Risk-sensitive filtering and smoothing for hidden Markov models

In this paper, we address the problem of risk-sensitive filtering and smoothing for discrete-time Hidden Markov Models (HMM) with finite-discrete states. The objective of risk-sensitive filtering is to minimise the expectation of the exponential of the squared estimation error weighted by a risk-sensitive parameter. We use the so-called Reference Probability Method in solving this problem. We achieve finite-dimensional linear recursions in the information state, and thereby the state estimate that minimises the risk-sensitive cost index. Also, fixed-interval smoothing results are derived. We show that L₂ or risk-neutral filtering for HMMs can be extracted as a limiting case of the risk-sensitive filtering problem when the risk-sensitive parameter approaches zero.     

Relative Entropy and Error Bounds for Filtering of Markov Processes

This paper considers the relative entropy between the conditional distribution and an incorrectly initialized filter for the estimation of one component of a Markov process given observations of the second component. Using the Markov property, we first establish a decomposition of the relative entropy between the measures on observation path space associated to different initial conditions. Using this decomposition, it is shown that the relative entropy of the optimal filter relative to an incorrectly initialized filter is a positive supermartingale. By applying the decomposition to signals observed in additive, white noise, a relative entropy bound is obtained on the integrated, expected, mean square difference between the optimal and incorrectly initialized estimates of the observation function. Date received: October 6, 1997. Date revised: April 9, 1999.     

Private predictions on hidden Markov models

Hidden Markov models (HMMs) are widely used in practice to make predictions. They are becoming increasingly popular models as part of prediction systems in finance, marketing, bio-informatics, speech recognition, signal processing, and so on. However, traditional HMMs do not allow people and model owners to generate predictions without disclosing their private information to each other. To address the increasing needs for privacy, this work identifies and studies the private prediction problem; it is demonstrated with the following scenario: Bob has a private HMM, while Alice has a private input; and she wants to use Bob’s model to make a prediction based on her input. However, Alice does not want to disclose her private input to Bob, while Bob wants to prevent Alice from deriving information about his model. How can Alice and Bob perform HMMs-based predictions without violating their privacy? We propose privacy-preserving protocols to produce predictions on HMMs without greatly exposing Bob’s and Alice’s privacy. We then analyze our schemes in terms of accuracy, privacy, and performance. Since they are conflicting goals, due to privacy concerns, it is expected that accuracy or performance might degrade. However, our schemes make it possible for Bob and Alice to produce the same predictions efficiently while preserving their privacy.     

Exponential stability of discrete-time filters for bounded observation noise

This paper proves exponential asymptotic stability of discrete-time filters for the estimation of solutions to stochastic difference equations, when the observation noise is bounded. No assumption is made on the ergodicity of the signal. The proof uses the Hilbert projective metric, introduced into filter stability analysis by Atar and Zeitouni [1,2]. It is shown that when the signal noise is sufficiently regular, boundedness of the observation noise implies that the filter update operation is, on average, a strict contraction with respect to the Hilbert metric. Asymptotic stability then follows.     

Evolving the structure of hidden Markov models

A genetic algorithm (GA) is proposed for finding the structure of hidden Markov Models (HMMs) used for biological sequence analysis. The GA is designed to preserve biologically meaningful building blocks. The search through the space of HMM structures is combined with optimization of the emission and transition probabilities using the classic Baum-Welch algorithm. The system is tested on the problem of finding the promoter and coding region of C. jejuni. The resulting HMM has a superior discrimination ability to a handcrafted model that has been published in the literature.     

Asymptotical statistics of misspecified hidden Markov models

This paper deals with the problem of modeling data generated by an ergodic stochastic process as the output of a hidden Markov model (HMM). More specifically, we consider the problem of fitting a parametric family of HMM with continuous output to an ergodic stochastic process with continuous values, which does not necessarily belong to the family. In this context, we derive the main asymptotic results: almost sure consistency of the maximum likelihood estimator, asymptotic normality of the estimation error and the exact rates of almost sure convergence.     

Measure change estimates for hidden Markov models

Using a change of measure, the finite state observation process of a Markov chain is transformed into a sequence of independent random variables. By computing unnormalized conditional estimates under the new measure, simple, recursive formulate are obtained.     

