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Many natural systems exhibit chaotic behaviour such as the weather, hydrology, neuroscience and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can…
Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power.…
Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…
For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles…
To generate dance that temporally and aesthetically matches the music is a challenging problem, as the following factors need to be considered. First, the aesthetic styles and messages conveyed by the motion and music should be consistent.…
Four-dimensional variational data assimilation (4D-Var) on a seasonal-to-interdecadal time scale under the existence of unstable modes can be viewed as an optimization problem of synchronized, coupled chaotic systems. The problem is tackled…
Many real-valued stochastic time-series are locally linear (Gassian), but globally non-linear. For example, the trajectory of a human hand gesture can be viewed as a linear dynamic system driven by a nonlinear dynamic system that represents…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology…
We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.
This paper presents a solution for persistent monitoring of real-world stochastic phenomena, where the underlying covariance structure changes sharply across time, using a small number of mobile robot sensors. We propose an adaptive…
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
Predicting how much mixing occurs when a given amount of energy is injected into a Boussinesq fluid is a longstanding problem in stratified turbulence. The huge number of degrees of freedom involved in those processes renders extremely…
Advances in data collection are producing growing volumes of temporal count observations, making adapted modeling increasingly necessary. In this work, we introduce a generative framework for independent component analysis of temporal count…
In this paper, we postulate that combining the domains of information visualization and music studies paves the ground for a more structured analysis of the design space of music notation, enabling the creation of alternative music…
On time-series data, most causal discovery methods fit a new model whenever they encounter samples from a new underlying causal graph. However, these samples often share relevant information which is lost when following this approach.…
We present a model for capturing musical features and creating novel sequences of music, called the Convolutional Variational Recurrent Neural Network. To generate sequential data, the model uses an encoder-decoder architecture with latent…
Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In…
Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on…