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Knowledge Graph Representation Learning using Ordinary Differential Equations
Many KGEs use the Euclidean geometry which renders them incapable of preserving complex structures and consequently causes wrong inferences by the models.
Bayesian Posterior Perturbation Analysis with Integral Probability Metrics
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention.
Spectral Analysis Of Weighted Laplacians Arising In Data Clustering
Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a central role in a number of unsupervised and semi-supervised learning algorithms.
Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods
Graph-based semi-supervised learning is the problem of propagating labels from a small number of labelled data points to a larger set of unlabelled data.
Geometric structure of graph Laplacian embeddings
More precisely, we assume that the data is sampled from a mixture model supported on a manifold $\mathcal{M}$ embedded in $\mathbb{R}^d$, and pick a connectivity length-scale $\varepsilon>0$ to construct a kernelized graph Laplacian.
