相关论文: eXponential FAmily Dynamical Systems (XFADS): Larg…
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…
Understanding the structure of complex, nonstationary, high-dimensional time-evolving signals is a central challenge in scientific data analysis. In many domains, such as speech and biomedical signal processing, the ability to learn…
In this note we present a generative model of natural images consisting of a deep hierarchy of layers of latent random variables, each of which follows a new type of distribution that we call rectified Gaussian. These rectified Gaussian…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
A key goal of unsupervised learning is to go beyond density estimation and sample generation to reveal the structure inherent within observed data. Such structure can be expressed in the pattern of interactions between explanatory latent…
Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman, particle) presuppose full knowledge of the true dynamics, which is not always satisfied in…
One's ability to learn a generative model of the world without supervision depends on the extent to which one can construct abstract knowledge representations that generalize across experiences. To this end, capturing an accurate…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
This work studies the problem of modeling visual processes by leveraging deep generative architectures for learning linear, Gaussian representations from observed sequences. We propose a joint learning framework, combining a vector…
Probability density function estimation with weighted samples is the main foundation of all adaptive importance sampling algorithms. Classically, a target distribution is approximated either by a non-parametric model or within a parametric…
Ensuring accurate and stable state estimation is a challenging task crucial to safety-critical domains such as high-speed autonomous racing, where measurement uncertainty must be both adaptive to the environment and temporally smooth for…
State-space models effectively model multivariate time series by updating over time a representation of the system state from which predictions are made. The state representation is usually a vector without any explicit structure.…
Complex multivariate time series arise in many fields, ranging from computer vision to robotics or medicine. Often we are interested in the independent underlying factors that give rise to the high-dimensional data we are observing. While…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
We develop Bayesian machine learning methods for mixed data sampling (MIDAS) regressions. This involves handling frequency mismatches and specifying functional relationships between many predictors and the dependent variable. We use…
Variational autoencoders (VAEs) have been used extensively to discover low-dimensional latent factors governing neural activity and animal behavior. However, without careful model selection, the uncovered latent factors may reflect noise in…
We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are…
Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…
New technologies for recording the activity of large neural populations during complex behavior provide exciting opportunities for investigating the neural computations that underlie perception, cognition, and decision-making. Nonlinear…