Variable Order Markov Models Research Articles

Synthesis of Longitudinal Human Location Sequences: Balancing Utility and Privacy

People’s location data are continuously tracked from various devices and sensors, enabling an ongoing analysis of sensitive information that can violate people’s privacy and reveal confidential information. Synthetic data have been used to generate representative location sequences yet to maintain the users’ privacy. Nonetheless, the privacy-accuracy tradeoff between these two measures has not been addressed systematically. In this article, we analyze the use of different synthetic data generation models for long location sequences, including extended short-term memory networks (LSTMs), Markov Chains (MC), and variable-order Markov models (VMMs). We employ different performance measures, such as data similarity and privacy, and discuss the inherent tradeoff. Furthermore, we introduce other measurements to quantify each of these measures. Based on the anonymous data of 300 thousand cellular-phone users, our work offers a road map for developing policies for synthetic data generation processes. We propose a framework for building data generation models and evaluating their effectiveness regarding those accuracy and privacy measures.

Complex event forecasting with prediction suffix trees

Complex event recognition (CER) systems have become popular in the past two decades due to their ability to “instantly” detect patterns on real-time streams of events. However, there is a lack of methods for forecasting when a pattern might occur before such an occurrence is actually detected by a CER engine. We present a formal framework that attempts to address the issue of complex event forecasting (CEF). Our framework combines two formalisms: (a) symbolic automata which are used to encode complex event patterns and (b) prediction suffix trees which can provide a succinct probabilistic description of an automaton’s behavior. We compare our proposed approach against state-of-the-art methods and show its advantage in terms of accuracy and efficiency. In particular, prediction suffix trees, being variable-order Markov models, have the ability to capture long-term dependencies in a stream by remembering only those past sequences that are informative enough. We also discuss how CEF solutions should be best evaluated on the quality of their forecasts.

Multivariate Time Series Clustering and its Application in Industrial Systems

Multivariate Time Series (MTS) data obtained from large scale systems carry resourceful information about the internal system status. Multivariate Time Series Clustering is one of the exploratory methods that can enable one to discover the different types of behavior that is manifested in different working periods of a system. This knowledge can then be used for tasks such as anomaly detection or system maintenance. In this study, we make use of the statistical method, Variable Order Markov Models (VOMMs) to model each individual MTS and employ a new metric to calculate the distances between those VOMMs. The pairwise distances are then used to accomplish the MTS Clustering task. Two other MTS Clustering methods are presented and the superiority of the proposed method is confirmed with the experiments on two data sets from Cyber-Physical Systems. The computational complexity of the presented methods is also discussed.

A framework for space-efficient variable-order Markov models.

Markov models with contexts of variable length are widely used in bioinformatics for representing sets of sequences with similar biological properties. When models contain many long contexts, existing implementations are either unable to handle genome-scale training datasets within typical memory budgets, or they are optimized for specific model variants and are thus inflexible. We provide practical, versatile representations of variable-order Markov models and of interpolated Markov models, that support a large number of context-selection criteria, scoring functions, probability smoothing methods, and interpolations, and that take up to four times less space than previous implementations based on the suffix array, regardless of the number and length of contexts, and up to ten times less space than previous trie-based representations, or more, while matching the size of related, state-of-the-art data structures from Natural Language Processing. We describe how to further compress our indexes to a quantity related to the redundancy of the training data, saving up to 90% of their space on very repetitive datasets, and making them become up to 60 times smaller than previous implementations based on the suffix array. Finally, we show how to exploit constraints on the length and frequency of contexts to further shrink our compressed indexes to half of their size or more, achieving data structures that are a hundred times smaller than previous implementations based on the suffix array, or more. This allows variable-order Markov models to be used with bigger datasets and with longer contexts on the same hardware, thus possibly enabling new applications. https://github.com/jnalanko/VOMM. Supplementary data are available at Bioinformatics online.

