This paper introduces a new similarity measure, the covering similarity, which we formally define for evaluating the similarity between a symbolic sequence and a set of symbolic sequences. A pairwise similarity can also be directly derived from the covering similarity to compare two symbolic sequences. An efficient implementation to compute the covering similarity is proposed which uses a suffix-tree data structure, but other implementations, based on suffix array for instance, are possible and are possibly necessary for handling very large-scale problems. We have used this similarity to isolate attack sequences from normal sequences in the scope of host-based intrusion detection. We have assessed the covering similarity on two well-known benchmarks in the field. In view of the results reported on these two datasets for the state-of-the-art methods, according to the comparative study, we have carried out based on three challenging similarity measures commonly used for string processing, or in bioinformatics, we show that the covering similarity is particularly relevant to address the detection of anomalies in sequences of system calls.
, essentially Hidden Markov Models (HMM) @cite_50 @cite_32 @cite_12 , Conditional random Fields (CRF) @cite_45 @cite_36 or Recurrent Neural Networks (RNN, LSTM, etc.) @cite_13 @cite_38 have been used with apparent success on various intrusion detection tasks, such as payload analysis or Network Layer Intrusion Detection or HIDS. However, the choice of parameters such as the order of the Markovian dependency, number of hidden variables, etc., is often the result of a compromise to avoid over-fitting, and long-term dependency is not necessarily easily modeled.
@cite_38 @cite_36 @cite_32 @cite_45 @cite_50 @cite_13 @cite_12
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We have already shown that extracting long-term dependencies from sequential data is difficult, both for determimstic dynamical systems such as recurrent networks, and probabilistic models such as hidden Markov models (HMMs) or input output hidden Markov models (IOHMMs). In practice, to avoid this problem, researchers have used domain specific a-priori knowledge to give meaning to the hidden or state variables representing past context. In this paper, we propose to use a more general type of a-priori knowledge, namely that the temporal dependencies are structured hierarchically. This implies that long-term dependencies are represented by variables with a long time scale. This principle is applied to a recurrent network which includes delays and multiple time scales. Experiments confirm the advantages of such structures. A similar approach is proposed for HMMs and IOHMMs. Hidden Markov models (HMMs) have during the last decade become a widespread tool for modeling sequences of dependent random variables. Inference for such models is usually based on the maximum-likelihood estimator (MLE), and consistency of the MLE for general HMMs was recently proved by Leroux. In this paper we show that under mild conditions the MLE is also asymptotically normal and prove that the observed information matrix is a consistent estimator of the Fisher information. Hidden Markov models (HMMs) have proven to be one of the most widely used tools for learning probabilistic models of time series data. In an HMM, information about the past is conveyed through a single discrete variable—the hidden state. We discuss a generalization of HMMs in which this state is factored into multiple state variables and is therefore represented in a distributed manner. We describe an exact algorithm for inferring the posterior probabilities of the hidden state variables given the observations, and relate it to the forward–backward algorithm for HMMs and to algorithms for more general graphical models. Due to the combinatorial nature of the hidden state representation, this exact algorithm is intractable. As in other intractable systems, approximate inference can be carried out using Gibbs sampling or variational methods. Within the variational framework, we present a structured approximation in which the the state variables are decoupled, yielding a tractable algorithm for learning the parameters of the model. Empirical comparisons suggest that these approximations are efficient and provide accurate alternatives to the exact methods. Finally, we use the structured approximation to model Bach‘s chorales and show that factorial HMMs can capture statistical structure in this data set which an unconstrained HMM cannot. We consider finite state space stationary hidden Markov models (HMMs) in the situation where the number of hidden states is unknown. We provide a frequentist asymptotic evaluation of Bayesian analysis methods. Our main result gives posterior concentration rates for the marginal densities, that is for the density of a fixed number of consecutive observations. Using conditions on the prior, we are then able to define a consistent Bayesian estimator of the number of hidden states. It is known that the likelihood ratio test statistic for overfitted HMMs has a nonstandard behaviour and is unbounded. Our conditions on the prior may be seen as a way to penalize parameters to avoid this phenomenon. Inference of parameters is a much more difficult task than inference of marginal densities, we still provide a precise description of the situation when the observations are i.i.d. and we allow for 2 possible hidden states. In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations. The emission distributions are often supposed to belong to some