We introduce a framework for the modeling of sequential data capturing pathways of varying lengths observed in a network. Such data are important, e.g., when studying click streams in the Web, travel patterns in transportation systems, information cascades in social networks, biological pathways, or time-stamped social interactions. While it is common to apply graph analytics and network analysis to such data, recent works have shown that temporal correlations can invalidate the results of such methods. This raises a fundamental question: When is a network abstraction of sequential data justified?Addressing this open question, we propose a framework that combines Markov chains of multiple, higher orders into a multi-layer graphical model that captures temporal correlations in pathways at multiple length scales simultaneously. We develop a model selection technique to infer the optimal number of layers of such a model and show that it outperforms baseline Markov order detection techniques. An application to eight real-world data sets on pathways and temporal networks shows that it allows to infer graphical models that capture both topological and temporal characteristics of such data. Our work highlights fallacies of network abstractions and provides a principled answer to the open question when they are justified. Generalizing network representations to multi-order graphical models, it opens perspectives for new data mining and knowledge discovery algorithms.
The analysis of sequential data has important applications in areas like natural language processing, data compression, behavioral modeling or bioinformatics @cite_25 @cite_23 @cite_6 . Considering the focus of this paper, here we limit our review of the relevant literature to works addressing the modeling of (i) sequential data on pathways in graphs, or (ii) time-stamped data on temporal or dynamic graphs.
@cite_25 @cite_23 @cite_6
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Sequential data is being increasingly used in a variety of applications. Publishing sequential data is of vital importance to the advancement of these applications. However, as shown by the re-identification attacks on the AOL and Netflix datasets, releasing sequential data may pose considerable threats to individual privacy. Recent research has indicated the failure of existing sanitization techniques to provide claimed privacy guarantees. It is therefore urgent to respond to this failure by developing new schemes with provable privacy guarantees. Differential privacy is one of the only models that can be used to provide such guarantees. Due to the inherent sequentiality and high-dimensionality, it is challenging to apply differential privacy to sequential data. In this paper, we address this challenge by employing a variable-length n-gram model, which extracts the essential information of a sequential database in terms of a set of variable-length n-grams. Our approach makes use of a carefully designed exploration tree structure and a set of novel techniques based on the Markov assumption in order to lower the magnitude of added noise. The published n-grams are useful for many purposes. Furthermore, we develop a solution for generating a synthetic database, which enables a wider spectrum of data analysis tasks. Extensive experiments on real-life datasets demonstrate that our approach substantially outperforms the state-of-the-art techniques. Predicting personalized sequential behavior is a key task for recommender systems. In order to predict user actions such as the next product to purchase, movie to watch, or place to visit, it is essential to take into account both long-term user preferences and sequential patterns (i.e., short-term dynamics). Matrix Factorization and Markov Chain methods have emerged as two separate but powerful paradigms for modeling the two respectively. Combining these ideas has led to unified methods that accommodate long- and short-term dynamics simultaneously by modeling pairwise user-item and item-item interactions. In spite of the success of such methods for tackling dense data, they are challenged by sparsity issues, which are prevalent in real-world datasets. In recent years, similarity-based methods have been proposed for (sequentially-unaware) item recommendation with promising results on sparse datasets. In this paper, we propose to fuse such methods with Markov Chains to make personalized sequential recommendations. We evaluate our method, Fossil, on a variety of large, real-world datasets. We show quantitatively that Fossil outperforms alternative algorithms, especially on sparse datasets, and qualitatively that it captures personalized dynamics and is able to make meaningful recommendations. Predicting personalized sequential behavior is a key task for recommender systems. In order to predict user actions such as the next product to purchase, movie to watch, or place to visit, it is essential to take into account both long-term user preferences and sequential patterns (i.e., short-term dynamics). Matrix Factorization and Markov Chain methods have emerged as two separate but powerful paradigms for modeling the two respectively. Combining these ideas has led to unified methods that accommodate long-and short-term dynamics simultaneously by modeling pairwise user-item and item-item interactions. In spite of the success of such methods for tackling dense data, they are challenged by sparsity issues, which