Modeling Sequential Data Research Articles

State duration and interval modeling in hidden semi-Markov model for sequential data analysis

Sequential data modeling and analysis have become indispensable tools for analyzing sequential data, such as time-series data, because larger amounts of sensed event data have become available. These methods capture the sequential structure of data of interest, such as input-output relations and correlation among datasets. However, because most studies in this area are specialized or limited to their respective applications, rigorous requirement analysis of such models has not been undertaken from a general perspective. Therefore, we particularly examine the structure of sequential data, and extract the necessity of `state duration' and `state interval' of events for efficient and rich representation of sequential data. Specifically addressing the hidden semi-Markov model (HSMM) that represents such state duration inside a model, we attempt to add representational capability of a state interval of events onto HSMM. To this end, we propose two extended models: an interval state hidden semi-Markov model (IS-HSMM) to express the length of a state interval with a special state node designated as "interval state node"; and an interval length probability hidden semi-Markov model (ILP-HSMM) which represents the length of the state interval with a new probabilistic parameter "interval length probability." Exhaustive simulations have revealed superior performance of the proposed models in comparison with HSMM. These proposed models are the first reported extensions of HMM to support state interval representation as well as state duration representation.

Evaluation of Recurrent Neural Network and its Variants for Intrusion Detection System IDS

This article describes how sequential data modeling is a relevant task in Cybersecurity. Sequences are attributed temporal characteristics either explicitly or implicitly. Recurrent neural networks...

Evaluation of Recurrent Neural Network and its Variants for Intrusion Detection System (IDS)

This article describes how sequential data modeling is a relevant task in Cybersecurity. Sequences are attributed temporal characteristics either explicitly or implicitly. Recurrent neural networks (RNNs) are a subset of artificial neural networks (ANNs) which have appeared as a powerful, principle approach to learn dynamic temporal behaviors in an arbitrary length of large-scale sequence data. Furthermore, stacked recurrent neural networks (S-RNNs) have the potential to learn complex temporal behaviors quickly, including sparse representations. To leverage this, the authors model network traffic as a time series, particularly transmission control protocol / internet protocol (TCP/IP) packets in a predefined time range with a supervised learning method, using millions of known good and bad network connections. To find out the best architecture, the authors complete a comprehensive review of various RNN architectures with its network parameters and network structures. Ideally, as a test bed, they use the existing benchmark Defense Advanced Research Projects Agency / Knowledge Discovery and Data Mining (DARPA) / (KDD) Cup ‘99' intrusion detection (ID) contest data set to show the efficacy of these various RNN architectures. All the experiments of deep learning architectures are run up to 1000 epochs with a learning rate in the range [0.01-0.5] on a GPU-enabled TensorFlow and experiments of traditional machine learning algorithms are done using Scikit-learn. Experiments of families of RNN architecture achieved a low false positive rate in comparison to the traditional machine learning classifiers. The primary reason is that RNN architectures are able to store information for long-term dependencies over time-lags and to adjust with successive connection sequence information. In addition, the effectiveness of RNN architectures are shown for the UNSW-NB15 data set.

A hidden Markov model with dependence jumps for predictive modeling of multidimensional time-series

Hidden Markov models (HMMs) are a popular approach for modeling sequential data, typically based on the assumption of a first- or moderate-order Markov chain. However, in many real-world scenarios the modeled data entail temporal dynamics the patterns of which change over time. In this paper, we address this problem by proposing a novel HMM formulation, treating temporal dependencies as latent variables over which inference is performed. Specifically, we introduce a hierarchical graphical model comprising two hidden layers: on the first layer, we postulate a chain of latent observation-emitting states, the temporal dependencies between which may change over time; on the second layer, we postulate a latent first-order Markov chain modeling the evolution of temporal dynamics (dependence jumps) pertaining to the first-layer latent process. As a result of this construction, our method allows for effectively modeling non-homogeneous observed data, where the patterns of the entailed temporal dynamics may change over time. We devise efficient training and inference algorithms for our model, following the expectation-maximization paradigm. We demonstrate the efficacy and usefulness of our approach considering several real-world datasets.

Learning to Monitor Machine Health with Convolutional Bi-Directional LSTM Networks.

In modern manufacturing systems and industries, more and more research efforts have been made in developing effective machine health monitoring systems. Among various machine health monitoring approaches, data-driven methods are gaining in popularity due to the development of advanced sensing and data analytic techniques. However, considering the noise, varying length and irregular sampling behind sensory data, this kind of sequential data cannot be fed into classification and regression models directly. Therefore, previous work focuses on feature extraction/fusion methods requiring expensive human labor and high quality expert knowledge. With the development of deep learning methods in the last few years, which redefine representation learning from raw data, a deep neural network structure named Convolutional Bi-directional Long Short-Term Memory networks (CBLSTM) has been designed here to address raw sensory data. CBLSTM firstly uses CNN to extract local features that are robust and informative from the sequential input. Then, bi-directional LSTM is introduced to encode temporal information. Long Short-Term Memory networks (LSTMs) are able to capture long-term dependencies and model sequential data, and the bi-directional structure enables the capture of past and future contexts. Stacked, fully-connected layers and the linear regression layer are built on top of bi-directional LSTMs to predict the target value. Here, a real-life tool wear test is introduced, and our proposed CBLSTM is able to predict the actual tool wear based on raw sensory data. The experimental results have shown that our model is able to outperform several state-of-the-art baseline methods.

Convolutional bidirectional long short-term memory hidden Markov model hybrid system for polyphonic sound event detection

In this study, we propose a polyphonic sound event detection method based on a hybrid system of Convolutional Bidirectional Long Short-Term Memory Recurrent Neural Network and Hidden Markov Model (CBLSTM-HMM). Inspired by the state-of-the-art approach to integrating neural networks to HMM in speech recognition, the proposed method develops the hybrid system using CBLSTM to estimate the HMM state output probability, making it possible to model sequential data while handling its duration change. The proposed hybrid system is capable of detecting a segment of each sound event without post-processing, such as a smoothing process of detection results over multiple frames, usually required in the frame-wise detection methods. Moreover, we can easily apply it to a multi-label classification problem to achieve polyphonic sound event detection. We conduct experimental evaluations using the DCASE2016 task two dataset to compare the performance of the proposed method to that of the conventional methods, such as non-...

A Nonstationary Hidden Markov Model with Approximately Infinitely-Long Time-Dependencies

Hidden Markov models (HMMs) are a popular approach for modeling sequential data, typically based on the assumption of a first-order Markov chain. In other words, only one-step back dependencies are modeled which is a rather unrealistic assumption in most applications. In this paper, we propose a method for postulating HMMs with approximately infinitely-long time-dependencies. Our approach considers the whole history of model states in the postulated dependencies, by making use of a recently proposed nonparametric Bayesian method for modeling label sequences with infinitely-long time dependencies, namely the sequence memoizer. We manage to derive training and inference algorithms for our model with computational costs identical to simple first-order HMMs, despite its entailed infinitely-long time-dependencies, by employing a mean-field-like approximation. The efficacy of our proposed model is experimentally demonstrated.

A Sequential Regression Model for Big Data with Attributive Explanatory Variables

As the applications for modeling of big data and analysis advance in scope, computational efficiency faces greater challenges in terms of storage and speed. In many practical problems, a great amount of historical data is sequentially collected and used for online statistical modeling. For modeling sequential data, we propose a sequential linear regression method that extracts essential information from historical data. This carefully selected information is then utilized to update a model according to a sequential estimation scheme. With this technique, the earlier data no longer needs to be stored, and the sequential updating is computationally efficient in speed and storage. A weighted strategy is introduced on the current model to determine the impact of data from different periods. When compared with estimation methods that use historical data, our numerical experiments demonstrate that our solution increases the speed while decreasing the storage load.