parametric family. In this paper, a semiparametric model where the emission distributions are a mixture of parametric distributions is proposed to get a higher flexibility. We show that the standard EM algorithm can be adapted to infer the model parameters. For the initialization step, starting from a large number of components, a hierarchical method to combine them into the hidden states is proposed. Three likelihood-based criteria to select the components to be combined are discussed. To estimate the number of hidden states, BIC-like criteria are derived. A simulation study is carried out both to determine the best combination between the combining criteria and the model selection criteria and to evaluate the accuracy of classification. The proposed method is also illustrated using a biological dataset from the model plant Arabidopsis thaliana. A R package HMMmix is freely available on the CRAN. Hidden Markov model speech recognition systems typically use Gaussian mixture models to estimate the distributions of decorrelated acoustic feature vectors that correspond to individual subword units. By contrast, hybrid connectionist-HMM systems use discriminatively-trained neural networks to estimate the probability distribution among subword units given the acoustic observations. In this work we show a large improvement in word recognition performance by combining neural-net discriminative feature processing with Gaussian-mixture distribution modeling. By training the network to generate the subword probability posteriors, then using transformations of these estimates as the base features for a conventionally-trained Gaussian-mixture based system, we achieve relative error rate reductions of 35 or more on the multicondition Aurora noisy continuous digits task. The problem of estimating the number of hidden states in a hidden Markov model is considered. Emphasis is placed on cross-validated likelihood criteria. Using cross-validation to assess the number of hidden states allows to circumvent the well-documented technical difficulties of the order identification problem in mixture models. Moreover, in a predictive perspective, it does not require that the sampling distribution belongs to one of the models in competition. However, computing cross-validated likelihood for hidden Markov models for which only one training sample is available, involves difficulties since the data are not independent. Two approaches are proposed to compute cross-validated likelihood for a hidden Markov model. The first one consists of using a deterministic half-sampling procedure, and the second one consists of an adaptation of the EM algorithm for hidden Markov models, to take into account randomly missing values induced by cross-validation. Numerical experiments on both simulated and real data sets compare different versions of cross-validated likelihood criterion and penalised likelihood criteria, including BIC and a penalised marginal likelihood criterion. Those numerical experiments highlight a promising behaviour of the deterministic half-sampling criterion. Recently, hidden Markov models (HMMs) have achieved promising results for offline handwritten Chinese text recognition. However, due to the large vocabulary of Chinese characters with each modeled by a uniform and fixed number of hidden states, a high demand of memory and computation is required. In this study, to address this issue, we present parsimonious HMMs via the state tying which can fully utilize the similarities among different Chinese characters. Two-step algorithm with the data-driven question-set is adopted to generate the tied-state pool using the likelihood measure. The proposed parsimonious HMMs with both Gaussian mixture models (GMMs) and deep neural networks (DNNs) as the emission distributions not only lead to a compact model but also improve the recognition accuracy via the data sharing for the tied states and the confusion decreasing among state classes. Tested on ICDAR-2013 competition database, in the best configured case, the new parsimonious DNN-HMM can yield a relative character error rate (CER) reduction of 6.2 , 25 reduction of model size and 60 reduction of decoding time over the conventional DNN-HMM. In the compact setting case of average 1-state HMM, our parsimonious DNN-HMM significantly outperforms the conventional DNN-HMM with a relative CER reduction of 35.5 . We present algorithms for recognizing human motion in monocular video sequences, based on discriminative conditional random field (CRF) and maximum entropy Markov models (MEMM). Existing approaches to this problem typically use generative (joint) structures like the hidden Markov model (HMM). Therefore they have to make simplifying, often unrealistic assumptions on the conditional independence of observations given the motion class labels and cannot accommodate overlapping features or long term contextual dependencies in the observation sequence. In contrast, conditional models like the CRFs seamlessly represent contextual dependencies, support efficient, exact inference using dynamic programming, and their parameters can be trained using convex optimization. We introduce conditional graphical models as complementary tools for human motion recognition and present an extensive set of experiments that show how these typically outperform HMMs in classifying not only diverse human activities like walking, jumping. running, picking or dancing, but also for discriminating among subtle motion styles like normal walk and wander walk Hidden Markov models (HMMs) are a powerful probabilistic tool