are prevalent in real-world datasets. In recent years, similarity-based methods have been proposed for (sequentially-unaware) item recommendation with promising results on sparse datasets. In this paper, we propose to fuse such methods with Markov Chains to make personalized sequential recommendations. We evaluate our method, Fossil, on a variety of large, real-world datasets. We show quantitatively that Fossil outperforms alternative algorithms, especially on sparse datasets, and qualitatively that it captures personalized dynamics and is able to make meaningful recommendations. We consider the problem of computing the convolution of two long vectors using parallel processing units in the presence of "stragglers". Stragglers refer to the small fraction of faulty or slow processors that delays the entire computation in time-critical distributed systems. We first show that splitting the vectors into smaller pieces and using a linear code to encode these pieces provides better resilience against stragglers than replication-based schemes under a simple, worst-case straggler analysis. We then demonstrate that under commonly used models of computation time, coding can dramatically improve the probability of finishing the computation within a target "deadline" time. As opposed to the more commonly used technique of expected computation time analysis, we quantify the exponents of the probability of failure in the limit of large deadlines. Our exponent metric captures the probability of failing to finish before a specified deadline time, i.e. , the behavior of the "tail". Moreover, our technique also allows for simple closed form expressions for more general models of computation time, e.g. shifted Weibull models instead of only shifted exponentials. Thus, through this problem of coded convolution, we establish the utility of a novel asymptotic failure exponent analysis for distributed systems. With the rapid growth of Internet applications, sequential prediction in collaborative filtering has become an emerging and crucial task. Given the behavioral history of a specific user, predicting his or her next choice plays a key role in improving various online services. Meanwhile, there are more and more scenarios with multiple types of behaviors, while existing works mainly study sequences with a single type of behavior. As a widely used approach, Markov chain based models are based on a strong independence assumption. As two classical neural network methods for modeling sequences, recurrent neural networks cannot well model short-term contexts, and the log-bilinear model is not suitable for long-term contexts. In this paper, we propose a Recurrent Log-BiLinear (RLBL) model. It can model multiple types of behaviors in historical sequences with behavior-specific transition matrices. RLBL applies a recurrent structure for modeling long-term contexts. It models several items in each hidden layer and employs position-specific transition matrices for modeling short-term contexts. Moreover, considering continuous time difference in behavioral history is a key factor for dynamic prediction, we further extend RLBL and replace position-specific transition matrices with time-specific transition matrices, and accordingly propose a Time-Aware Recurrent Log-BiLinear (TA-RLBL) model. Experimental results show that the proposed RLBL model and TA-RLBL model yield significant improvements over the competitive compared methods on three datasets, i.e., Movielens-1M dataset, Global Terrorism Database and Tmall dataset with different numbers of behavior types. Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences continuously measured by weather stations across the US. These data are often referred to as un structured. The first task in its analytics is to derive a low dimensional representation, a graph or discrete manifold, that describes well the inter relations among the time series and their intra relations across time. This paper presents a computationally tractable algorithm for estimating this graph that structures the data. The resulting graph is directed and weighted, possibly capturing causal relations, not just reciprocal correlations as in many existing approaches in the literature. A convergence analysis is carried out. The algorithm is demonstrated on random graph datasets and real network time series datasets, and its performance is compared to that of related methods. The adjacency matrices estimated with the new method are close to the true graph in the simulated data and consistent with prior physical knowledge in the real dataset tested. Sequential data often possesses a hierarchical structure with complex dependencies between subsequences, such as found between the utterances in a dialogue. In an effort to model this kind of generative process, we propose a neural network-based generative architecture, with latent stochastic variables that span a variable number of time steps. We apply the proposed model to the task of dialogue response generation and compare it with recent neural network architectures. We evaluate the model performance through automatic evaluation metrics and by carrying out a human evaluation. The experiments demonstrate that our model improves upon recently proposed models and that the latent variables facilitate the generation of long outputs and maintain the context. Deep autoregressive sequence-to-sequence models have demonstrated impressive performance