Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

Improved Hybrid Model of HMM/GMM for Speech Recognition

In this paper, we propose a speech recognition engine using hybrid model of Hidden Markov Model (HMM) and Gaussian Mixture Model (GMM). Both the models have been trained independently and the respective likelihood values have been considered jointly and input to a decision logic which provides net likelihood as the output. This hybrid model has been compared with the HMM model. Training and testing has been done by using a database of 20 Hindi words spoken by 80 different speakers. Recognition rates achieved by normal HMM are 83.5% and it gets increased to 85% by using the hybrid approach of HMM and GMM.

Построение Логико-Вероятностных Моделей Временных Рядов с Использованием Цепей Маркова

The method of logic and probabilistic models constructing for multivariate heterogeneous time series is offered. There are some important properties of these models, e.g. universality. In this paper also discussed the logic and probabilistic models distinctive features in comparison with hidden Markov processes. The early proposed time series forecasting algorithm is tested on applied task.

An intelligent broker agent for energy trading:an MDP approach

This paper details the development and evaluation of AstonTAC, an energy broker that successfully participated in the 2012 Power Trading Agent Competition (Power TAC). AstonTAC buys electrical energy from the wholesale market and sells it in the retail market. The main focus of the paper is on the broker’s bidding strategy in the wholesale market. In particular, it employs Markov Decision Processes (MDP) to purchase energy at low prices in a day-ahead power wholesale market, and keeps energy supply and demand balanced. Moreover, we explain how the agent uses Non-Homogeneous Hidden Markov Model (NHHMM) to forecast energy demand and price. An evaluation and analysis of the 2012 Power TAC finals show that AstonTAC is the only agent that can buy energy at low price in the wholesale market and keep energy imbalance low.

Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

Maximal Number of Successors in a Nginar(1) Process

2000 Mathematics Subject Classification: 60J80, 60J20, 60J10, 60G10, 60G70, 60F99.

A Note on the Extinction Problem for Controlled Multitype Branching Processes

2000 Mathematics Subject Classification: 60J80, 60J10.

Using observation ageing to improve Markovian model learning in QoS engineering

Markovian models are widely used to analyse quality-of-service properties of both system designs and deployed systems. Thanks to the emergence of probabilistic model checkers, this analysis can be performed with high accuracy. However, its usefulness is heavily dependent on how well the model captures the actual behaviour of the analysed system. Our work addresses this problem for a class of Markovian models termed discrete-time Markov chains (DTMCs). We propose a new Bayesian technique for learning the state transition probabilities of DTMCs based on observations of the modelled system. Unlike existing approaches, our technique weighs observations based on their age, to account for the fact that older observations are less relevant than more recent ones. A case study from the area of bioinformatics workflows demonstrates the effectiveness of the technique in scenarios where the model parameters change over time.

Secure information flow via stripping and fast simulation

Type systems for secure information flow aim to prevent a program from leaking information from H (high) to L (low) variables. Traditionally, bisimulation has been the prevalent technique for proving the soundness of such systems. This work introduces a new proof technique based on stripping and fast simulation, and shows that it can be applied in a number of cases where bisimulation fails. We present a progressive development of this technique over a representative sample of languages including a simple imperative language (core theory), a multiprocessing nondeterministic language, a probabilistic language, and a language with cryptographic primitives. In the core theory we illustrate the key concepts of this technique in a basic setting. A fast low simulation in the context of transition systems is a binary relation where simulating states can match the moves of simulated states while maintaining the equivalence of low variables; stripping is a function that removes high commands from programs. We show that we can prove secure information flow by arguing that the stripping relation is a fast low simulation. We then extend the core theory to an abstract distributed language under a nondeterministic scheduler. Next, we extend to a probabilistic language with a random assignment command; we generalize fast simulation to the setting of discrete time Markov Chains, and prove approximate probabilistic noninterference. Finally, we introduce cryptographic primitives into the probabilistic language and prove computational noninterference, provided that the underling encryption scheme is secure.

Learning Data-Driven Models of Non-Verbal Behaviors for Building Rapport Using an Intelligent Virtual Agent

There is a growing societal need to address the increasing prevalence of behavioral health issues, such as obesity, alcohol or drug use, and general lack of treatment adherence for a variety of health problems. The statistics, worldwide and in the USA, are daunting. Excessive alcohol use is the third leading preventable cause of death in the United States (with 79,000 deaths annually), and is responsible for a wide range of health and social problems. On the positive side though, these behavioral health issues (and associated possible diseases) can often be prevented with relatively simple lifestyle changes, such as losing weight with a diet and/or physical exercise, or learning how to reduce alcohol consumption. Medicine has therefore started to move toward finding ways of preventively promoting wellness, rather than solely treating already established illness. Evidence-based patient-centered Brief Motivational Interviewing (BMI) interven- tions have been found particularly effective in helping people find intrinsic motivation to change problem behaviors after short counseling sessions, and to maintain healthy lifestyles over the long-term. Lack of locally available personnel well-trained in BMI, however, often limits access to successful interventions for people in need. To fill this accessibility gap, Computer-Based Interventions (CBIs) have started to emerge. Success of the CBIs, however, critically relies on insuring engagement and retention of CBI users so that they remain motivated to use these systems and come back to use them over the long term as necessary. Because of their text-only interfaces, current CBIs can therefore only express limited empathy and rapport, which are the most important factors of health interventions. Fortunately, in the last decade, computer science research has progressed in the design of simulated human characters with anthropomorphic communicative abilities. Virtual characters interact using humans’ innate communication modalities, such as facial expressions, body language, speech, and natural language understanding. By advancing research in Artificial Intelligence (AI), we can improve the ability of artificial agents to help us solve CBI problems. To facilitate successful communication and social interaction between artificial agents and human partners, it is essential that aspects of human social behavior, especially empathy and rapport, be considered when designing human-computer interfaces. Hence, the goal of the present dissertation is to provide a computational model of rapport to enhance an artificial agent’s social behavior, and to provide an experimental tool for the psychological theories shaping the model. Parts of this thesis were already published in [LYL+12, AYL12, AL13, ALYR13, LAYR13, YALR13, ALY14].