Riemannian metrics for neural networks II: recurrent networks and learning symbolic data sequences

Recurrent neural networks are powerful models for sequential data, able to represent complex dependencies in the sequence that simpler models such as hidden Markov models cannot handle. Yet they are notoriously hard to train. Here we introduce a training procedure using a gradient ascent in a Riemannian metric: this produces an algorithm independent from design choices such as the encoding of parameters and unit activities. This metric gradient ascent is designed to have an algorithmic cost close to backpropagation through time for sparsely connected networks. We use this procedure on \emph{gated leaky neural networks} (GLNNs), a variant of recurrent neural networks with an architecture inspired by finite automata and an evolution equation inspired by continuous-time networks. GLNNs trained with a Riemannian gradient are demonstrated to effectively capture a variety of structures in synthetic problems: basic block nesting as in context-free grammars (an important feature of natural languages, but difficult to learn), intersections of multiple independent Markov-type relations, or long-distance relationships such as the distant-XOR problem. This method does not require adjusting the network structure or initial parameters: the network used is a sparse random graph and the initialization is identical for all problems considered.

Sequential Dependence Modeling Using Bayesian Theory and D-Vine Copula and Its Application on Chemical Process Risk Prediction

An emerging kind of prediction model for sequential data with multiple time series is proposed. Because D-vine copula provides more flexibility in dependence modeling, accounting for conditional dependence, asymmetries, and tail dependence, it is employed to describe sequential dependence between variables in the sample data. A D-vine model with the form of a time window is created to fit the correlation of variables well. To describe the randomness dynamically, Bayesian theory is also applied. As an application, a detailed modeling of prediction of abnormal events in a chemical process is given. Statistics (e.g., mean, variance, skewness, kurtosis, confidence interval, etc.) of the posterior predictive distribution are obtained by Markov chain Monte Carlo simulation. It is shown that the model created in this paper achieves a prediction performance better than that of some other system identification methods, e.g., autoregressive moving average model and back propagation neural network.

Echo-State Conditional Restricted Boltzmann Machines

Restricted Boltzmann machines (RBMs) are a powerful generative modeling technique, based on a complex graphical model of hidden (latent) variables. Conditional RBMs (CRBMs) are an extension of RBMs tailored to modeling temporal data. A drawback of CRBMs is their consideration of linear temporal dependencies, which limits their capability to capture complex temporal structure. They also require many variables to model long temporal dependencies, a fact that might provoke overfitting proneness. To resolve these issues, in this paper we propose the echo-state CRBM (ES-CRBM): our model uses an echo-state network reservoir in the context of CRBMs to efficiently capture long and complex temporal dynamics, with much fewer trainable parameters compared to conventional CRBMs. In addition, we introduce an (implicit) mixture of ES-CRBM experts (im-ES-CRBM) to enhance even further the capabilities of our ES-CRBM model. The introduced im-ES-CRBM allows for better modeling temporal observations which might comprise a number of latent or observable subpatterns that alternate in a dynamic fashion. It also allows for performing sequence segmentation using our framework. We apply our methods to sequential data modeling and classification experiments using public datasets. As we show, our approach outperforms both existing RBM-based approaches as well as related state-of-the-art methods, such as conditional random fields.

Formal model of time point-based sequential data for OLAP-like analysis

Abstract Numerous nowadays applications generate huge sets of data, whose natural feature is order, e.g,. sensor installations, RFID devices, workflow systems, Website monitors, health care applications. By analyzing the data and their order dependencies one can acquire new knowledge. However, nowadays commercial BI technologies and research prototypes allow to analyze mostly set oriented data, neglecting their order (sequential) dependencies. Few approaches to analyzing data of sequential nature have been proposed so far and all of them lack a comprehensive data model being able to represent and analyze sequential dependencies. In this paper, we propose a formal model for time point-based sequential data. The main elements of this model include an event and a sequence of events. Measures are associated with events and sequences. Measures are analyzed in the context set up by dimensions in an OLAP-like manner by means of the set of operations. The operations in our model are categorized as: operations on sequences, on dimensions, general operations, and analytical functions.

