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Found 11 papers, 2 papers with code
Wasserstein Archetypal Analysis
We prove a consistency result for the regularized problem, ensuring that if the data are iid samples from a probability measure, then as the number of samples is increased, a subsequence of the archetype points converges to the archetype points for the limiting data distribution, almost surely.
A dynamical systems based framework for dimension reduction
We also show how the DDR method can be trained using a gradient-based optimization method, where the gradients are computed using the adjoint method from optimal control theory.
Probabilistic methods for approximate archetypal analysis
Archetypal analysis is an unsupervised learning method for exploratory data analysis.
A non-autonomous equation discovery method for time signal classification
We view the time signal as a forcing function for a dynamical system that governs a time-evolving hidden variable.
Consistency of archetypal analysis
Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data.
A metric on directed graphs and Markov chains based on hitting probabilities
The shortest-path, commute time, and diffusion distances on undirected graphs have been widely employed in applications such as dimensionality reduction, link prediction, and trip planning.
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.
Consistency of Dirichlet Partitions
With probability one with respect to the choice of points $\{x_i\}_{i \in \mathbb{N}}$, we show that as $n \to \infty$ the discrete Dirichlet energies for functions $G_n \to \Sigma_k$ $\Gamma$-converge to (a scalar multiple of) the continuum Dirichlet energy for functions $U \to \Sigma_k$ with respect to a metric coming from the theory of optimal transport.
Analysis of Crowdsourced Sampling Strategies for HodgeRank with Sparse Random Graphs
In this setting, a pairwise comparison dataset is typically gathered via random sampling, either \emph{with} or \emph{without} replacement.
Minimal Dirichlet energy partitions for graphs
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components.
Optimal Data Collection For Informative Rankings Expose Well-Connected Graphs
Our approach, based on experimental design, is to view data collection as a bi-level optimization problem where the inner problem is the ranking problem and the outer problem is to identify data which maximizes the informativeness of the ranking.
