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Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that…

Structured variational autoencoders (SVAEs) combine probabilistic graphical model priors on latent variables, deep neural networks to link latent variables to observed data, and structure-exploiting algorithms for approximate posterior…

In principle, applying variational autoencoders (VAEs) to sequential data offers a method for controlled sequence generation, manipulation, and structured representation learning. However, training sequence VAEs is challenging:…

Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

To achieve reliable mining results for massive vessel trajectories, one of the most important challenges is how to efficiently compute the similarities between different vessel trajectories. The computation of vessel trajectory similarity…

Missing data persists as a major barrier to data analysis across numerous applications. Recently, deep generative models have been used for imputation of missing data, motivated by their ability to capture highly non-linear and complex…

Continuing advances in neural interfaces have enabled simultaneous monitoring of spiking activity from hundreds to thousands of neurons. To interpret these large-scale data, several methods have been proposed to infer latent dynamic…

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…

Metabonomics time-course experiments provide the opportunity to understand the changes to an organism by observing the evolution of metabolic profiles in response to internal or external stimuli. Along with other omic longitudinal profiling…

Continuous dynamical systems are cornerstones of many scientific and engineering disciplines. While machine learning offers powerful tools to model these systems from trajectory data, challenges arise when these trajectories are captured as…

Is there really much more to say about sparse autoencoders (SAEs)? Autoencoders in general, and SAEs in particular, represent deep architectures that are capable of modeling low-dimensional latent structure in data. Such structure could…

Human demonstrations of trajectories are an important source of training data for many machine learning problems. However, the difficulty of collecting human demonstration data for complex tasks makes learning efficient representations of…

We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general…

We propose a framework for the statistical evaluation of variational auto-encoders (VAEs) and test two instances of this framework in the context of modelling images of handwritten digits and a corpus of English text. Our take on evaluation…

Deep Learning (DL) methods have dramatically increased in popularity in recent years. While its initial success was demonstrated in the classification and manipulation of image data, there has been significant growth in the application of…

In this tutorial, we explore Variational Autoencoders (VAEs), an essential framework for unsupervised learning, particularly suited for high-dimensional datasets such as neuroimaging. By integrating deep learning with Bayesian inference,…

By composing graphical models with deep learning architectures, we learn generative models with the strengths of both frameworks. The structured variational autoencoder (SVAE) inherits structure and interpretability from graphical models,…

Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…

The symbolic discovery of Ordinary Differential Equations (ODEs) from trajectory data plays a pivotal role in AI-driven scientific discovery. Existing symbolic methods predominantly rely on fixed, pre-collected training datasets, which…