Pseudolikelihood equations for Potts MRF model parameter estimation on higher order neighborhood systems

This letter presents pseudolikelihood equations for the estimation of the Potts Markov random field model parameter on higher order neighborhood systems. The derived equation for second-order systems is a significantly reduced version of a recent result found in the literature (from 67 to 22 terms). Also, with the proposed method, a completely original equation for Potts model parameter estimation in third-order systems was obtained. These equations allow the modeling of less restrictive contextual systems for a large number of applications in a computationally feasible way. Experiments with both simulated and real remote sensing images provided good results.

Bayesian Estimation of the Logistic Positive Exponent IRT Model

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric ICC treats both correct and incorrect answers symmetrically, which results in a logical contradiction in ordering examinees on the ability scale. A data set corresponding to a mathematical test applied in Peruvian public schools is analyzed, where comparisons with other parametric IRT models also are conducted. Several model comparison criteria are discussed and implemented. The main conclusion is that the LPE and RLPE IRT models are easy to implement and seem to provide the best fit to the data set considered.

Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.

Generalized pseudo-likelihood estimates for markov random fields on lattice

In this paper we generalize Besag's pseudo-likelihood function for spatial statistical models on a region of a lattice. The correspondingly defined maximum generalized pseudo-likelihood estimates (MGPLEs) are natural extensions of Besag's maximum pseudo-likelihood estimate (MPLE). The MGPLEs connect the MPLE and the maximum likelihood estimate. We carry out experimental calculations of the MGPLEs for spatial processes on the lattice. These simulation results clearly show better performances of the MGPLEs than the MPLE, and the performances of differently defined MGPLEs are compared. These are also illustrated by the application to two real data sets.

Using Normative Markov Decision Processes for Evaluating Electronic Contracts: A Case Study in a Simulated Aerospace Aftermarket

Before signing electronic contracts, a rational agent should estimate the expected utilities of these contracts and calculate the violation risks related to them. In order to perform such pre-signing procedures, this agent has to be capable of computing a policy taking into account the norms and sanctions in the contracts. In relation to this, the contribution of this work is threefold. First, we present the Normative Markov Decision Process, an extension of the Markov Decision Process for explicitly representing norms. In order to illustrate the usage of our framework, we model an example in a simulated aerospace aftermarket. Second, we specify an algorithm for identifying the states of the process which characterize the violation of norms. Finally, we show how to compute policies with our framework and how to calculate the risk of violating the norms in the contracts by adopting a particular policy.

A performance model of speculative prefetching in distributed information systems

Previous studies in speculative prefetching focus on building and evaluating access models for the purpose of access prediction. This paper investigates a complementary area which has been largely ignored, that of performance modelling. We use improvement in access time as the performance metric, for which we derive a formula in terms of resource parameters (time available and time required for prefetching) and speculative parameters (probabilities for next access). The performance maximization problem is expressed as a stretch knapsack problem. We develop an algorithm to maximize the improvement in access time by solving the stretch knapsack problem, using theoretically proven apparatus to reduce the search space. Integration between speculative prefetching and caching is also investigated, albeit under the assumption of equal item sizes.

The hidden permutation model and location-based activity recognition

Permutation modeling is challenging because of the combinatorial nature of the problem. However, such modeling is often required in many real-world applications, including activity recognition where subactivities are often permuted and partially ordered. This paper introduces a novel Hidden Permutation Model (HPM) that can learn the partial ordering constraints in permuted state sequences. The HPM is parameterized as an exponential family distribution and is flexible so that it can encode constraints via different feature functions. A chain-flipping Metropolis-Hastings Markov chain Monte Carlo (MCMC) is employed for inference to overcome the O(n!) complexity. Gradient-based maximum likelihood parameter learning is presented for two cases when the permutation is known and when it is hidden. The HPM is evaluated using both simulated and real data from a location-based activity recognition domain. Experimental results indicate that the HPM performs far better than other baseline models, including the naive Bayes classifier, the HMM classifier, and Kirshner's multinomial permutation model. Our presented HPM is generic and can potentially be utilized in any problem where the modeling of permuted states from noisy data is needed.

Content structure discovery in educational videos using shared structures in the hierarchical hidden Markov models

In this paper, we present an application of the hierarchical HMM for structure discovery in educational videos. The HHMM has recently been extended to accommodate the concept of shared structure, ie: a state might multiply inherit from more than one parents. Utilising the expressiveness of this model, we concentrate on a specific class of video -educational videos - in which the hierarchy of semantic units is simpler and clearly defined in terms of topics and its subunits. We model the hierarchy of topical structures by an HHMM and demonstrate the usefulness of the model in detecting topic transitions.

