) Is the sequence obtained by fixing the card-holder or the payment terminal? (iii) Is it a sequence of spent amount or of elapsed time between the current and previous transactions? Combinations of the three binary perspective…
Qualcomm Institute, University of California, San Diego（加州大学圣地亚哥分校高通研究所）；Ben Gurion University（本·古里安大学）
We study k-median clustering under the sequential no-substitution setting. In this setting, a data stream is sequentially observed, and some of the points are selected by the algorithm as cluster centers. However, a point can be selected as a center only immediately after it is observed, before observing the next point. In addition, a selected center cannot be substituted later. We give the first algorithm for this setting that obtains a constant approximation factor on the optimal risk under a random arrival order, an exponential improvement over previous work. This is also the first constant…
Technical University of Vienna（维也纳技术大学）；Boston University（波士顿大学）；University of Guelph（圭尔夫大学）；Vector Institute for Artificial Intelligence（向量人工智能研究所）；University of Texas, Austin（德克萨斯大学奥斯汀分校）
Interaction graphs, such as those recording emails between individuals or transactions between institutions, tend to be sparse yet structured, and often grow in an unbounded manner. Such behavior can be well-captured by structured, nonparametric edge-exchangeable graphs. However, such exchangeable models necessarily ignore temporal dynamics in the network. We propose a dynamic nonparametric model for interaction graphs that combine the sparsity of the exchangeable models with dynamic clustering patterns that tend to reinforce recent behavioral patterns. We show that our method yields improved …
We study the sample-based k-median clustering objective under a sequential setting without substitutions. In this setting, an i.i.d. sequence of examples is observed. An example can be selected as a center only immediately after it is observed, and it cannot be substituted later. The goal is to select a set of centers with a good k-median cost on the distribution which generated the sequence. We provide an efficient algorithm for this setting, and show that its multiplicative approximation factor is twice the approximation factor of an efficient offline algorithm. In addition, we show that if …
McGill University（麦吉尔大学）；MILA（蒙特利尔学习算法研究所）；Université de Montréal（蒙特利尔大学）
Weighted finite automata (WFAs) have been widely applied in many fields. One of the classic problems for WFAs is probability distribution estimation over sequences of discrete symbols. Although WFAs have been extended to deal with continuous input data, namely continuous WFAs (CWFAs), it is still unclear how to approximate density functions over sequences of continuous random variables using WFA-based models, due to the limitation on the expressiveness of the model as well as the tractability of approximating density functions via CWFAs. In this paper, we propose a nonlinear extension to the C…
Universidad Carlos III de Madrid（马德里卡洛斯三世大学）；Escuela Politécnica Superior（高等理工学院）
This paper proposes a novel similarity measure for clustering sequential data. We first construct a common state-space by training a single probabilistic model with all the sequences in order to get a unified representation for the dataset. Then, distances are obtained attending to the transition matrices induced by each sequence in that state-space. This approach solves some of the usual overfitting and scalability issues of the existing semi-parametric techniques, that rely on training a model for each sequence. Empirical studies on both synthetic and real-world datasets illustrate the advan…
INESC TEC（INESC TEC（葡萄牙系统与计算机工程研究所））；University of Porto（波尔图大学）
We propose a framework to model the distribution of sequential data coming from a set of entities connected in a graph with a known topology. The method is based on a mixture of shared hidden Markov models (HMMs), which are jointly trained in order to exploit the knowledge of the graph structure and in such a way that the obtained mixtures tend to be sparse. Experiments in different application domains demonstrate the effectiveness and versatility of the method.
An efficient solution to Hidden Markov Models on trees with coupled branches
Center of Mathematical Sciences and Applications, Harvard University（哈佛大学数学科学与应用中心）；Dana-Farber Cancer Institute（丹娜法伯癌症研究院）；Harvard Medical School（哈佛医学院）；Broad Institute of MIT and Harvard（麻省理工学院与哈佛大学布罗德研究所）
Hidden Markov models (HMMs) are widely used statistical models for modeling sequential data. The parameter estimation for HMMs from time series data is an important learning problem. The predominant methods for parameter estimation are based on local search heuristics, most notably the expectation-maximization (EM) algorithm. These methods are prone to local optima and oftentimes suffer from high computational and sample complexity. Recent years saw the emergence of spectral methods for the parameter estimation of HMMs, based on a method of moments approach. Two spectral learning algorithms as…
University of California San Diego（加利福尼亚大学圣迭戈分校）；University of Wisconsin（威斯康星大学）
We consider the task of learning mappings from sequential data to real-valued responses. We present and evaluate an approach to learning a type of hidden Markov model (HMM) for regression. The learning process involves inferring the structure and parameters of a conventional HMM, while simultaneously learning a regression model that maps features that characterize paths through the model to continuous responses. Our results, in both synthetic and biological domains, demonstrate the value of jointly learning the two components of our approach.
Telecom SudParis（南巴黎电信学院）；Institut Polytechnique de Paris（巴黎综合理工学院）；IBM GSB France（IBM法国全球业务咨询服务部）；Watson Department（沃森部门）
Nowadays, neural network models achieve state-of-the-art results in many areas as computer vision or speech processing. For sequential data, especially for Natural Language Processing (NLP) tasks, Recurrent Neural Networks (RNNs) and their extensions, the Long Short Term Memory (LSTM) network and the Gated Recurrent Unit (GRU), are among the most used models, having a "term-to-term" sequence processing. However, if many works create extensions and improvements of the RNN, few have focused on developing other ways for sequential data processing with neural networks in a "term-to-term" way. This…
Contraction Clustering (RASTER): A Very Fast Big Data Algorithm for Sequential and Parallel Density-Based Clustering in Linear Time, Constant Memory, and a Single Pass
Fraunhofer-Chalmers Research Centre for Industrial Mathematics（弗劳恩霍夫-查尔默斯工业数学研究中心）；Fraunhofer Center for Machine Learning（弗劳恩霍夫机器学习中心）
A wide range of Bayesian models have been proposed for data that is divided hierarchically into groups. These models aim to cluster the data at different levels of grouping, by assigning a mixture component to each datapoint, and a mixture distribution to each group. Multi-level clustering is facilitated by the sharing of these components and distributions by the groups. In this paper, we introduce the concept of Degree of Sharing (DoS) for the mixture components and distributions, with an aim to analyze and classify various existing models. Next we introduce a generalized hierarchical Bayesia…
South China University of Technology（华南理工大学）；Institute for Infocomm Research（资讯通信研究院）；Peng Cheng Laboratory（鹏城实验室）
Deploying models on target domain data subject to distribution shift requires adaptation. Test-time training (TTT) emerges as a solution to this adaptation under a realistic scenario where access to full source domain data is not available and instant inference on target domain is required. Despite many efforts into TTT, there is a confusion over the experimental settings, thus leading to unfair comparisons. In this work, we first revisit TTT assumptions and categorize TTT protocols by two key factors. Among the multiple protocols, we adopt a realistic sequential test-time training (sTTT) prot…