Automatic 3D Model Annotation by a Two-Dimensional Hidden Markov Model

In this paper, a new method of 3D model automatic annotation is proposed based on a two-dimensional Hidden Markov Model(2-D HMM). Growing importance in the last years Hidden Markov Models are a widely used methodology for sequential data modeling. Recent years, HMMs are applied to research of automatic annotation, such as images and models annotation. The three basic problems with HMM-liked model are also solved in our model. Our modeling process has two steps, those are training and testing. In the proposed approach, each object is separated into several bins by a spiderweb model and a shape function D2 is computed for each bin. These feature vectors are then arranged in a sequential fashion to compose a sequence vector, which is used to train HMMs. In 2-D HMM, we assume that feature vectors are statistically dependent on an underlying state process which has transition probabilities conditioning the states of two neighboring bins. Thus the dependency of two dimensions is reflected simultaneously. To classify an object, the maximized posteriori probability is calculated by a given model and the observed sequence of an unknown object. Comparing with the general HMM, 2-D HMM gets more information from the neighboring bins. So the system of 2-D HMM performs well on images and model annotation. Analysis and experimental results show that the proposed approach performs better than existing ones in database. DOI : http://dx.doi.org/10.11591/telkomnika.v12i5.4946

3D Object Classification Using a Two-Dimensional Hidden Markov Model

In this paper, we develop a novel method of 3D object classification based on a Two-Dimensional Hidden Markov Model (2D HMM). Hidden Markov Models are a widely used methodology for sequential data modeling, of growing importance in the last years. In the proposed approach, each object is decomposed by a spiderweb model and a shape function D2 is computed for each bin. These feature vectors are then arranged in a sequential fashion to compose a sequence vector, which is used to train HMMs. In 2D HMM, we assume that feature vectors are statistically dependent on an underlying state process which has transition probabilities conditioning the states of two neighboring bins. Thus the dependency of two dimensions is reflected simultaneously. To classify an object, the maximized posteriori probability is calculated by a given model and the observed sequence of an unknown object. Comparing with 1D HMM, the 2D HMM gets more information from the neighboring bins. Analysis and experimental results show that the proposed approach performs better than existing ones in database.

The Infinite-Order Conditional Random Field Model for Sequential Data Modeling

Sequential data labeling is a fundamental task in machine learning applications, with speech and natural language processing, activity recognition in video sequences, and biomedical data analysis being characteristic examples, to name just a few. The conditional random field (CRF), a log-linear model representing the conditional distribution of the observation labels, is one of the most successful approaches for sequential data labeling and classification, and has lately received significant attention in machine learning as it achieves superb prediction performance in a variety of scenarios. Nevertheless, existing CRF formulations can capture only one- or few-timestep interactions and neglect higher order dependences, which are potentially useful in many real-life sequential data modeling applications. To resolve these issues, in this paper we introduce a novel CRF formulation, based on the postulation of an energy function which entails infinitely long time-dependences between the modeled data. Building blocks of our novel approach are: 1) the sequence memoizer (SM), a recently proposed nonparametric Bayesian approach for modeling label sequences with infinitely long time dependences, and 2) a mean-field-like approximation of the model marginal likelihood, which allows for the derivation of computationally efficient inference algorithms for our model. The efficacy of the so-obtained infinite-order CRF (CRF(∞)) model is experimentally demonstrated.