Learning people movement model from multiple cameras for behaviour recognition

In surveillance systems for monitoring people behaviours, it is important to build systems that can adapt to the signatures of people's tasks and movements in the environment. At the same time, it is important to cope with noisy observations produced by a set of cameras with possibly different characteristics. In previous work, we have implemented a distributed surveillance system designed for complex indoor environments [1]. The system uses the Abstract Hidden Markov mEmory Model (AHMEM) for modelling and specifying complex human behaviours that can take place in the environment. Given a sequence of observations from a set of cameras, the system employs approximate probabilistic inference to compute the likelihood of different possible behaviours in real-time. This paper describes the techniques that can be used to learn the different camera noise models and the human movement models to be used in this system. The system is able to monitor and classify people behaviours as data is being gathered, and we provide classification results showing the system is able to identify behaviours of people from their movement signatures.

Hierarchical semi-markov conditional random fields for recursive sequential data

Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of embedded undirected Markov chains to model complex hierarchical, nested Markov processes. It is parameterised in a discriminative framework and has polynomial time algorithms for learning and inference. Importantly, we develop efficient algorithms for learning and constrained inference in a partially-supervised setting, which is important issue in practice where labels can only be obtained sparsely. We demonstrate the HSCRF in two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show that the HSCRF is capable of learning rich hierarchical models with reasonable accuracy in both fully and partially observed data cases.

On the recognition of abstract Markov policies

Abstraction plays an essential role in the way the agents plan their behaviours, especially to reduce the computational complexity of planning in large domains. However, the effects of abstraction in the inverse process – plan recognition – are unclear. In this paper, we present a method for recognising the agent’s behaviour in noisy and uncertain domains, and across multiple levels of abstraction. We use the concept of abstract Markov policies in abstract probabilistic planning as the model of the agent’s behaviours and employ probabilistic inference in Dynamic Bayesian Networks (DBN) to infer the correct policy from a sequence of observations. When the states are fully observable, we show that for a broad and often-used class of abstract policies, the complexity of policy recognition scales well with the number of abstraction levels in the policy hierarchy. For the partially observable case, we derive an efficient hybrid inference scheme on the corresponding DBN to overcome the exponential complexity.

Non-homogeneous volatility correlations in the bivariate multifractal model

In this paper, we consider an extension of the recently proposed bivariate Markov-switching multifractal model of Calvet, Fisher, and Thompson [2006. "Volatility Comovement: A Multifrequency Approach." Journal of Econometrics {131}: 179-215]. In particular, we allow correlations between volatility components to be non-homogeneous with two different parameters governing the volatility correlations at high and low frequencies. Specification tests confirm the added explanatory value of this specification. In order to explore its practical performance, we apply the model for computing value-at-risk statistics for different classes of financial assets and compare the results with the baseline, homogeneous bivariate multifractal model and the bivariate DCC-GARCH of Engle [2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models." Journal of Business & Economic Statistics 20 (3): 339-350]. As it turns out, the multifractal model with heterogeneous volatility correlations provides more reliable results than both the homogeneous benchmark and the DCC-GARCH model. © 2014 Taylor & Francis.

Tree-based iterated local search for Markov random fields with applications in image analysis

The maximum a posteriori assignment for general structure Markov random fields is computationally intractable. In this paper, we exploit tree-based methods to efficiently address this problem. Our novel method, named Tree-based Iterated Local Search (T-ILS), takes advantage of the tractability of tree-structures embedded within MRFs to derive strong local search in an ILS framework. The method efficiently explores exponentially large neighborhoods using a limited memory without any requirement on the cost functions. We evaluate the T-ILS on a simulated Ising model and two real-world vision problems: stereo matching and image denoising. Experimental results demonstrate that our methods are competitive against state-of-the-art rivals with significant computational gain.

Noise level classification for EEG using Hidden Markov Models

EEG signal is one of the most important signals for diagnosing some diseases. EEG is always recorded with an amount of noise, the more noise is recorded the less quality is the EEG signal. The included noise can represent the quality of the recorded EEG signal, this paper proposes a signal quality assessment method for EEG signal. The method generates an automated measure to detect the noise level of the recorded EEG signal. Mel-Frequency Cepstrum Coefficient is used to represent the signals. Hidden Markov Models were used to build a classification model that classifies the EEG signals based on the noise level associated with the signal. This EEG quality assessment measure will help doctors and researchers to focus on the patterns in the signal that have high signal to noise ratio and carry more information. Moreover, our model was applied on an uncontrolled environment and on controlled environment and a result comparison was applied.

Improving mutual fund market timing measures: a markov switching approach

Market timing performance of mutual funds is usually evaluated with linear models with dummy variables which allow for the beta coefficient of CAPM to vary across two regimes: bullish and bearish market excess returns. Managers, however, use their predictions of the state of nature to deÞne whether to carry low or high beta portfolios instead of the observed ones. Our approach here is to take this into account and model market timing as a switching regime in a way similar to Hamilton s Markov-switching GNP model. We then build a measure of market timing success and apply it to simulated and real world data.