arXiv research

Solves partial assignment problems using random clique complexes.

Given a triangulated region in the complex plane, a discrete vector field $Y$ assigns a vector $Y_i\in \mathbb{C}$ to every vertex. We call such a vector field holomorphic if it defines an infinitesimal deformation of the triangulation that preserves length cross ratios. We show that each holomorphic vector field can b…

The Heights Theorem is extended to all Riemann surfaces with a first kind fundamental group.

GRAMPA spectral method solves graph matching problem with high probability.

A new algorithm improves solving QAP with better performance.

A new method for few-shot learning using Laplacian regularization.

Paper solves Gromov-Wasserstein for point clouds efficiently.

We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be assigned to categories they are dissimilar to), and an item-item similarity mat…

Network learns graph matching directly from edge affinity matrices.

We investigate classification results for general quadratic functions on torsion abelian groups. Unlike the previously studied situations, general quadratic functions are allowed to be inhomogeneous or degenerate. We study the discriminant construction which assigns, to an integral lattice with a distinguished characte…

Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems, not only in the worst case, but in an average-complexity sense under this same i…

The study connects triangulated surfaces to complex projective structures and circle patterns.

A new OT discrepancy derived from GW for faster large-scale comparisons.

Unified approach to graph matching using Hilbert spaces and entropy-regularized Frank-Wolfe algorithm.

GRAMPA algorithm recovers latent vertex correspondence in correlated graphs with high probability.

In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is challenging with data having a nonconvex or manifold structure, as with images or text…

Various applications involve assigning discrete label values to a collection of objects based on some pairwise noisy data. Due to the discrete---and hence nonconvex---structure of the problem, computing the optimal assignment (e.g.~maximum likelihood assignment) becomes intractable at first sight. This paper makes prog…

Paper solves graph matching problem using convex relaxation to the simplex.

Graph alignment problem solved with convex relaxations for correlated matrices.

Paper compares expressive power of GNNs, proving approximation guarantees for practical architectures.

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal modules of Lie algebras with involution. Then we construct a fu…

Paper analyzes Birkhoff relaxation for graph alignment, providing theoretical guarantees.

Paper introduces a new outer measure for continuous price paths with instant enforcement.

Improved R-QDA classifier performs well in unbalanced data settings.

A weighted random survival forest is presented in the paper. It can be regarded as a modification of the random forest improving its performance. The main idea underlying the proposed model is to replace the standard procedure of averaging used for estimation of the random survival forest hazard function by weighted av…

Improved graph matching using covariates for network data integration.

Matching correlated VAR time series databases by recovering matching permutations.

This work optimizes RL algorithms using entropy regularisation for continuous-time LQ problems.

We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso ($\ell_1$) sparsity penalty with a quadratic penalty that shrinks the coefficient vector toward the leading principal components of …

Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different p…

The paper develops a method for self-normalized inference in adaptive experiments.

Unified view on selective credit assignment for reinforcement learning.

A new method estimates mutual information with fewer paired samples using optimal transport.

Optimizes train schedules and maintenance using CP and QA.

The period mapping assigns to each rank n, marked metric graph Gamma a positive definite quadratic form on H_1(Gamma). This defines maps Phi* and Phi on Culler--Vogtmann's outer space CV_n, and its Torelli space quotient T_n, respectively. The map Phi is a free group analog of the classical period mapping that sends a …

New algorithms assign credit to past decisions based on hindsight.

New formulations for comparing metric measure spaces with arbitrary positive measures.

EgalMAB solves fair resource allocation in stochastic bandits.

Hybrid Policy Optimization tackles reinforcement learning in hybrid spaces, improving performance over PPO.

Error bounds based on worst likely assignments use permutation tests to validate classifiers. Worst likely assignments can produce effective bounds even for data sets with 100 or fewer training examples. This paper introduces a statistic for use in the permutation tests of worst likely assignments that improves error b…

Assignment methods are at the heart of many algorithms for unsupervised learning and clustering - in particular, the well-known K-means and Expectation-Maximization (EM) algorithms. In this work, we study several different methods of assignment, including the "hard" assignments used by K-means and the ?soft' assignment…

COCOA improves credit assignment in reinforcement learning by measuring contributions to rewards.

Bayesian optimization method for permutations accelerates combinatorial search.

Matching one set of objects to another is a ubiquitous task in machine learning and computer vision that often reduces to some form of the quadratic assignment problem (QAP). The QAP is known to be notoriously hard, both in theory and in practice. Here, we investigate if this difficulty can be mitigated when some addit…

In this short note, we compare the combinatorial sign assignment of Manolescu, Ozsvath, Szabo and Thurston for grid homology of knots and links in 3-sphere with the sign assignment coming from a coherent system of orientations on Whitney disks. Although these constructions produce different signs, a small modification …

Sampling a fraction of pairs can match full evaluation in machine learning losses.

New methods optimize personalized treatment assignment in trials with many arms.

Proposes unbiased estimators for training mixture of experts models.