A Personal Location Prediction Method Based on Individual Trajectory and Group Trajectory

With the rapid development of communication technology, a large amount of spatiotemporal trajectory data has been produced. One of the critical applications of trajectory data is location prediction that is important for urban traffic planning and location-based services. Although many methods for personal location prediction have been proposed, to the best of our knowledge, some users always have sparse historical trajectory data in practical applications, resulting in poor location prediction precision. Targeting on this challenge, we propose an Individual Trajectory-Group Trajectory (ITGT) location prediction model by utilizing the pattern of group travels. First, the model performs the stay point extraction and conducts the spatial clustering to construct the clustering link. Second, Fano's inequality and clustering link are used to evaluate the predictability of location. Third, two variable order Markov models, named prediction by partial match (PPM) and probabilistic suffix tree (PST), are adopted to predict the clustering link. Finally, our approach is evaluated by using 608 712 points from 5000 volunteers at Shenzhen, China. The results show that: 1) when using individual trajectory, the PPM individual model is superior to the conventional N-order Markov model and PST individual model; 2) when all group trajectories are used, the PPM group model is not as accurate as the PPM individual model; and 3) when it classifies the group trajectory into different traffic zones, the PPM zone model is better than the PPM group model and the PPM individual model. The prediction precision of 1-3 order PPM zone model is 83.21%, 86.75%, and 87.35%, respectively, which introduces approximately 3% performance gains by utilizing the characters of traffic zone groups.

Design and Evaluation of Agents that Sequence and Juxtapose Short Musical Patterns in Real Time

AbstractWe present and discuss the Agent Designer, a system that enables users of digital audio workstations to generate novel high-level structures for their compositions based on previous examples. The system uses variable-order Markov models and rule induction to learn both temporal relations and structural relations between parts in a piece of music. As is usual in machine learning, however, the quality of the learning can be improved greatly by users specifying relevant features. The Agent Designer therefore points to important design and human–computer interaction problems, as well as algorithmic challenges. We present a number of studies that help to understand how effective the Agent Designer is and how we might design a user interface that best enables users to obtain quality results from the system. We show that the Agent Designer is effective for certain musical styles, such as loop-based electronic music, and that we as expert users can design agents that produce the most effective results. We also note that it remains a challenge to automate this process fully.

Maximum entropy models capture melodic styles

We introduce a Maximum Entropy model able to capture the statistics of melodies in music. The model can be used to generate new melodies that emulate the style of a given musical corpus. Instead of using the n–body interactions of (n−1)–order Markov models, traditionally used in automatic music generation, we use a k-nearest neighbour model with pairwise interactions only. In that way, we keep the number of parameters low and avoid over-fitting problems typical of Markov models. We show that long-range musical phrases don’t need to be explicitly enforced using high-order Markov interactions, but can instead emerge from multiple, competing, pairwise interactions. We validate our Maximum Entropy model by contrasting how much the generated sequences capture the style of the original corpus without plagiarizing it. To this end we use a data-compression approach to discriminate the levels of borrowing and innovation featured by the artificial sequences. Our modelling scheme outperforms both fixed-order and variable-order Markov models. This shows that, despite being based only on pairwise interactions, our scheme opens the possibility to generate musically sensible alterations of the original phrases, providing a way to generate innovation.

Cell-related location area planning for 4G PCS networks with variable-order Markov model

Location management is a critical issue in personal communication service (PCS) networks, tracking the location of user equipment (UE) with the goal of minimizing total signaling cost. Previous work can be classified into two categories: static and dynamic. Static schemes partition networks into fixed size LAs. However, these schemes are inefficient because they do not take UEs’ mobility and the call arrival rate into account. On the other hand, focusing on individual UEs, dynamic schemes have minimized the location management cost. However, they are difficult to implement because recording the individual information of numerous UEs and planning each of their LAs consume uncontrollable cost. Because of these reasons, we propose a cell-based scheme between static and dynamic schemes. Considering people usually stay in specific zones for long periods and the movement of UEs usually presents a strong moving direction in areas, this study presents a distributed algorithm by employing variable-order Markov models to find the mobility characteristic shared by UEs to plan better LAs with lower location management cost. When the order of Markov model is set to 1, our method is equal to a pure cell-centric LAP scheme; while the order of Markov model is high, it is more like a profile-based dynamic scheme. So, the setting of the order actually is a trade-off problem between the overall location management cost and the computing complexity. We present to retrieve a balance by using the expected location management cost and the number of total states of Markov models. In simulations, the origin–destination matrix (O–D matrix) from the Taipei Rapid Transit Corporation is used for representing the association between two cells. Simulation results demonstrate that the proposed scheme achieves good performance.