Controlling eye movements with hidden Markov models

Advances in technology and in active vision research allow and encourage sequential visual information acquisition. Hidden Markov models (HMMs) can represent probabilistic sequences and probabilistic graph structures: here we explore their use in controlling the acquisition of visual information. We include a brief tutorial with two examples: (1) use input sequences to derive an aspect graph and (2) similarly derive a finite state machine for control of visual processing.The first main topic is the use of HMMs in both their learning and generative modes, and their augmentation to allow inputs sensed during generation to modify the generated outputs temporarily or permanently. We propose these augmented HMMs as a theory of adaptive skill acquisition and generation. The second main topic builds on the first: the augmented HMMs can be used for knowledge fusion. We give an example, the what-where-AHMM, which creates a hybrid skill from separate skills based on object location and object identity. Insofar as low-level skills can be learned from the output of high-level cognitive processes, AHMMs can provide a link between high-level and low-level vision.     

Masquerade detection using profile hidden Markov models

In this paper, we consider the problem of masquerade detection, based on user-issued UNIX commands. We present a novel detection technique based on profile hidden Markov models (PHMMs). For comparison purposes, we implement an existing modeling technique based on hidden Markov models (HMMs). We compare these approaches and show that, in general, our PHMM technique is competitive with HMMs. However, the standard test data set lacks positional information. We conjecture that such positional information would give our PHMM a significant advantage over HMM-based detection. To lend credence to this conjecture, we generate a simulated data set that includes positional information. Based on this simulated data, experimental results show that our PHMM-based approach outperforms other techniques when limited training data is available.     

Robot introspection through learned hidden Markov models

In this paper we describe a machine learning approach for acquiring a model of a robot behaviour from raw sensor data. We are interested in automating the acquisition of behavioural models to provide a robot with an introspective capability. We assume that the behaviour of a robot in achieving a task can be modelled as a finite stochastic state transition system.Beginning with data recorded by a robot in the execution of a task, we use unsupervised learning techniques to estimate a hidden Markov model (HMM) that can be used both for predicting and explaining the behaviour of the robot in subsequent executions of the task. We demonstrate that it is feasible to automate the entire process of learning a high quality HMM from the data recorded by the robot during execution of its task.The learned HMM can be used both for monitoring and controlling the behaviour of the robot. The ultimate purpose of our work is to learn models for the full set of tasks associated with a given problem domain, and to integrate these models with a generative task planner. We want to show that these models can be used successfully in controlling the execution of a plan. However, this paper does not develop the planning and control aspects of our work, focussing instead on the learning methodology and the evaluation of a learned model. The essential property of the models we seek to construct is that the most probable trajectory through a model, given the observations made by the robot, accurately diagnoses, or explains, the behaviour that the robot actually performed when making these observations. In the work reported here we consider a navigation task. We explain the learning process, the experimental setup and the structure of the resulting learned behavioural models. We then evaluate the extent to which explanations proposed by the learned models accord with a human observer's interpretation of the behaviour exhibited by the robot in its execution of the task.     

Speech recognition with continuous-parameter hidden Markov models

The acoustic modeling problem in automatic speech recognition is examined from an information-theoretic point of view. This problem is to design a speech-recognition system which can extract from the speech waveform as much information as possible about the corresponding word sequence. The information extraction process is broken down into two steps: a signal-processing step which converts a speech waveform into a sequence of information-bearing acoustic feature vectors, and a step which models such a sequence. We are primarily concerned with the use of hidden Markov models to model sequences of feature vectors which lie in a continuous space. We explore the trade-off between packing information into such sequences and being able to model them accurately. The difficulty of developing accurate models of continuous-parameter sequences is addressed by investigating a method of parameter estimation which is designed to cope with inaccurate modeling assumptions.     

Parametric hidden Markov models for gesture recognition

A method for the representation, recognition, and interpretation of parameterized gesture is presented. By parameterized gesture we mean gestures that exhibit a systematic spatial variation; one example is a point gesture where the relevant parameter is the two-dimensional direction. Our approach is to extend the standard hidden Markov model method of gesture recognition by including a global parametric variation in the output probabilities of the HMM states. Using a linear model of dependence, we formulate an expectation-maximization (EM) method for training the parametric HMM. During testing, a similar EM algorithm simultaneously maximizes the output likelihood of the PHMM for the given sequence and estimates the quantifying parameters. Using visually derived and directly measured three-dimensional hand position measurements as input, we present results that demonstrate the recognition superiority of the PHMM over standard HMM techniques, as well as greater robustness in parameter estimation with respect to noise in the input features. Finally, we extend the PHMM to handle arbitrary smooth (nonlinear) dependencies. The nonlinear formulation requires the use of a generalized expectation-maximization (GEM) algorithm for both training and the simultaneous recognition of the gesture and estimation of the value of the parameter. We present results on a pointing gesture, where the nonlinear approach permits the natural spherical coordinate parameterization of pointing direction     