for modeling sequential data, and have been applied with success to many text-related tasks, such as part-of-speech tagging, text segmentation and information extraction. In these cases, the observations are usually modeled as multinomial distributions over a discrete vocabulary, and the HMM parameters are set to maximize the likelihood of the observations. This paper presents a new Markovian sequence model, closely related to HMMs, that allows observations to be represented as arbitrary overlapping features (such as word, capitalization, formatting, part-of-speech), and defines the conditional probability of state sequences given observation sequences. It does this by using the maximum entropy framework to fit a set of exponential models that represent the probability of a state given an observation and the previous state. We present positive experimental results on the segmentation of FAQ’s. This paper proposes an effective segmentation-free approach using a hybrid neural network hidden Markov model (NN-HMM) for offline handwritten Chinese text recognition (HCTR). In the general Bayesian framework, the handwritten Chinese text line is sequentially modeled by HMMs with each representing one character class, while the NN-based classifier is adopted to calculate the posterior probability of all HMM states. The key issues in feature extraction, character modeling, and language modeling are comprehensively investigated to show the effectiveness of NN-HMM framework for offline HCTR. First, a conventional deep neural network (DNN) architecture is studied with a well-designed feature extractor. As for the training procedure, the label refinement using forced alignment and the sequence training can yield significant gains on top of the frame-level cross-entropy criterion. Second, a deep convolutional neural network (DCNN) with automatically learned discriminative features demonstrates its superiority to DNN in the HMM framework. Moreover, to solve the challenging problem of distinguishing quite confusing classes due to the large vocabulary of Chinese characters, NN-based classifier should output 19900 HMM states as the classification units via a high-resolution modeling within each character. On the ICDAR 2013 competition task of CASIA-HWDB database, DNN-HMM yields a promising character error rate (CER) of 5.24 by making a good trade-off between the computational complexity and recognition accuracy. To the best of our knowledge, DCNN-HMM can achieve a best published CER of 3.53 . Recent works have shown that exploiting multi-scale representations deeply learned via convolutional neural networks (CNN) is of tremendous importance for accurate contour detection. This paper presents a novel approach for predicting contours which advances the state of the art in two fundamental aspects, i.e. multi-scale feature generation and fusion. Different from previous works directly considering multi-scale feature maps obtained from the inner layers of a primary CNN architecture, we introduce a hierarchical deep model which produces more rich and complementary representations. Furthermore, to refine and robustly fuse the representations learned at different scales, the novel Attention-Gated Conditional Random Fields (AG-CRFs) are proposed. The experiments ran on two publicly available datasets (BSDS500 and NYUDv2) demonstrate the effectiveness of the latent AG-CRF model and of the overall hierarchical framework. Hidden Markov Models (HMMs) are one of the most fundamental and widely used statistical tools for modeling discrete time series. In general, learning HMMs from data is computationally hard (under cryptographic assumptions), and practitioners typically resort to search heuristics which suffer from the usual local optima issues. We prove that under a natural separation condition (bounds on the smallest singular value of the HMM parameters), there is an efficient and provably correct algorithm for learning HMMs. The sample complexity of the algorithm does not explicitly depend on the number of distinct (discrete) observations-it implicitly depends on this quantity through spectral properties of the underlying HMM. This makes the algorithm particularly applicable to settings with a large number of observations, such as those in natural language processing where the space of observation is sometimes the words in a language. The algorithm is also simple, employing only a singular value decomposition and matrix multiplications. Dynamic Probabilistic Networks (DPNs) are exploited for modeling the temporal relationships among a set of different object temporal events in the scene for a coherent and robust scene-level behaviour interpretation. In particular, we develop a Dynamically Multi-Linked Hidden Markov Model (DML-HMM) to interpret group activities involving multiple objects captured in an outdoor scene. The model is based on the discovery of salient dynamic interlinks among multiple temporal events using DPNs. Object temporal events are detected and labeled using Gaussian Mixture Models with automatic model order selection. A DML-HMM is built using Schwarz's Bayesian Information Criterion based factorisation resulting in its topology being intrinsically determined by the underlying causality and temporal order among different object events. Our experiments demonstrate that its performance on modelling group activities in a noisy outdoor scene is superior compared to that of a Multi-Observation Hidden Markov Model (MOHMM), a Parallel Hidden Markov Model (PaHMM) and a Coupled Hidden Markov Model (CHMM). The statistical use of