Sequential Bayesian inference for implicit hidden Markov models and current limitations

Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to estimate the hidden Markov process given the observations and a fixed parameter value. We review some of the recent developments allowing the inclusion of parameter uncertainty as well as model uncertainty. The shortcomings of the currently available methodology are emphasised from an algorithmic complexity perspective. The statistical objects of interest for time series analysis are illustrated on a toy "Lotka-Volterra" model used in population ecology. Some open challenges are discussed regarding the scalability of the reviewed methodology to longer time series, higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages, 10 figure

Latent tree models

Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. This article offers a concise introduction to the theory of latent tree models. We emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned

Anticipatory Mobile Computing: A Survey of the State of the Art and Research Challenges

Today's mobile phones are far from mere communication devices they were ten years ago. Equipped with sophisticated sensors and advanced computing hardware, phones can be used to infer users' location, activity, social setting and more. As devices become increasingly intelligent, their capabilities evolve beyond inferring context to predicting it, and then reasoning and acting upon the predicted context. This article provides an overview of the current state of the art in mobile sensing and context prediction paving the way for full-fledged anticipatory mobile computing. We present a survey of phenomena that mobile phones can infer and predict, and offer a description of machine learning techniques used for such predictions. We then discuss proactive decision making and decision delivery via the user-device feedback loop. Finally, we discuss the challenges and opportunities of anticipatory mobile computing.Comment: 29 pages, 5 figure

Two types of densification scaling in the evolution of temporal networks

Many real-world social networks constantly change their global properties over time, such as the number of edges, size and density. While temporal and local properties of social networks have been extensively studied, the origin of their dynamical nature is not yet well understood. Networks may grow or shrink if a) the total population of nodes changes and/or b) the chance of two nodes being connected varies over time. Here, we develop a method that allows us to classify the source of time-varying nature of temporal networks. In doing so, we first show empirical evidence that real-world dynamical systems could be categorized into two classes, the difference of which is characterized by the way the number of edges grows with the number of active nodes, i.e., densification scaling. We develop a dynamic hidden-variable model to formally characterize the two dynamical classes. The model is fitted to the empirical data to identify whether the origin of scaling comes from a changing population in the system or shifts in the connecting probabilities.Comment: 12 pages, 6 figures (plus 7 figures in SI

Semi-parametric analysis of multi-rater data

Datasets that are subjectively labeled by a number of experts are becoming more common in tasks such as biological text annotation where class definitions are necessarily somewhat subjective. Standard classification and regression models are not suited to multiple labels and typically a pre-processing step (normally assigning the majority class) is performed. We propose Bayesian models for classification and ordinal regression that naturally incorporate multiple expert opinions in defining predictive distributions. The models make use of Gaussian process priors, resulting in great flexibility and particular suitability to text based problems where the number of covariates can be far greater than the number of data instances. We show that using all labels rather than just the majority improves performance on a recent biological dataset