Technological breakthroughs allow us to collect data with increasing spatio-temporal resolution from complex interaction systems. The combination of high-resolution observations, expressive dynamic models, and efficient machine learning algorithms can lead to crucial insights into complex interaction dynamics and the functions of these systems. In this paper, we formulate the dynamics of a complex interacting network as a stochastic process driven by a sequence of events, and develop expectation propagation algorithms to make inferences from noisy observations. To avoid getting stuck at a local optimum, we formulate the problem of minimizing Bethe free energy as a constrained primal problem and take advantage of the concavity of dual problem in the feasible domain of dual variables guaranteed by duality theorem. Our expectation propagation algorithms demonstrate better performance in inferring the interaction dynamics in complex transportation networks than competing models such as particle filter, extended Kalman filter, and deep neural networks.

Technological breakthroughs allow us to collect data with increasing spatiotemporal resolution from complex interaction systems.

Examples of such events include disease transmission, opinion transition in elections, and rumor propagation.

Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the availability of large-scale data from social networks and sensor networks offers an unprecedented opportunity to predict state-changing events at the individual level. Examples of such events include disease transmission, opinion transition in elections, and rumor propagation. Unlike previous research focusing on the collective effects of social systems, this study makes efficient inferences at the individual level. In order to cope with dynamic interactions among a large number of individuals, we introduce the stochastic kinetic model to capture adaptive transition probabilities and propose an efficient variational inference algorithm the complexity of which grows linearly -- rather than exponentially-- with the number of individuals.

This paper considers the variational approach to the inference problem on certain type of temporal graphical models. It defines a convex formulation of the Bethe free energy, resulting in a method with optimal convergence guarantees. The authors derive Expectation-Propagation fixed point equations and gradient-based updates for solving the optimization problem. A toy example is used to illustrate the approach in the context of transportation dynamics and it is shown that the proposed method outperforms sampling, extended Kalman Filtering and a neural network method. In the variational formulation, the optimization problem is generally non-convex, due to the entropy terms.

Technological breakthroughs allow us to collect data with increasing spatiotemporal resolution from complex interaction systems. The combination of highresolution observations, expressive dynamic models, and efficient machine learning algorithms can lead to crucial insights into complex interaction dynamics and the functions of these systems. In this paper, we formulate the dynamics of a complex interacting network as a stochastic process driven by a sequence of events, and develop expectation propagation algorithms to make inferences from noisy observations. To avoid getting stuck at a local optimum, we formulate the problem of minimizing Bethe free energy as a constrained primal problem and take advantage of the concavity of dual problem in the feasible domain of dual variables guaranteed by duality theorem. Our expectation propagation algorithms demonstrate better performance in inferring the interaction dynamics in complex transportation networks than competing models such as particle filter, extended Kalman filter, and deep neural networks.

Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the availability of large-scale data from social networks and sensor networks offers an unprecedented opportunity to predict state-changing events at the individual level. Examples of such events include disease transmission, opinion transition in elections, and rumor propagation. Unlike previous research focusing on the collective effects of social systems, this study makes efficient inferences at the individual level. In order to cope with dynamic interactions among a large number of individuals, we introduce the stochastic kinetic model to capture adaptive transition probabilities and propose an efficient variational inference algorithm the complexity of which grows linearly -- rather than exponentially-- with the number of individuals. To validate this method, we have performed epidemic-dynamics experiments on wireless sensor network data collected from more than ten thousand people over three years. The proposed algorithm was used to track disease transmission and predict the probability of infection for each individual. Our results demonstrate that this method is more efficient than sampling while nonetheless achieving high accuracy.

Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the availability of large-scale data from social networks and sensor networks offers an unprecedented opportunity to predict state-changing events at the individual level. Examples of such events include disease transmission, opinion transition in elections, and rumor propagation. Unlike previous research focusing on the collective effects of social systems, this study makes efficient inferences at the individual level. In order to cope with dynamic interactions among a large number of individuals, we introduce the stochastic kinetic model to capture adaptive transition probabilities and propose an efficient variational inference algorithm the complexity of which grows linearly -- rather than exponentially-- with the number of individuals.

Technological breakthroughs allow us to collect data with increasing spatio-temporal resolution from complex interaction systems. The combination of high-resolution observations, expressive dynamic models, and efficient machine learning algorithms can lead to crucial insights into complex interaction dynamics and the functions of these systems. In this paper, we formulate the dynamics of a complex interacting network as a stochastic process driven by a sequence of events, and develop expectation propagation algorithms to make inferences from noisy observations. To avoid getting stuck at a local optimum, we formulate the problem of minimizing Bethe free energy as a constrained primal problem and take advantage of the concavity of dual problem in the feasible domain of dual variables guaranteed by duality theorem. Our expectation propagation algorithms demonstrate better performance in inferring the interaction dynamics in complex transportation networks than competing models such as particle filter, extended Kalman filter, and deep neural networks.

We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run for a finite time. We propose a simple way of coupling two MCMC chains built using Particle Independent Metropolis-Hastings (PIMH) to produce unbiased smoothing estimators. Unbiased estimators are appealing in the context of parallel computing, and facilitate the construction of confidence intervals. The proposed scheme only requires access to off-the-shelf Particle Filters (PF) and is thus easier to implement than recently proposed unbiased smoothers. The approach is demonstrated on a L\'evy-driven stochastic volatility model and a stochastic kinetic model.