Small-world networks in neuronal populations: A computational perspective

The analysis of the brain in terms of integrated neural networks may offer insights on the reciprocal relation between structure and information processing. Even with inherent technical limits, many studies acknowledge neuron spatial arrangements and communication modes as key factors.In this perspective, we investigated the functional organization of neuronal networks by explicitly assuming a specific functional topology, the small-world network. We developed two different computational approaches. Firstly, we asked whether neuronal populations actually express small-world properties during a definite task, such as a learning task. For this purpose we developed the Inductive Conceptual Network (ICN), which is a hierarchical bio-inspired spiking network, capable of learning invariant patterns by using variable-order Markov models implemented in its nodes. As a result, we actually observed small-world topologies during learning in the ICN. Speculating that the expression of small-world networks is not solely related to learning tasks, we then built a de facto network assuming that the information processing in the brain may occur through functional small-world topologies. In this de facto network, synchronous spikes reflected functional small-world network dependencies. In order to verify the consistency of the assumption, we tested the null-hypothesis by replacing the small-world networks with random networks. As a result, only small world networks exhibited functional biomimetic characteristics such as timing and rate codes, conventional coding strategies and neuronal avalanches, which are cascades of bursting activities with a power-law distribution.Our results suggest that small-world functional configurations are liable to underpin brain information processing at neuronal level.

Computational investigations of small-worlds networks in neuronal populations

Event Abstract Back to Event Computational investigations of small-worlds networks in neuronal populations Antonio G. Zippo1*, Giuliana Gelsomino1, Sara Nencini1, Gian Carlo Caramenti2, Maurizio Valente1 and Gabriele E. Biella1 1 National Research Council, Institute of Molecular Bioimaging and Physiology, Italy 2 National Research Council, Institute of Biomedical Technologies, Italy The study of the brain as neuronal network allows gaining insights to the analysis of information processing [1]. Network interactions can play a crucial role in this scenario. In fact many studies identify in the modality of neuronal interaction the key of the problem, but limitations in neuronal recordings makes the clear mechanisms elusive [2-4]. In this perspective, we investigated the functional organization of neuronal networks hypothesizing that they work as small-world networks [5]. We developed two different computational approaches: in the first, we asked whether neuronal populations actually express small-world properties during a learning task. To this purpose we developed the Inductive Conceptual Network (ICN), a hierarchical bio-inspired spiking network, able to learn invariant patterns by Variable-order Markov Models implemented in its nodes [6]. We found that the ICN model expressed small-word networks during learning. As control, we exerted the ICN with random binary inputs, where no patterns can be learnt, and we obtained no small-world network functional organization among nodes. Conjecturing that the expression of small-world networks is not only related to learning, in the second part, we built the de facto network assuming that every information process in brain occurs exhibiting functionally a small-world network. In the de facto network the functional dependencies of the small-world networks, were reflected by synchronous spikes. From the analysis of spiking activity, versus the null hypothesis where small-world networks were replaced by random networks, we detected mainly three functional characteristics, observed in biological networks: timing and rate codes, conventional coding strategies [7], and the neuronal avalanches, cascades of bursting activities distributed as a power-law distribution [8]. Interestingly, rate and timing codes are thus allowed to coexist in the same network model yet in nodes at different hierarchical positions. Our results suggest that small-word functional configurations represent a milestone of brain information processing at the level of neurons. In conclusion, accordingly with other theoretical and experimental works, short path length and sparse connectivity may promote simultaneous performance of information segregation (information retention) and integration (generalization) within neuronal systems. Acknowledgements We thank Riccardo Storchi and Jianyi Lin for his helpful suggestions.

