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Found 15 papers, 10 papers with code
Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms
In particular, we show the discrete eigenvalues and eigenvectors converge to their continuum analogues at a dimension-dependent rate, which allows us to interpret the efficacy of discrete spectral clustering using Fermat distances in terms of the resulting continuum limit.
It begins with a boundary: A geometric view on probabilistically robust learning
Although deep neural networks have achieved super-human performance on many classification tasks, they often exhibit a worrying lack of robustness towards adversarially generated examples.
Learning to Solve Integer Linear Programs with Davis-Yin Splitting
In many applications, a combinatorial problem must be repeatedly solved with similar, but distinct parameters.
Curvature-Aware Derivative-Free Optimization
Zeroth-order methods have been gaining popularity due to the demands of large-scale machine learning applications, and the paper focuses on the selection of the step size $\alpha_k$ in these methods.
Operator Splitting for Learning to Predict Equilibria in Convex Games
Systems of competing agents can often be modeled as games.
JFB: Jacobian-Free Backpropagation for Implicit Networks
Unlike traditional networks, implicit networks solve a fixed point equation to compute inferences.
A Zeroth-Order Block Coordinate Descent Algorithm for Huge-Scale Black-Box Optimization
We consider the zeroth-order optimization problem in the huge-scale setting, where the dimension of the problem is so large that performing even basic vector operations on the decision variables is infeasible.
Balancing Geometry and Density: Path Distances on High-Dimensional Data
New geometric and computational analyses of power-weighted shortest-path distances (PWSPDs) are presented.
Who killed Lilly Kane? A case study in applying knowledge graphs to crime fiction
We present a preliminary study of a knowledge graph created from season one of the television show Veronica Mars, which follows the eponymous young private investigator as she attempts to solve the murder of her best friend Lilly Kane.
A One-bit, Comparison-Based Gradient Estimator
By treating the gradient as an unknown signal to be recovered, we show how one can use tools from one-bit compressed sensing to construct a robust and reliable estimator of the normalized gradient.
Zeroth-Order Regularized Optimization (ZORO): Approximately Sparse Gradients and Adaptive Sampling
We consider the problem of minimizing a high-dimensional objective function, which may include a regularization term, using (possibly noisy) evaluations of the function.
Power Weighted Shortest Paths for Clustering Euclidean Data
We study the use of power weighted shortest path distance functions for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of disjoint low dimensional manifolds.
On the neighborliness of dual flow polytopes of quivers
In this note we investigate under which conditions the dual of the flow polytope (henceforth referred to as the `dual flow polytope') of a quiver is k-neighborly, for generic weights near the canonical weight.
Combinatorics 14M25, 52B20
Compressive Sensing for cut improvement and local clustering
We show how one can phrase the cut improvement problem for graphs as a sparse recovery problem, whence one can use algorithms originally developed for use in compressive sensing (such as SubspacePursuit or CoSaMP) to solve it.
Information Theory Numerical Analysis Social and Information Networks Information Theory Numerical Analysis 68Q25, 68R10, 68U05, 94A12
A Compressive Sensing Approach to Community Detection with Applications
The community detection problem for graphs asks one to partition the n vertices V of a graph G into k communities, or clusters, such that there are many intracluster edges and few intercluster edges.