Behavioural profiles of captive capuchin monkeys (Sapajus spp.): analyses at group and individual levels

The use of behavioural indicators of suffering and welfare in captive animals has produced ambiguous results. In comparisons between groups, those in worse condition tend to exhibit increased overall rate of Behaviours Potentially Indicative of Stress (BPIS), but when comparing within groups, individuals differ in their stress coping strategies. This dissertation presents analyses to unravel the Behavioural Profile of a sample of 26 captive capuchin monkeys, of three different species (Sapajus libidinosus, S. flavius and S. xanthosternos), kept in different enclosure types. In total, 147,17 hours of data were collected. We explored four type of analysis: Activity Budgets, Diversity indexes, Markov chains and Sequence analyses, and Social Network Analyses, resulting in nine indexes of behavioural occurrence and organization. In chapter One we explore group differences. Results support predictions of minor sex and species differences and major differences in behavioural profile due to enclosure type: i. individuals in less enriched enclosures exhibited a more diverse BPIS repertoire and a decreased probability of a sequence with six Genus Normative Behaviour; ii. number of most probable behavioural transitions including at least one BPIS was higher in less enriched enclosures; iii. proeminence indexes indicate that BPIS function as dead ends of behavioural sequences, and proeminence of three BPIS (pacing, self-direct, active I) were higher in less enriched enclosures. Overall, these data are not supportive of BPIS as a repetitive pattern, with a mantra-like calming effect. Rather, the picture that emerges is more supportive of BPIS as activities that disrupt organization of behaviours, introducing “noise” that compromises optimal activity budget. In chapter Two we explored individual differences in stress coping strategies. We classified individuals along six axes of exploratory behaviour. These were only weakly correlated indicating low correlation among behavioural indicators of syndromes. Nevertheless, the results are suggestive of two broad stress coping strategies, similar to the bold/proactive and shy/reactive pattern: more exploratory capuchin monkeys exhibited increased values of proeminence in Pacing, aberrant sexual display and Active 1 BPIS, while less active animals exhibited increased probability in significant sequences involving at least one BPIS, and increased prominence in own stereotypy. Capuchin monkeys are known for their cognitive capacities and behavioural flexibility, therefore, the search for a consistent set of behavioural indictors of welfare and individual differences requires further studies and larger data sets. With this work we aim contributing to design scientifically grounded and statistically correct protocols for collection of behavioural data that permits comparability of results and meta-analyses, from whatever theoretical perspective interpretation it may receive.

Riconoscimento real-time di gesture tramite tecniche di machine learning

Il riconoscimento delle gesture è un tema di ricerca che sta acquisendo sempre più popolarità, specialmente negli ultimi anni, grazie ai progressi tecnologici dei dispositivi embedded e dei sensori. Lo scopo di questa tesi è quello di utilizzare alcune tecniche di machine learning per realizzare un sistema in grado di riconoscere e classificare in tempo reale i gesti delle mani, a partire dai segnali mioelettrici (EMG) prodotti dai muscoli. Inoltre, per consentire il riconoscimento di movimenti spaziali complessi, verranno elaborati anche segnali di tipo inerziale, provenienti da una Inertial Measurement Unit (IMU) provvista di accelerometro, giroscopio e magnetometro. La prima parte della tesi, oltre ad offrire una panoramica sui dispositivi wearable e sui sensori, si occuperà di analizzare alcune tecniche per la classificazione di sequenze temporali, evidenziandone vantaggi e svantaggi. In particolare, verranno considerati approcci basati su Dynamic Time Warping (DTW), Hidden Markov Models (HMM), e reti neurali ricorrenti (RNN) di tipo Long Short-Term Memory (LSTM), che rappresentano una delle ultime evoluzioni nel campo del deep learning. La seconda parte, invece, riguarderà il progetto vero e proprio. Verrà impiegato il dispositivo wearable Myo di Thalmic Labs come caso di studio, e saranno applicate nel dettaglio le tecniche basate su DTW e HMM per progettare e realizzare un framework in grado di eseguire il riconoscimento real-time di gesture. Il capitolo finale mostrerà i risultati ottenuti (fornendo anche un confronto tra le tecniche analizzate), sia per la classificazione di gesture isolate che per il riconoscimento in tempo reale.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Gaussian Process Kernels for Cross-Spectrum Analysis in Electrophysiological Time Series

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.

Human behaviour recognition in data-scarce domains

This paper presents the novel theory for performing multi-agent activity recognition without requiring large training corpora. The reduced need for data means that robust probabilistic recognition can be performed within domains where annotated datasets are traditionally unavailable. Complex human activities are composed from sequences of underlying primitive activities. We do not assume that the exact temporal ordering of primitives is necessary, so can represent complex activity using an unordered bag. Our three-tier architecture comprises low-level video tracking, event analysis and high-level inference. High-level inference is performed using a new, cascading extension of the Rao–Blackwellised Particle Filter. Simulated annealing is used to identify pairs of agents involved in multi-agent activity. We validate our framework using the benchmarked PETS 2006 video surveillance dataset and our own sequences, and achieve a mean recognition F-Score of 0.82. Our approach achieves a mean improvement of 17% over a Hidden Markov Model baseline.