Texture classification using noncausal hidden Markov models

This paper addresses the problem of using noncausal hidden Markov models (HMMs) for texture classification. In noncausal models, the state of each pixel may be dependent on its neighbors in all directions. New algorithms are given to learn the parameters of a noncausal HMM of a texture and to classify it into one of several learned categories. Texture classification results using these algorithms are provided     

Fire detection based on hidden Markov models

In this paper, a novel method of real-time fire detection based on HMMs is presented. First, we present an analysis of fire characteristics that provides evidence supporting the use of HMMs to detect fire; second, we propose an algorithm for detecting candidate fire pixels that entails the detection of moving pixels, fire-color inspection, and pixels clustering. The main contribution of this paper is the establishment and application of a hidden Markov fire model by combining the state transition between fire and non-fire with fire motion information to reduce data redundancy. The final decision is based on this model which includes training and application; the training provides parameters for the HMM application. The experimental results show that the method provides both a high detection rate and a low false alarm rate. Furthermore, real-time detection has been effectively realized via the learned parameters of the HMM, since the most time-consuming components such as HMM training are performed off-line.     

Denoising and recognition using hidden Markov models with observation distributions modeled by hidden Markov trees

Hidden Markov models have been found very useful for a wide range of applications in machine learning and pattern recognition. The wavelet transform has emerged as a new tool for signal and image analysis. Learning models for wavelet coefficients have been mainly based on fixed-length sequences, but real applications often require to model variable-length, very long or real-time sequences. In this paper, we propose a new learning architecture for sequences analyzed on short-term basis, but not assuming stationarity within each frame. Long-term dependencies will be modeled with a hidden Markov model which, in each internal state, will deal with the local dynamics in the wavelet domain, using a hidden Markov tree. The training algorithms for all the parameters in the composite model are developed using the expectation-maximization framework. This novel learning architecture could be useful for a wide range of applications. We detail two experiments with artificial and real data: model-based denoising and speech recognition. Denoising results indicate that the proposed model and learning algorithm are more effective than previous approaches based on isolated hidden Markov trees. In the case of the ‘Doppler’ benchmark sequence, with 1024 samples and additive white noise, the new method reduced the mean squared error from 1.0 to 0.0842. The proposed methods for feature extraction, modeling and learning, increased the phoneme recognition rates in 28.13%, with better convergence than models based on Gaussian mixtures.     

Storage workload modelling by hidden Markov models: Application to Flash memory

A workload analysis technique is presented that processes data from operation type traces and creates a hidden Markov model (HMM) to represent the workload that generated those traces. The HMM can be used to create representative traces for performance models, such as simulators, avoiding the need to repeatedly acquire suitable traces. It can also be used to estimate the transition probabilities and rates of a Markov modulated arrival process directly, for use as input to an analytical performance model of Flash memory. The HMMs obtained from industrial workloads-both synthetic benchmarks, preprocessed by a file translation layer, and real, time-stamped user traces-are validated by comparing their autocorrelation functions and other statistics with those of the corresponding monitored time series. Further, the performance model applications, referred to above, are illustrated by numerical examples.     

Similarity-based classification of sequences using hidden Markov models

Hidden Markov models (HMM) are a widely used tool for sequence modelling. In the sequence classification case, the standard approach consists of training one HMM for each class and then using a standard Bayesian classification rule. In this paper, we introduce a novel classification scheme for sequences based on HMMs, which is obtained by extending the recently proposed similarity-based classification paradigm to HMM-based classification. In this approach, each object is described by the vector of its similarities with respect to a predetermined set of other objects, where these similarities are supported by HMMs. A central problem is the high dimensionality of resulting space, and, to deal with it, three alternatives are investigated. Synthetic and real experiments show that the similarity-based approach outperforms standard HMM classification schemes.