Margin-maximizing classification of sequential data with infinitely-long temporal dependencies

Generative models for sequential data are usually based on the assumption of temporal dependencies described by a first-order Markov chain. To ameliorate this shallow modeling assumption, several authors have proposed models with higher-order dependencies. However, the practical applicability of these approaches is hindered by their prohibitive computational costs in most cases. In addition, most existing approaches give rise to model training algorithms with objective functions that entail multiple spurious local optima, thus requiring application of tedious countermeasures to avoid getting trapped to bad model estimates. In this paper, we devise a novel margin-maximizing model with convex objective function that allows for capturing infinitely-long temporal dependencies in sequential datasets. This is effected by utilizing a recently proposed nonparametric Bayesian model of label sequences with infinitely-long temporal dependencies, namely the sequence memoizer, and training our model using margin maximization and a versatile mean-field-like approximation to allow for increased computational efficiency. As we experimentally demonstrate, the devised margin-maximizing construction of our model, which leads to a convex optimization scheme, without any spurious local optima, combined with the capacity of our model to capture long and complex temporal dependencies, allow for obtaining exceptional pattern recognition performance in several applications.

A reservoir-driven non-stationary hidden Markov model

In this work, we propose a novel approach towards sequential data modeling that leverages the strengths of hidden Markov models and echo-state networks (ESNs) in the context of non-parametric Bayesian inference approaches. We introduce a non-stationary hidden Markov model, the time-dependent state transition probabilities of which are driven by a high-dimensional signal that encodes the whole history of the modeled observations, namely the state vector of a postulated observations-driven ESN reservoir. We derive an efficient inference algorithm for our model under the variational Bayesian paradigm, and we examine the efficacy of our approach considering a number of sequential data modeling applications.

On equivalent parameter learning in simplified feature space based on Bayesian asymptotic analysis

Parametric models for sequential data, such as hidden Markov models, stochastic context-free grammars, and linear dynamical systems, are widely used in time-series analysis and structural data analysis. Computation of the likelihood function is one of primary considerations in many learning methods. Iterative calculation of the likelihood such as the model selection is still time-consuming though there are effective algorithms based on dynamic programming. The present paper studies parameter learning in a simplified feature space to reduce the computational cost. Simplifying data is a common technique seen in feature selection and dimension reduction though an oversimplified space causes adverse learning results. Therefore, we mathematically investigate a condition of the feature map to have an asymptotically equivalent convergence point of estimated parameters, referred to as the vicarious map. As a demonstration to find vicarious maps, we consider the feature space, which limits the length of data, and derive a necessary length for parameter learning in hidden Markov models.

The echo state conditional random field model for sequential data modeling

Sequential data labeling is a fundamental task in machine learning applications, with speech and natural language processing, activity recognition in video sequences, and biomedical data analysis being characteristic such examples, to name just a few. The conditional random field (CRF), a log-linear model representing the conditional distribution of the observation labels, is one of the most successful approaches for sequential data labeling and classification, and has lately received significant attention in machine learning, as it achieves superb prediction performance in a variety of scenarios. Nevertheless, existing CRF formulations do not account for temporal dependencies between the observed variables – they only postulate Markovian interdependencies between the predicted label variables. To resolve these issues, in this paper we propose a non-linear hierarchical CRF formulation that combines the power of echo state networks to extract high level temporal features with the graphical framework of CRF models, yielding a powerful and scalable probabilistic model that we apply to signal labeling tasks.

The copula echo state network

Echo state networks (ESNs) constitute a novel approach to recurrent neural network (RNN) training, with an RNN (the reservoir) being generated randomly, and only a readout being trained using a simple, computationally efficient algorithm. ESNs have greatly facilitated the practical application of RNNs, outperforming classical approaches on a number of benchmark tasks. This paper studies the formulation of a class of copula-based semiparametric models for sequential data modeling, characterized by nonparametric marginal distributions modeled by postulating suitable echo state networks, and parametric copula functions that help capture all the scale-free temporal dependence of the modeled processes. We provide a simple algorithm for the data-driven estimation of the marginal distribution and the copula parameters of our model under the maximum-likelihood framework. We exhibit the merits of our approach by considering a number of applications; as we show, our method offers a significant enhancement in the dynamical data modeling capabilities of ESNs, without significant compromises in the algorithm's computational efficiency.