Tracking with a mixed continuous-discrete Conditional Random Field

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Are you going to the party: depends, who else is coming? [Learning hidden group dynamics via conditional latent tree models]

Scalable probabilistic modeling and prediction in high dimensional multivariate time-series is a challenging problem, particularly for systems with hidden sources of dependence and/or homogeneity. Examples of such problems include dynamic social networks with co-evolving nodes and edges and dynamic student learning in online courses. Here, we address these problems through the discovery of hierarchical latent groups. We introduce a family of Conditional Latent Tree Models (CLTM), in which tree-structured latent variables incorporate the unknown groups. The latent tree itself is conditioned on observed covariates such as seasonality, historical activity, and node attributes. We propose a statistically efficient framework for learning both the hierarchical tree structure and the parameters of the CLTM. We demonstrate competitive performance in multiple real world datasets from different domains. These include a dataset on students' attempts at answering questions in a psychology MOOC, Twitter users participating in an emergency management discussion and interacting with one another, and windsurfers interacting on a beach in Southern California. In addition, our modeling framework provides valuable and interpretable information about the hidden group structures and their effect on the evolution of the time series

Simultaneous motion detection and background reconstruction with a conditional mixed-state markov random field

In this work we present a new way of simultaneously solving the problems of motion detection and background image reconstruction. An accurate estimation of the background is only possible if we locate the moving objects. Meanwhile, a correct motion detection is achieved if we have a good available background model. The key of our joint approach is to define a single random process that can take two types of values, instead of defining two different processes, one symbolic (motion detection) and one numeric (background intensity estimation). It thus allows to exploit the (spatio-temporal) interaction between a decision (motion detection) and an estimation (intensity reconstruction) problem. Consequently, the meaning of solving both tasks jointly, is to obtain a single optimal estimate of such a process. The intrinsic interaction and simultaneity between both problems is shown to be better modeled within the so-called mixed-state statistical framework, which is extended here to account for symbolic states and conditional random fields. Experiments on real sequences and comparisons with existing motion detection methods support our proposal. Further implications for video sequence inpainting will be also discussed. © 2011 Springer Science+Business Media, LLC.postprin

Maximum Entropy Limit of Small-scale Magnetic Field Fluctuations in the Quiet Sun

The observed magnetic field on the solar surface is characterized by a very complex spatial and temporal behavior. Although feature-tracking algorithms have allowed us to deepen our understanding of this behavior, subjectivity plays an important role in the identification and tracking of such features. In this paper, we continue studies Gorobets, A. Y., Borrero, J. M., & Berdyugina, S. 2016, ApJL, 825, L18 of the temporal stochasticity of the magnetic field on the solar surface without relying either on the concept of magnetic features or on subjective assumptions about their identification and interaction. We propose a data analysis method to quantify fluctuations of the line-of-sight magnetic field by means of reducing the temporal field's evolution to the regular Markov process. We build a representative model of fluctuations converging to the unique stationary (equilibrium) distribution in the long time limit with maximum entropy. We obtained different rates of convergence to the equilibrium at fixed noise cutoff for two sets of data. This indicates a strong influence of the data spatial resolution and mixing-polarity fluctuations on the relaxation process. The analysis is applied to observations of magnetic fields of the relatively quiet areas around an active region carried out during the second flight of the Sunrise/IMaX and quiet Sun areas at the disk center from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory satellite.Comment: 11 pages, 5 figures, The Astrophysical Journal Supplement Series (accepted