arXiv research

Landmark-based node embeddings approximate shortest path distances in random graphs.

There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into ac…

Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges …

The present work extends the randomized shortest-paths framework (RSP), interpolating between shortest-path and random-walk routing in a network, in three directions. First, it shows how to deal with equality constraints on a subset of transition probabilities and develops a generic algorithm for solving this constrain…

Extends RSP model with net flow and capacity constraints for better network analysis.

The classical theorem of Fáry states that every planar graph can be represented by an embedding in which every edge is represented by a straight line segment. We consider generalizations of Fáry's theorem to surfaces equipped with Riemannian metrics. In this setting, we require that every edge is drawn as a shortest pa…

EntroPath learns manifold geometry from diffusion paths.

The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface nearby the intersection and result in incorrect clustering. The Isomap algorithm uses the shortest path between points. The main draw…

Generative Flow Networks solve shortest path problems in graphs.

Deep learning approximates shortest path distances in large graphs.

Paper studies CLO with partial feedback, improving decision-making in uncertain contexts.

Proposes a method to improve graph embedding by removing least frequent nodes.

Real-world data sets often provide multiple types of information about the same set of entities. This data is well represented by multi-view graphs, which consist of several distinct sets of edges over the same nodes. These can be used to analyze how entities interact from different viewpoints. Combining multiple views…

Sparse RSP routing improves graph exploration and classification.

Algorithm reduces regret in SSP problems with LFA.

We present a simple, yet effective, approach to Semi-Supervised Learning. Our approach is based on estimating density-based distances (DBD) using a shortest path calculation on a graph. These Graph-DBD estimates can then be used in any distance-based supervised learning method, such as Nearest Neighbor methods and SVMs…

In this paper, we prove some convergence results of a special case of optimistic policy iteration algorithm for stochastic shortest path problem. We consider both Monte Carlo and $TD(λ)$ methods for the policy evaluation step under the condition that the termination state will eventually be reached almost surely.

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. We argue, theoretically and experimentally, that this leads to higher clustering accuracy. We also pres…

Paper tackles offline SSP with value iteration for policy evaluation and learning.

Matching datasets of multiple modalities has become an important task in data analysis. Existing methods often rely on the embedding and transformation of each single modality without utilizing any correspondence information, which often results in sub-optimal matching performance. In this paper, we propose a nonlinear…

Q-learning for average cost MDPs gets a concentration bound.

Generative models use Riemannian manifolds to improve latent space interpretation.

Study examines how information flows in Indian stock market during crises.

The aim of this paper is to establish two fundamental measure-metric properties of particular random geometric graphs. We consider $\varepsilon$-neighborhood graphs whose vertices are drawn independently and identically distributed from a common distribution defined on a regular submanifold of $\mathbb{R}^K$. We show t…

Control Contraction Metrics (CCMs) provide a nonlinear controller design involving an offline search for a Riemannian metric and an online search for a shortest path between the current and desired trajectories. In this paper, we generalize CCMs to Finsler geometry, allowing the use of non-Riemannian metrics. We provid…

New algorithms for planning with adversarial changes in costs.

New algorithm reduces regret in stochastic shortest path problems.

We examine the existence of tangent hyperplanes to subriemannian balls. Strictly abnormal shortest paths are allowed

New algorithms minimize regret in SSP with optimal sparse updates.

Unified algorithm for optimizing rewards in stochastic path problems.

A new method extracts events and their arguments efficiently from text.

The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs-Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature $T$) controlling the entropic level of the distribution. This formalism enables…

New RL approach builds short ancestral recombination graphs.

Study examines how wind affects shortest paths on Finsler manifolds.

The paper studies the shortest closed multi-geodesics on hyperbolic surfaces as their genus grows.

Paper finds shortest geodesic paths on hyperbolic surfaces.

This work develops a generic framework, called the bag-of-paths (BoP), for link and network data analysis. The central idea is to assign a probability distribution on the set of all paths in a network. More precisely, a Gibbs-Boltzmann distribution is defined over a bag of paths in a network, that is, on a representati…

New bounds on shortest geodesic loops on a sphere.

New algorithm reduces regret in linear mixture SSPs without cost bounds.

Study shows sample complexity for learning optimal policies in SSP with generative model.

PathNNs improve graph neural networks by distinguishing non-isomorphic graphs.

Agent learns to navigate uncertain 3D maps using a hybrid planner.

Revisits Isomap, showing it constructs Euclidean representations of geodesic structure.

We propose a fast, simple and robust algorithm for computing shortest paths and distances on Riemannian manifolds learned from data. This amounts to solving a system of ordinary differential equations (ODEs) subject to boundary conditions. Here standard solvers perform poorly because they require well-behaved Jacobians…

Study shows hard sample complexity for learning optimal policies in stochastic shortest path problems.

It is common to encounter situations where one must solve a sequence of similar computational problems. Running a standard algorithm with worst-case runtime guarantees on each instance will fail to take advantage of valuable structure shared across the problem instances. For example, when a commuter drives from work to…

New algorithm learns optimal path in reinforcement learning with linear approximations.

This paper approximates 1-Wasserstein distance using tree-based embedding.