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Found 19 papers, 2 papers with code
Manifold learning in Wasserstein space
This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures on a compact and convex subset of $\mathbb{R}^d$, metrized with the Wasserstein-2 distance $W$.
PT$\mathrm{L}^{p}$: Partial Transport $\mathrm{L}^{p}$ Distances
In this paper, we introduce partial transport $\mathrm{L}^{p}$ distances as a new family of metrics for comparing generic signals, benefiting from the robustness of partial transport distances.
Rates of Convergence for Regression with the Graph Poly-Laplacian
In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation.
Classification of datasets with imputed missing values: does imputation quality matter?
Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial.
GRAND++: Graph Neural Diffusion with A Source Term
We propose GRAph Neural Diffusion with a source term (GRAND++) for graph deep learning with a limited number of labeled nodes, i. e., low-labeling rate.
Robust Certification for Laplace Learning on Geometric Graphs
Graph Laplacian (GL)-based semi-supervised learning is one of the most used approaches for classifying nodes in a graph.
The Linearized Hellinger--Kantorovich Distance
Working with the local linearization and the corresponding embeddings allows for the advantages of the Euclidean setting, such as faster computations and a plethora of data analysis tools, whilst still enjoying approximately the descriptive power of the Hellinger--Kantorovich metric.
Optimization and Control
Certifying Robustness of Graph Laplacian Based Semi-Supervised Learning
Within a certain adversarial perturbation regime, we prove that GL with a $k$-nearest neighbor graph is intrinsically more robust than the $k$-nearest neighbor classifier.
A Linear Transportation $\mathrm{L}^p$ Distance for Pattern Recognition
The transportation $\mathrm{L}^p$ distance, denoted $\mathrm{TL}^p$, has been proposed as a generalisation of Wasserstein $\mathrm{W}^p$ distances motivated by the property that it can be applied directly to colour or multi-channelled images, as well as multivariate time-series without normalisation or mass constraints.
Common pitfalls and recommendations for using machine learning to detect and prognosticate for COVID-19 using chest radiographs and CT scans
Machine learning methods offer great promise for fast and accurate detection and prognostication of COVID-19 from standard-of-care chest radiographs (CXR) and computed tomography (CT) images.
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.
From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds
In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of Cheeger cuts.
PDE-Inspired Algorithms for Semi-Supervised Learning on Point Clouds
In this paper we extend the labels by minimising the constrained discrete $p$-Dirichlet energy.
Representing and Learning High Dimensional Data With the Optimal Transport Map From a Probabilistic Viewpoint
With experiments using 4 different datasets, we show that the generative tangent plane model in the optimal transport (OT) manifold can be learned with small numbers of images and can be used to create infinitely many `unseen' images.
Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms
Scalings in which the graph Laplacian approaches a differential operator in the large graph limit are used to develop understanding of a number of algorithms for semi-supervised learning; in particular the extension, to this graph setting, of the probit algorithm, level set and kriging methods, are studied.
Analysis of $p$-Laplacian Regularization in Semi-Supervised Learning
The task is to assign real-valued labels to a set of $n$ sample points, provided a small training subset of $N$ labeled points.
A Transportation $L^p$ Distance for Signal Analysis
Transport based distances, such as the Wasserstein distance and earth mover's distance, have been shown to be an effective tool in signal and image analysis.
Transport-based analysis, modeling, and learning from signal and data distributions
Transport-based techniques for signal and data analysis have received increased attention recently.
