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A common problem in time series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system. For data on a smooth compact manifold, Takens theorem proves a time delayed embedding of the…

In order to explore and act autonomously in an environment, an agent needs to learn from the sensorimotor information that is captured while acting. By extracting the regularities in this sensorimotor stream, it can learn a model of the…

We describe a procedure for the generation of functional digraphs up to isomorphism; these are digraphs with uniform outdegree 1, also called mapping patterns, finite endofunctions, or finite discrete-time dynamical systems. This procedure…

A single dynamical system with time-delayed feedback can emulate networks. This property of delay systems made them extremely useful tools for Machine Learning applications. Here we describe several possible setups, which allow emulating…

In this article, we present a method to reconstruct the topology of a partially observed radial network of linear dynamical systems with bi-directional interactions. Our approach exploits the structure of the inverse power spectral density…

We are interested in enabling autonomous agents to learn and reason about systems with hidden states, such as locking mechanisms. We cast this problem as learning the parameters of a discrete Partially Observable Markov Decision Process…

We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to…

Rather than simply recognizing the action of a person individually, collective activity recognition aims to find out what a group of people is acting in a collective scene. Previ- ous state-of-the-art methods using hand-crafted potentials…

We propose a probabilistic modeling framework for learning the dynamic patterns in the collective behaviors of social agents and developing profiles for different behavioral groups, using data collected from multiple information sources.…

We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…

We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…

We propose to deal with sequential processes where only partial observations are available by learning a latent representation space on which policies may be accurately learned.

We develop a method for learning periodic tasks from visual demonstrations. The core idea is to leverage periodicity in the policy structure to model periodic aspects of the tasks. We use active learning to optimize parameters of rhythmic…

We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders,…

The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of…

Multivariate time series present challenges to standard machine learning techniques, as they are often unlabeled, high dimensional, noisy, and contain missing data. To address this, we propose T-Rep, a self-supervised method to learn time…

A novel approach to perform unsupervised sequential learning for functional data is proposed. Our goal is to extract reference shapes (referred to as templates) from noisy, deformed and censored realizations of curves and images. Our model…

Hamiltonian systems describe a broad class of dynamical systems governed by Hamiltonian functions, which encode the total energy and dictate the evolution of the system. Data-driven approaches, such as symbolic regression and neural…