a particular classic form of a connectionist system, the multilayer perceptron (MLP), is described in the context of the recognition of continuous speech. A discriminant hidden Markov model (HMM) is defined, and it is shown how a particular MLP with contextual and extra feedback input units can be considered as a general form of such a Markov model. A link between these discriminant HMMs, trained along the Viterbi algorithm, and any other approach based on least mean square minimization of an error function (LMSE) is established. It is shown theoretically and experimentally that the outputs of the MLP (when trained along the LMSE or the entropy criterion) approximate the probability distribution over output classes conditioned on the input, i.e. the maximum a posteriori probabilities. Results of a series of speech recognition experiments are reported. The possibility of embedding MLP into HMM is described. Relations with other recurrent networks are also explained. > We propose a novel context-dependent (CD) model for large-vocabulary speech recognition (LVSR) that leverages recent advances in using deep belief networks for phone recognition. We describe a pre-trained deep neural network hidden Markov model (DNN-HMM) hybrid architecture that trains the DNN to produce a distribution over senones (tied triphone states) as its output. The deep belief network pre-training algorithm is a robust and often helpful way to initialize deep neural networks generatively that can aid in optimization and reduce generalization error. We illustrate the key components of our model, describe the procedure for applying CD-DNN-HMMs to LVSR, and analyze the effects of various modeling choices on performance. Experiments on a challenging business search dataset demonstrate that CD-DNN-HMMs can significantly outperform the conventional context-dependent Gaussian mixture model (GMM)-HMMs, with an absolute sentence accuracy improvement of 5.8 and 9.2 (or relative error reduction of 16.0 and 23.2 ) over the CD-GMM-HMMs trained using the minimum phone error rate (MPE) and maximum-likelihood (ML) criteria, respectively. Dynamic Bayesian networks such as Hidden Markov Models (HMMs) are successfully used as probabilistic models for human motion. The use of hidden variables makes them expressive models, but inference is only approximate and requires procedures such as particle filters or Markov chain Monte Carlo methods. In this work we propose to instead use simple Markov models that only model observed quantities. We retain a highly expressive dynamic model by using interactions that are nonlinear and non-parametric. A presentation of our approach in terms of latent variables shows logarithmic growth for the computation of exact log-likelihoods in the number of latent states. We validate our model on human motion capture data and demonstrate state-of-the-art performance on action recognition and motion completion tasks. Hidden Markov modeling (HMM) techniques have been used successfully for connected speech recognition in the last several years. In the traditional HMM algorithms, the probability of duration of a state decreases exponentially with time which is not appropriate for representing the temporal structure of speech. Non-parametric modeling of duration using semi-Markov chains does accomplish the task with a large increase in the computational complexity. Applying a postprocessing state duration penalty after Viterbi decoding adds very little computation but does not affect the forward recognition path. The authors present a way of modeling state durations in HMM using time-dependent state transitions. This inhomogeneous HMM (IHMM) does increase the computation by a small amount but reduces recognition error rates by 14-25 . Also, a suboptimal implementation of this scheme that requires no more computation than the traditional HMM is presented which also has reduced errors by 14-22 on a variety of databases. > The context-independent deep belief network (DBN) hidden Markov model (HMM) hybrid architecture has recently achieved promising results for phone recognition. In this work, we propose a context-dependent DBN-HMM system that dramatically outperforms strong Gaussian mixture model (GMM)-HMM baselines on a challenging, large vocabulary, spontaneous speech recognition dataset from the Bing mobile voice search task. Our system achieves absolute sentence accuracy improvements of 5.8 and 9.2 over GMM-HMMs trained using the minimum phone error rate (MPE) and maximum likelihood (ML) criteria, respectively, which translate to relative error reductions of 16.0 and 23.2 . Acoustic models used in hidden Markov model neural-network (HMM NN) speech recognition systems are usually trained with a frame-based cross-entropy error criterion. In contrast, Gaussian mixture HMM systems are discriminatively trained using sequence-based criteria, such as minimum phone error or maximum mutual information, that are more directly related to speech recognition accuracy. This paper demonstrates that neural-network acoustic models can be trained with sequence classification criteria using exactly the same lattice-based methods that have been developed for Gaussian mixture HMMs, and that using a sequence classification criterion in training leads to considerably better performance. A neural network acoustic model with 153K weights trained on 50 hours of broadcast news has a word error rate of 34.0 on the rt04 English broadcast news test set. When this model is trained with the state-level minimum Bayes risk criterion, the rt04 word error rate is 27.7 .