across a wide variety of tasks in recent years. While several common architecture classes including recurrent, convolutional, and self-attention networks make different trade-offs between the amount of computation needed per layer and the length of the critical path at training time, inference for novel inputs still remains an inherently sequential process. We propose a novel blockwise parallel decoding scheme that takes advantage of the fact that some architectures can score sequences in sublinear time. By generating predictions for multiple time steps at once then backing off to the longest prefix validated by the scoring model, we can substantially improve the speed of greedy decoding without compromising performance. When tested on state-of-the-art self-attention models for machine translation and image super-resolution, our approach achieves iteration reductions of up to 2x over a baseline greedy decoder with no loss in quality. Relaxing the acceptance criterion and fine tuning model parameters allows for reductions of up to 7x in exchange for a slight decrease in performance. Our fastest models achieve a 4x speedup in wall-clock time. Sequential pattern mining is an important problem in data mining. State of the art techniques for mining sequential patterns, such as frequent subsequences, are often based on the pattern-growth approach, which recursively projects conditional databases. Explicitly creating database projections is thought to be a major computational bottleneck, but we will show in this paper that it can be beneficial when the appropriate data structure is used. Our technique uses a canonical directed acyclic graph as the sequence database representation, which can be represented as a binary decision diagram (BDD). In this paper, we introduce a new type of BDD, namely a sequence BDD (SeqBDD), and show how it can be used for efficiently mining frequent subsequences. A novel feature of the SeqBDD is its ability to share results between similar intermediate computations and avoid redundant computation. We perform an experimental study to compare the SeqBDD technique with existing pattern growth techniques, that are based on other data structures such as prefix trees. Our results show that a SeqBDD can be half as large as a prefix tree, especially when many similar sequences exist. In terms of mining time, it can be substantially more efficient when the support is low, the number of patterns is large, or the input sequences are long and highly similar. In the past few years there has been increased interest in using data-mining techniques to extract interesting patterns from time series data generated by sensors monitoring temporally varying phenomenon. Most work has assumed that raw data is somehow processed to generate a sequence of events, which is then mined for interesting episodes. In some cases the rule for determining when a sensor reading should generate an event is well known. However, if the phenomenon is ill-understood, stating such a rule is difficult. Detection of events in such an environment is the focus of this paper. Consider a dynamic phenomenon whose behavior changes enough over time to be considered a qualitatively significant change. The problem we investigate is of identifying the time points at which the behavior change occurs. In the statistics literature this has been called the change-point detection problem. The standard approach has been to (a) upriori determine the number of change-points that are to be discovered, and (b) decide the function that will be used for curve fitting in the interval between successive change-points. In this paper we generalize along both these dimensions. We propose an iterative algorithm that fits a model to a time segment, and uses a likelihood criterion to determine if the segment should be partitioned further, i.e. if it contains a new changepoint. In this paper we present algorithms for both the batch and incremental versions of the problem, and evaluate their behavior with synthetic and real data. Finally, we present initial results comparing the change-points detected by the batch algorithm with those detected by people using visual inspection. In a wide range of business areas dealing with text data streams, including CRM, knowledge management, and Web monitoring services, it is an important issue to discover topic trends and analyze their dynamics in real-time. Specifically we consider the following three tasks in topic trend analysis: 1)Topic Structure Identification; identifying what kinds of main topics exist and how important they are, 2)Topic Emergence Detection; detecting the emergence of a new topic and recognizing how it grows, 3)Topic Characterization; identifying the characteristics for each of main topics. For real topic analysis systems, we may require that these three tasks be performed in an on-line fashion rather than in a retrospective way, and be dealt with in a single framework. This paper proposes a new topic analysis framework which satisfies this requirement from a unifying viewpoint that a topic structure is modeled using a finite mixture model and that any change of a topic trend is tracked by learning the finite mixture model dynamically. In this framework we propose the usage of a time-stamp based discounting learning algorithm in order to realize real-time topic structure identification. This enables tracking the topic structure adaptively by forgetting out-of-date statistics. Further we apply the theory of dynamic model selection to detecting changes of main components in the finite mixture model in order to realize topic emergence detection. We demonstrate the effectiveness of our framework using real data collected at a help desk to show that we are able to track dynamics of topic trends in a timely fashion. Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. > We present a sequential model for temporal relation classification between intra-sentence events. The key observation is that the overall syntactic structure and compositional meanings of the multi-word context between events are important for distinguishing among fine-grained temporal relations. Specifically, our approach first extracts a sequence of context words that indicates the temporal relation between two events, which well align with the dependency path between two event mentions. The context word sequence, together with a parts-of-speech tag sequence and a dependency relation sequence that are generated corresponding to the word sequence, are then provided as input to bidirectional recurrent neural network (LSTM) models. The neural nets learn compositional syntactic and semantic representations of contexts surrounding the two events and predict the temporal relation between them. Evaluation of the proposed approach on TimeBank corpus shows that sequential modeling is capable of accurately recognizing temporal relations between events, which outperforms a neural net model using various discrete features as input that imitates previous feature based models. Given a large time-evolving graph, how can we model and characterize the temporal behaviors of individual nodes (and network states)? How can we model the behavioral transition patterns of nodes? We propose a temporal behavior model that captures the "roles" of nodes in the graph and how they evolve over time. The proposed dynamic behavioral mixed-membership model (DBMM) is scalable, fully automatic (no user-defined parameters), non-parametric data-driven (no specific functional form or parameterization), interpretable (identifies explainable patterns), and flexible (applicable to dynamic and streaming networks). Moreover, the interpretable behavioral roles are generalizable and computationally efficient. We applied our model for (a) identifying patterns and trends of nodes and network states based on the temporal behavior, (b) predicting future structural changes, and (c) detecting unusual temporal behavior transitions. The experiments demonstrate the scalability, flexibility, and effectiveness of our model for identifying interesting patterns, detecting unusual structural transitions, and predicting the future structural changes of the network and individual nodes. We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our model discovers a latent set of dynamical behaviors shared among the sequences, and segments each time series into regions defined by a subset of these behaviors. Using a beta process prior, the size of the behavior set and the sharing pattern are both inferred from data. We develop Markov chain Monte Carlo (MCMC) methods based on the Indian buffet process representation of the predictive distribution of the beta process. Our MCMC inference algorithm efficiently adds and removes behaviors via novel split-merge moves as well as data-driven birth and death proposals, avoiding the need to consider a truncated model. We demonstrate promising results on unsupervised segmentation of human motion capture data. 1. Introduction. Classical time series analysis has generally focused on the study of a single (potentially multivariate) time series. Instead, we consider analyzing collections of related time series, motivated by the increasing abundance of such data in many domains. In this work we explore this problem by considering time series produced by motion capture sensors on the joints of people performing exercise routines. An individual recording provides a multivariate time series that can be segmented into types of exercises (e.g., jumping jacks, arm-circles, and twists). Each exercise type describes locally coherent and simple dynamics that persist over a segment of time. We have such motion capture recordings from multiple individuals, each of whom performs some subset of a global set of exercises, as shown in Figure1. Our goal is to discover the set of global exercise types (“behaviors”) and their occurrences in each individual’s data stream. We would like to take advantage of the overlap between individuals: if a jumping-jack behavior is discovered in one sequence, then it can be used to model data for other individuals. Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diagnosis and prediction, design, hardware and software verification, and bioinformatics. These problems can be stated as the formal tasks of constraint satisfaction and satisfiability, combinatorial optimization, and probabilistic inference. It is well known that the tasks are computationally hard, but research during the past three decades has yielded a variety of principles and techniques that significantly advanced the state of the art. In this book we provide comprehensive coverage of the primary exact algorithms for reasoning with such models. The main feature exploited by the algorithms is the model's graph. We present inference-based, message-passing schemes (e.g., variable-elimination) and search-based, conditioning schemes (e.g., cycle-cutset conditioning and AND OR search). Each class possesses distinguished characteristics and in particular has different time vs. space behavior. We emphasize the dependence of both schemes on few graph parameters such as the treewidth, cycle-cutset, and (the pseudo-tree) height. We believe the principles outlined here would serve well in moving forward to approximation and anytime-based schemes. The target audience of this book is researchers and students in the artificial intelligence and machine learning area, and beyond. Table of Contents: Preface Introduction What are Graphical Models Inference: Bucket Elimination for Deterministic Networks Inference: Bucket Elimination for Probabilistic Networks Tree-Clustering Schemes AND OR Search Spaces and Algorithms for Graphical Models Combining Search and Inference: Trading Space for Time Conclusion Bibliography Author's Biography While the reconstruction of the control-flow graph of a binary has received wide attention, the challenge of categorizing code into defect-free and possibly incorrect remains a challenge for current static analyses. We present the intermediate language RREIL and a corresponding analysis framework that is able to infer precise numeric information on variables without resorting to an expensive analysis at the bit-level. Specifically, we propose a hierarchy of three interfaces to abstract domains, namely for inferring memory layout, bit-level information and numeric information. Our framework can be easily enriched with new abstract domains at each level. We demonstrate the extensibility of our framework by detailing a novel acceleration technique (a so-called widening) as an abstract domain that helps to find precise fix points of loops. We present a simple sequential sentence encoder for multi-domain natural language inference. Our encoder is based on stacked bidirectional LSTM-RNNs with shortcut connections and fine-tuning of word embeddings. The overall supervised model uses the above encoder to encode two input sentences into two vectors, and then uses a classifier over the vector combination to label the relationship between these two sentences as that of entailment, contradiction, or neural. Our Shortcut-Stacked sentence encoders achieve strong improvements over existing encoders on matched and mismatched multi-domain natural language inference (top non-ensemble single-model result in the EMNLP RepEval 2017 Shared Task (, 2017)). Moreover, they achieve the new state-of-the-art encoding result on the original SNLI dataset (, 2015). Celebrated and its fruitful variants are powerful models to achieve excellent performance on the tasks that map sequences to sequences. However, these are many machine learning tasks with inputs naturally represented in a form of graphs, which imposes significant challenges to existing Seq2Seq models for lossless conversion from its graph form to the sequence. In this work, we present a general end-to-end approach to map the input graph to a sequence of vectors, and then another attention-based LSTM to decode the target sequence from these vectors. Specifically, to address inevitable information loss for data conversion, we introduce a novel graph-to-sequence neural network model that follows the encoder-decoder architecture. Our method first uses an improved graph-based neural network to generate the node and graph embeddings by a novel aggregation strategy to incorporate the edge direction information into the node embeddings. We also propose an attention based mechanism that aligns node embeddings and decoding sequence to better cope with large graphs. Experimental results on bAbI task, Shortest Path Task, and Natural Language Generation Task demonstrate that our model achieves the state-of-the-art performance and significantly outperforms other baselines. We also show that with the proposed aggregation strategy, our proposed model is able to quickly converge to good performance. A fundamental problem in text data mining is to extract meaningful structure from document streams that arrive continuously over time. E-mail and news articles are two natural examples of such streams, each characterized by topics that appear, grow in intensity for a period of time, and then fade away. The published literature in a particular research field can be seen to exhibit similar phenomena over a much longer time scale. Underlying much of the text mining work in this area is the following intuitive premise—that the appearance of a topic in a document stream is signaled by a “burst of activity,” with certain features rising sharply in frequency as the topic emerges. The goal of the present work is to develop a formal approach for modeling such “bursts,” in such a way that they can be robustly and efficiently identified, and can provide an organizational framework for analyzing the underlying content. The approach is based on modeling the stream using an infinite-state automaton, in which bursts appear naturally as state transitionss it can be viewed as drawing an analogy with models from queueing theory for bursty network traffic. The resulting algorithms are highly efficient, and yield a nested representation of the set of bursts that imposes a hierarchical structure on the overall stream. Experiments with e-mail and research paper archives suggest that the resulting structures have a natural meaning in terms of the content that gave rise to them.