109 citations · 243 across the 25 of their papers we have counts for
34 papers
A Kalman Filter Based Approach to NV Diamond Data Fusion For Improved Temperature Sensing
Shraddha Rajpal, Qiaochu Guo, Brendon A. McCullian +2
Nitrogen-vacancy (NV) centers in diamond have been demonstrated to enable highly sensitive temperature measurements using multiple modalities. Standalone optically detected magneti…
Orthogonal Dendritic Intrinsic Networks: An Architecture for Significance-Ordered, Orthogonal Latent Spaces
Jeanie Schreiber, Tyrus Berry, Zeeshan Ahmed
Principal Component Analysis or PCA-like properties (orthogonality, variance ranking) are seldom realized in deep autoencoder architectures. In this work, we present ODIN (Orthogon…
Dependence of Microstructure Classification Accuracy on Crystallographic Data Representation
Shrunal Pothagoni, Dylan Miley, Tyrus Berry +2
Convolutional neural networks are increasingly being used to analyze and classify material microstructures, motivated by the possibility that they will be able to identify relevant…
Limits of Learning Dynamical Systems
Tyrus Berry, Suddhasattwa Das
A dynamical system is a transformation of a phase space, and the transformation law is the primary means of defining as well as identifying the dynamical system. It is the object o…
Reconstruction of network dynamics from partial observations
Tyrus Berry, Timothy Sauer
We investigate the reconstruction of time series from dynamical networks that are partially observed. In particular, we address the extent to which the time series at a node of the…
On-Manifold Projected Gradient Descent
Aaron Mahler, Tyrus Berry, Tom Stephens +4
This work provides a computable, direct, and mathematically rigorous approximation to the differential geometry of class manifolds for high-dimensional data, along with nonlinear p…
ActUp: Analyzing and Consolidating tSNE and UMAP
Andrew Draganov, Jakob Rødsgaard Jørgensen, Katrine Scheel Nellemann +4
tSNE and UMAP are popular dimensionality reduction algorithms due to their speed and interpretable low-dimensional embeddings. Despite their popularity, however, little work has be…
Learning theory for dynamical systems
Tyrus Berry, Suddhasattwa Das
The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynami…
GiDR-DUN; Gradient Dimensionality Reduction -- Differences and Unification
Andrew Draganov, Tyrus Berry, Jakob Rødsgaard Jørgensen +3
TSNE and UMAP are two of the most popular dimensionality reduction algorithms due to their speed and interpretable low-dimensional embeddings. However, while attempts have been mad…
Convergence Analysis of the Rank-Restricted Soft SVD Algorithm
Mahendra Panagoda, Tyrus Berry, Harbir Antil
The soft SVD is a robust matrix decomposition algorithm and a key component of matrix completion methods. However, computing the soft SVD for large sparse matrices is often impract…
A Generalized Unscented Transformation for Probability Distributions
Donald Ebeigbe, Tyrus Berry, Michael M. Norton +4
The unscented transform uses a weighted set of samples called sigma points to propagate the means and covariances of nonlinear transformations of random variables. However, unscent…
A Higher Order Unscented Transform
Deanna Easley, Tyrus Berry
We develop a new approach for estimating the expected values of nonlinear functions applied to multivariate random variables with arbitrary distributions. Rather than assuming a pa…
A Poisson Kalman filter for disease surveillance
Donald Ebeigbe, Tyrus Berry, Steven J. Schiff +1
An optimal filter for Poisson observations is developed as a variant of the traditional Kalman filter. Poisson distributions are characteristic of infectious diseases, which model…
Bridging data science and dynamical systems theory
Tyrus Berry, Dimitrios Giannakis, John Harlim
This short review describes mathematical techniques for statistical analysis and prediction in dynamical systems. Two problems are discussed, namely (i) the supervised learning pro…
Diffusion Maps for Embedded Manifolds with Boundary with Applications to PDEs
Ryan Vaughn, Tyrus Berry, Harbir Antil
Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equ…
Fractional Diffusion Maps
Harbir Antil, Tyrus Berry, John Harlim
In this paper, we extend the diffusion maps algorithm on a family of heat kernels that are either local (having exponential decay) or nonlocal (having polynomial decay), arising in…
Applications of topological graph theory to -manifold learning
Tyrus Berry, Steven Schluchter
We show how, given a sufficiently large point cloud sampled from an embedded 2-manifold in , we may obtain a global representation as a cell complex with vertices giv…
Limits on reconstruction of dynamical networks
Jiajing Guan, Tyrus Berry, Timothy Sauer
An observability condition number is defined for physical systems modeled by network dynamics. Assuming the dynamical equations of the network are known and a noisy trajectory is o…
Correcting Observation Model Error in Data Assimilation
Franz Hamilton, Tyrus Berry, Timothy Sauer
Standard methods of data assimilation assume prior knowledge of a model that describes the system dynamics and an observation function that maps the model state to a predicted outp…
Spectral exterior calculus
Tyrus Berry, Dimitrios Giannakis
A spectral approach to building the exterior calculus in manifold learning problems is developed. The spectral approach is shown to converge to the true exterior calculus in the li…
Kalman-Takens filtering in the presence of dynamical noise
Franz Hamilton, Tyrus Berry, Timothy Sauer
The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman f…
Correcting biased observation model error in data assimilation
John Harlim, Tyrus Berry
While the formulation of most data assimilation schemes assumes an unbiased observation model error, in real applications, model error with nontrivial biases is unavoidable. A prac…
Consistent Manifold Representation for Topological Data Analysis
Tyrus Berry, Timothy Sauer
For data sampled from an arbitrary density on a manifold embedded in Euclidean space, the Continuous k-Nearest Neighbors (CkNN) graph construction is introduced. It is shown that C…
Density Estimation on Manifolds with Boundary
Tyrus Berry, Timothy Sauer
Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant…