Search Results for author:
Found 30 papers, 13 papers with code
Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian
In this paper we give a broad overview of the intersection of partial differential equations (PDEs) and graph-based semi-supervised learning.
Novel Batch Active Learning Approach and Its Application to Synthetic Aperture Radar Datasets
Active learning improves the performance of machine learning methods by judiciously selecting a limited number of unlabeled data points to query for labels, with the aim of maximally improving the underlying classifier's performance.
Poisson Reweighted Laplacian Uncertainty Sampling for Graph-based Active Learning
We show that uncertainty sampling is sufficient to achieve exploration versus exploitation in graph-based active learning, as long as the measure of uncertainty properly aligns with the underlying model and the model properly reflects uncertainty in unexplored regions.
Use and Misuse of Machine Learning in Anthropology
Machine learning (ML), being now widely accessible to the research community at large, has fostered a proliferation of new and striking applications of these emergent mathematical techniques across a wide range of disciplines.
Using machine learning on new feature sets extracted from 3D models of broken animal bones to classify fragments according to break agent
Distinguishing agents of bone modification at paleoanthropological sites is at the root of much of the research directed at understanding early hominin exploitation of large animal resources and the effects those subsistence behaviors had on early hominin evolution.
The Batch Artifact Scanning Protocol: A new method using computed tomography (CT) to rapidly create three-dimensional models of objects from large collections en masse
Within anthropology, the use of three-dimensional (3D) imaging has become increasingly standard and widespread since it broadens the available avenues for addressing a wide range of key issues.
Graph-based Active Learning for Semi-supervised Classification of SAR Data
We use a Convolutional Neural Network Variational Autoencoder (CNNVAE) to embed SAR data into a feature space, and then construct a similarity graph from the embedded data and apply graph-based semi-supervised learning techniques.
Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth
We show that the $p$-eikonal equation with $p=1$ is a provably robust distance-type function on a graph, and the $p\to \infty$ limit recovers shortest path distances.
Uniform Convergence Rates for Lipschitz Learning on Graphs
In this work we prove uniform convergence rates for solutions of the graph infinity Laplace equation as the number of vertices grows to infinity.
Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications
We introduce new estimators for the normal vector to the boundary, distance of a point to the boundary, and a test for whether a point lies within a boundary strip.
The Virtual Goniometer: A new method for measuring angles on 3D models of fragmentary bone and lithics
The contact goniometer is a commonly used tool in lithic and zooarchaeological analysis, despite suffering from a number of shortcomings due to the physical interaction between the measuring implement, the object being measured, and the individual taking the measurements.
Asymptotically optimal strategies for online prediction with history-dependent experts
The prediction problem is played (in part) over a discrete graph called the $d$ dimensional de Bruijn graph, where $d$ is the number of days of history used by the experts.
Online Prediction With History-Dependent Experts: The General Case
We consider the problem with history-dependent experts, in which each expert uses the previous $d$ days of history of the market in making their predictions.
Lipschitz regularity of graph Laplacians on random data clouds
As a byproduct of our general regularity results, we obtain high probability $L^\infty$ and approximate $\mathcal{C}^{0, 1}$ convergence rates for the convergence of graph Laplacian eigenvectors towards eigenfunctions of the corresponding weighted Laplace-Beltrami operators.
Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates
We propose a new framework, called Poisson learning, for graph based semi-supervised learning at very low label rates.
Rates of Convergence for Laplacian Semi-Supervised Learning with Low Labeling Rates
The proofs of our well-posedness results use the random walk interpretation of Laplacian learning and PDE arguments, while the proofs of the ill-posedness results use $\Gamma$-convergence tools from the calculus of variations.
A continuum limit for the PageRank algorithm
In this paper, we propose a new framework for rigorously studying continuum limits of learning algorithms on directed graphs.
Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs
In this paper we improve the spectral convergence rates for graph-based approximations of Laplace-Beltrami operators constructed from random data.
Computation of Circular Area and Spherical Volume Invariants via Boundary Integrals
We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively.
Lipschitz regularized Deep Neural Networks generalize
We show that if the usual training loss is augmented by a Lipschitz regularization term, then the networks generalize.
Analysis and algorithms for $\ell_p$-based semi-supervised learning on graphs
In the first part of the paper we prove new discrete to continuum convergence results for $p$-Laplace problems on $k$-nearest neighbor ($k$-NN) graphs, which are more commonly used in practice than random geometric graphs.
Properly-weighted graph Laplacian for semi-supervised learning
The performance of traditional graph Laplacian methods for semi-supervised learning degrades substantially as the ratio of labeled to unlabeled data decreases, due to a degeneracy in the graph Laplacian.
PDE Acceleration: A convergence rate analysis and applications to obstacle problems
This paper provides a rigorous convergence rate and complexity analysis for a recently introduced framework, called PDE acceleration, for solving problems in the calculus of variations, and explores applications to obstacle problems.
Numerical Analysis Numerical Analysis Analysis of PDEs Dynamical Systems Optimization and Control 65M06, 35Q93, 65K10, 49K20
Lipschitz regularized Deep Neural Networks generalize and are adversarially robust
In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness.
The game theoretic p-Laplacian and semi-supervised learning with few labels
We study the game theoretic p-Laplacian for semi-supervised learning on graphs, and show that it is well-posed in the limit of finite labeled data and infinite unlabeled data.
Consistency of Lipschitz learning with infinite unlabeled data and finite labeled data
We study the consistency of Lipschitz learning on graphs in the limit of infinite unlabeled data and finite labeled data.
Anomaly detection and classification for streaming data using PDEs
We propose in this paper a fast real-time streaming version of the PDA algorithm for anomaly detection that exploits the computational advantages of PDE continuum limits.
Multi-criteria Similarity-based Anomaly Detection using Pareto Depth Analysis
If the relative importance of the different dissimilarity measures are not known in advance, as in many anomaly detection applications, the anomaly detection algorithm may need to be executed multiple times with different choices of weights in the linear combination.
Pareto-depth for Multiple-query Image Retrieval
Most content-based image retrieval systems consider either one single query, or multiple queries that include the same object or represent the same semantic information.
Multi-criteria Anomaly Detection using Pareto Depth Analysis
In such a case, multiple criteria can be defined, and one can test for anomalies by scalarizing the multiple criteria by taking some linear combination of them.