Modeling sequences of user actions for statistical goal recognition

User goals are of major importance for an interface agent because they serve as a context to define what the user's focus of attention is at a given moment. The user's goals should be detected as soon as possible, after observing few user actions, in order to provide the user with timely assistance. In this article, we describe an approach for modeling and recognizing user goals from observed sequences of user actions by using Variable Order Markov models combined with an exponential moving average (EMA) on the prediction probabilities. The validity of our approach has been tested using data collected from real users in the Unix domain. The results obtained show that an interface agent can achieve near 90% average accuracy and over 58% online accuracy in predicting the most probable user goal after each observed action, in a time linear to the number of goals being modeled. We also found that the use of an EMA allows a faster convergence in the actual user goal.

Method of the estimation of the parameters of a variable length Markov chain based on Fisher’s exact test

A method of the estimation of the parameters of a variable length Markov chain based on the use of Fisher’s exact test is proposed. The method has been applied to the problem of classification of convolutionally coded binary signals. Computer simulation has shown that the constructed models have a considerably smaller number of parameters as compared to the models based on the Kullbak-Leibler criterion, which is very popular in constructing variable-order Markov models.

RECOGNITION OF CIS-REGULATORY ELEMENTS WITH VOMBAT

Variable order Markov models and variable order Bayesian trees have been proposed for the recognition of cis-regulatory elements, and it has been demonstrated that they outperform traditional models such as position weight matrices, Markov models, and Bayesian trees for the recognition of binding sites in prokaryotes. Here, we study to which degree variable order models can improve the recognition of eukaryotic cis-regulatory elements. We find that variable order models can improve the recognition of binding sites of all the studied transcription factors. To ease a systematic evaluation of different model combinations based on problem-specific data sets and allow genomic scans of cis-regulatory elements based on fixed and variable order Markov models and Bayesian trees, we provide the VOMBATserver to the public community.

Using a VOM model for reconstructing potential coding regions in EST sequences

This paper presents a method for annotating coding and noncoding DNA regions by using variable order Markov (VOM) models. A main advantage in using VOM models is that their order may vary for different sequences, depending on the sequences' statistics. As a result, VOM models are more flexible with respect to model parameterization and can be trained on relatively short sequences and on low-quality datasets, such as expressed sequence tags (ESTs). The paper presents a modified VOM model for detecting and correcting insertion and deletion sequencing errors that are commonly found in ESTs. In a series of experiments the proposed method is found to be robust to random errors in these sequences.

Learning invariant features using inertial priors

We address the technical challenges involved in combining key features from several theories of the visual cortex in a single coherent model. The resulting model is a hierarchical Bayesian network factored into modular component networks embedding variable-order Markov models. Each component network has an associated receptive field corresponding to components residing in the level directly below it in the hierarchy. The variable-order Markov models account for features that are invariant to naturally occurring transformations in their inputs. These invariant features give rise to increasingly stable, persistent representations as we ascend the hierarchy. The receptive fields of proximate components on the same level overlap to restore selectivity that might otherwise be lost to invariance.

VOMBAT: prediction of transcription factor binding sites using variable order Bayesian trees

Variable order Markov models and variable order Bayesian trees have been proposed for the recognition of transcription factor binding sites, and it could be demonstrated that they outperform traditional models, such as position weight matrices, Markov models and Bayesian trees. We develop a web server for the recognition of DNA binding sites based on variable order Markov models and variable order Bayesian trees offering the following functionality: (i) given datasets with annotated binding sites and genomic background sequences, variable order Markov models and variable order Bayesian trees can be trained; (ii) given a set of trained models, putative DNA binding sites can be predicted in a given set of genomic sequences and (iii) given a dataset with annotated binding sites and a dataset with genomic background sequences, cross-validation experiments for different model combinations with different parameter settings can be performed. Several of the offered services are computationally demanding, such as genome-wide predictions of DNA binding sites in mammalian genomes or sets of 104-fold cross-validation experiments for different model combinations based on problem-specific data sets. In order to execute these jobs, and in order to serve multiple users at the same time, the web server is attached to a Linux cluster with 150 processors. VOMBAT is available at .

Bayesian classifiers for detecting HGT using fixed and variable order markov models of genomic signatures

Analyses of genomic signatures are gaining attention as they allow studies of species-specific relationships without involving alignments of homologous sequences. A naïve Bayesian classifier was built to discriminate between different bacterial compositions of short oligomers, also known as DNA words. The classifier has proven successful in identifying foreign genes in Neisseria meningitis. In this study we extend the classifier approach using either a fixed higher order Markov model (Mk) or a variable length Markov model (VLMk). We propose a simple algorithm to lock a variable length Markov model to a certain number of parameters and show that the use of Markov models greatly increases the flexibility and accuracy in prediction to that of a naïve model. We also test the integrity of classifiers in terms of false-negatives and give estimates of the minimal sizes of training data. We end the report by proposing a method to reject a false hypothesis of horizontal gene transfer. Software and Supplementary information available at www.cs.chalmers.se/~dalevi/genetic_sign_classifiers/.

Identification of transcription factor binding sites with variable-order Bayesian networks

We propose a new class of variable-order Bayesian network (VOBN) models for the identification of transcription factor binding sites (TFBSs). The proposed models generalize the widely used position weight matrix (PWM) models, Markov models and Bayesian network models. In contrast to these models, where for each position a fixed subset of the remaining positions is used to model dependencies, in VOBN models, these subsets may vary based on the specific nucleotides observed, which are called the context. This flexibility turns out to be of advantage for the classification and analysis of TFBSs, as statistical dependencies between nucleotides in different TFBS positions (not necessarily adjacent) may be taken into account efficiently--in a position-specific and context-specific manner. We apply the VOBN model to a set of 238 experimentally verified sigma-70 binding sites in Escherichia coli. We find that the VOBN model can distinguish these 238 sites from a set of 472 intergenic 'non-promoter' sequences with a higher accuracy than fixed-order Markov models or Bayesian trees. We use a replicated stratified-holdout experiment having a fixed true-negative rate of 99.9%. We find that for a foreground inhomogeneous VOBN model of order 1 and a background homogeneous variable-order Markov (VOM) model of order 5, the obtained mean true-positive (TP) rate is 47.56%. In comparison, the best TP rate for the conventional models is 44.39%, obtained from a foreground PWM model and a background 2nd-order Markov model. As the standard deviation of the estimated TP rate is approximately 0.01%, this improvement is highly significant.

On prediction using variable order Markov models

This paper is concerned with algorithms for prediction of discrete sequences over a finite alphabet, using variable order Markov models. The class of such algorithms is large and in principle inclu...

On Prediction Using Variable Order Markov Models

This paper is concerned with algorithms for prediction of discrete sequences over a finite alphabet, using variable order Markov models. The class of such algorithms is large and in principle includes any lossless compression algorithm. We focus on six prominent prediction algorithms, including Context Tree Weighting (CTW), Prediction by Partial Match (PPM) and Probabilistic Suffix Trees (PSTs). We discuss the properties of these algorithms and compare their performance using real life sequences from three domains: proteins, English text and music pieces. The comparison is made with respect to prediction quality as measured by the average log-loss. We also compare classification algorithms based on these predictors with respect to a number of large protein classification tasks. Our results indicate that a ``decomposed'' CTW (a variant of the CTW algorithm) and PPM outperform all other algorithms in sequence prediction tasks. Somewhat surprisingly, a different algorithm, which is a modification of the Lempel-Ziv compression algorithm, significantly outperforms all algorithms on the protein classification problems.