Search Results for author:
Found 27 papers, 8 papers with code
Thinner Latent Spaces: Detecting dimension and imposing invariance through autoencoder gradient constraints
Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables towards achieving disentangled representations of data.
Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel
Modeling multi-agent systems on networks is a fundamental challenge in a wide variety of disciplines.
DIMON: Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domains
DIMON is based on transporting a given problem (initial/boundary conditions and domain $\Omega_{\theta}$) to a problem on a reference domain $\Omega_{0}$, where training data from multiple problems is used to learn the map to the solution on $\Omega_{0}$, which is then re-mapped to the original domain $\Omega_{\theta}$.
Learning Transition Operators From Sparse Space-Time Samples
This Spatio-Temporal Transition Operator Recovery problem is motivated by the recent interest in learning time-varying graph signals that are driven by graph operators depending on the underlying graph topology.
Learning Interaction Variables and Kernels from Observations of Agent-Based Systems
Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e. g. pairwise distances, pairwise differences of phases, etc...), functions of the state of pairs of agents.
Unsupervised learning of observation functions in state-space models by nonparametric moment methods
Assuming abundant data of the observation process along with the distribution of the state process, we introduce a nonparametric generalized moment method to estimate the observation function via constrained regression.
Machine Learning for Discovering Effective Interaction Kernels between Celestial Bodies from Ephemerides
Building accurate and predictive models of the underlying mechanisms of celestial motion has inspired fundamental developments in theoretical physics.
Nonlinear model reduction for slow-fast stochastic systems near unknown invariant manifolds
Given only access to a black box simulator from which short bursts of simulation can be obtained, we design an algorithm that outputs an estimate of the invariant manifold, a process of the effective stochastic dynamics on it, which has averaged out the fast modes, and a simulator thereof.
Learning Interaction Kernels for Agent Systems on Riemannian Manifolds
Interacting agent and particle systems are extensively used to model complex phenomena in science and engineering.
Multiscale regression on unknown manifolds
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $.
Anatomically-Informed Deep Learning on Contrast-Enhanced Cardiac MRI for Scar Segmentation and Clinical Feature Extraction
Visualizing disease-induced scarring and fibrosis in the heart on cardiac magnetic resonance (CMR) imaging with contrast enhancement (LGE) is paramount in characterizing disease progression and quantifying pathophysiological substrates of arrhythmias.
Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems
Modeling the complex interactions of systems of particles or agents is a fundamental scientific and mathematical problem that is studied in diverse fields, ranging from physics and biology, to economics and machine learning.
Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories
Finally, we exhibit an efficient parallel algorithm to construct the estimator from data, and we demonstrate the effectiveness of our algorithm with numerical tests on prototype systems including stochastic opinion dynamics and a Lennard-Jones model.
Data-driven Discovery of Emergent Behaviors in Collective Dynamics
We consider the fundamental problem of inferring interaction kernels from observations of agent-based dynamical systems given observations of trajectories, in particular for collective dynamical systems exhibiting emergent behaviors with complicated interaction kernels, in a nonparametric fashion, and for kernels which are parametrized by a single unknown parameter.
Learning interaction kernels in heterogeneous systems of agents from multiple trajectories
These simulations also suggest that our estimators are robust to noise in the observations, and produce accurate predictions of dynamics in relative large time intervals, even when they are learned from data collected in short time intervals.
Learning by Active Nonlinear Diffusion
This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs.
Spectral-Spatial Diffusion Geometry for Hyperspectral Image Clustering
The explicit incorporation of spatial regularity into the diffusion construction leads to smoother random processes that are more adapted for unsupervised machine learning than those based on spectra alone.
Nonparametric inference of interaction laws in systems of agents from trajectory data
Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines.
Learning by Unsupervised Nonlinear Diffusion
This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation.
Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms
We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters.
Supervised Dimensionality Reduction for Big Data
To solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences.
Multiscale Strategies for Computing Optimal Transport
The approach is based on an adaptive multiscale decomposition of the point sets.
Unsupervised Clustering and Active Learning of Hyperspectral Images with Nonlinear Diffusion
The problem of unsupervised learning and segmentation of hyperspectral images is a significant challenge in remote sensing.
Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data
We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example supported on a $d$-dimensional Riemannian manifold.
Discovering and Deciphering Relationships Across Disparate Data Modalities
Understanding the relationships between different properties of data, such as whether a connectome or genome has information about disease status, is becoming increasingly important in modern biological datasets.
High Dimensional Data Modeling Techniques for Detection of Chemical Plumes and Anomalies in Hyperspectral Images and Movies
We briefly review recent progress in techniques for modeling and analyzing hyperspectral images and movies, in particular for detecting plumes of both known and unknown chemicals.
Sparse Projection Oblique Randomer Forests
Unfortunately, these extensions forfeit one or more of the favorable properties of decision forests based on axis-aligned splits, such as robustness to many noise dimensions, interpretability, or computational efficiency.
