New algorithm improves PPS for multi-object matching.
problem Efficiently synchronize partial permutations for multi-object matching.
method Proposed CEMP-Partial algorithm for partial permutation synchronization (PPS). Uses sparse matrix operations and nonconvex weighted projected power method.
result Proves CEMP-Partial can exactly classify corrupted and clean partial permutations under adversarial corruption.
Many problems at the intersection of combinatorics and computer science require solving for a permutation that optimally matches, ranks, or sorts some data. These problems usually have a task-specific, often non-differentiable objective function that data-driven algorithms can use as a learning signal. In this paper, w…
Matching correlated VAR time series databases by recovering matching permutations.
problem Matching perturbed and permuted correlated VAR time series.
method Probabilistic framework modeling, maximum likelihood estimator (MLE), linear assignment, convex relaxations.
result Recovery guarantees for perfect or partial recovery of matching permutations, thresholds for σ. In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that the set of pairwise matchings is cycle-consistent, i.e. in the full…
Signed-permutation coordinate transport improves model alignment across checkpoints.
problem Improper alignment of coordinate-indexed objects across model checkpoints.
method Introduces sign-marginalized Hungarian matching and coordinate-preserving transport.
result Recovering signed-permutation gauge improves coordinate alignment and model performance.
A new method resolves permutation issues in shuffled linear regression for large-scale applications.
problem Estimating latent features through linear transformation with unknown permutations.
method Spectral matching method to align spectral components of measurement and feature covariances.
result Achieves accurate estimates in shuffled LS and LASSO settings with sufficient samples.
A tacit assumption in linear regression is that (response, predictor)-pairs correspond to identical observational units. A series of recent works have studied scenarios in which this assumption is violated under terms such as ``Unlabeled Sensing and ``Regression with Unknown Permutation''. In this paper, we study the s…
New algorithm finds sparse matrices on Stiefel manifold for optimisation.
problem Finding sparse matrices on Stiefel manifold for optimisation.
method Modified Orthogonal Iteration algorithm for sparse global optimality.
result Proposed method finds globally optimal sparse Stiefel matrices.
ShuffleNet is a state-of-the-art light weight convolutional neural network architecture. Its basic operations include group, channel-wise convolution and channel shuffling. However, channel shuffling is manually designed empirically. Mathematically, shuffling is a multiplication by a permutation matrix. In this paper, …
Novel algorithm estimates local permutations in unlabeled multi-view sensing.
problem Estimating local permutations in unlabeled multi-view sensing.
method Graph alignment and Gromov-Wasserstein alignment exploiting multiple views.
result The proposed algorithm is scalable and applicable to challenging SNR regimes.
Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these combinatorial objects is intractable. In response, this paper introduces a collectio…
Algorithm recovers permutations of high-dimensional Gaussian vectors with constant correlation.
problem Recovering permutations of high-dimensional Gaussian vectors with constant correlation.
method Computing and comparing weighted counts of specially chosen wide trees.
result Polynomial-time algorithm for exact recovery at constant correlation.
Many matching, tracking, sorting, and ranking problems require probabilistic reasoning about possible permutations, a set that grows factorially with dimension. Combinatorial optimization algorithms may enable efficient point estimation, but fully Bayesian inference poses a severe challenge in this high-dimensional, di…
We consider the question of existence of ramified covers over P_1 matching certain prescribed ramification conditions. This problem has already been faced in a number of papers, but we discuss alternative approaches for an existence proof, involving elliptic curves and universal ramified covers with signature. We also …
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational dif…
A new method learns graph distributions invariant to node ordering.
problem Graphs are hard to model due to node ordering invariance issues.
method Score-based generative modeling with permutation equivariant graph neural network.
result The method achieves better or comparable graph generation results.
Paper solves graph matching for correlated Erdős--Rényi graphs.
problem Matching vertices of correlated Erdős--Rényi graphs.
method Polynomial-time algorithm based on comparison of partition trees.
result Exact matching achieved with high probability.
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries of the image domain. In comparison, there are a number of problems in which the…
This work refines claims about neural network connectivity, showing that simultaneous linear connectivity is possible under certain conditions.
problem Neural networks' loss landscapes are non-convex due to permutation symmetries, leading to high loss barriers between permuted networks.
method The authors introduce and analyze three claims of increasing strength regarding the connectivity of neural networks, focusing on permutations that align networks.
result The authors provide evidence that strong linear connectivity may be possible under certain conditions, specifically when interpolating among three networks of increasing width.
A new training method for efficient Boltzmann generators.
problem Training equivariant continuous normalizing flows (CNFs) is computationally expensive.
method Equivariant flow matching, based on optimal transport flow matching.
result Equivariant flow matching yields more efficient flows with shorter integration paths.
New method uses Multiple Choice Learning for speech separation.
problem Ambiguous task of assigning model predictions to ground truth signals.
method Uses Multiple Choice Learning (MCL) instead of Permutation Invariant Training (PIT).
result MCL matches PIT performance but is computationally advantageous.
New bounds for SGD show improved performance in various settings.
problem Improving convergence bounds for SGD with random permutations.
method Analyzing convergence of SGD with random reshuffling and arbitrary permutations.
result Tighter lower bounds for weighted average iterates in both convex and strongly-convex cases.
New metric captures individual neuron tuning across neural networks.
problem Need a metric that respects individual neuron tuning across different neural networks.
method Derived a 'soft' permutation-based metric using optimal transport theory.
result Metric avoids counter-intuitive outcomes and captures geometric insights.
A permutation-based SW test achieves minimax-optimal power for two-sample testing.
problem Nonparametric two-sample testing using the sliced Wasserstein distance.
method Proposes a permutation-based SW test and analyzes its performance.
result Achieves minimax separation rate n−1/2 over multinomial and bounded-support alternatives. The task of aggregating and denoising crowd-labeled data has gained increased significance with the advent of crowdsourcing platforms and massive datasets. We propose a permutation-based model for crowd labeled data that is a significant generalization of the classical Dawid-Skene model, and introduce a new error metri…
New statistics improve kernel independence testing efficiency.
problem Improving efficiency in kernel independence testing.
method Adapting martingale MMD construction to joint independence problem.
result Two new statistics achieve finite-sample consistency with linear per-test cost.
Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating an unknown matrix in this class, based on noisy observations of (possibly, a su…
This work tackles Bayesian neural networks by addressing loss landscape symmetries.
problem Understanding and optimizing the loss landscape of Bayesian neural networks.
method The approach involves extending marginalized loss barrier formalism to BNNs, proposing a matching algorithm to search for linearly connected solutions using permutation matrices and combinatorial optimization.
result Nearly zero marginalized loss barriers for linearly connected solutions were found.
Spectral methods achieve near-optimal performance in orthogonal and permutation group synchronization.
problem Recovering group elements from pairwise measurements in computer vision.
method Spectral methods applied with the leave-one-out technique.
result Near-optimal performance bounds for orthogonal and permutation group synchronization established.
The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the minimax error rate that is sharp up to logarithmic factors. We also analyze the p…
Study recovers spike order in noisy tensor estimation without SNR assumptions.
problem Estimating multiple signal vectors from noisy tensor observations.
method Gradient flow optimization of a nonconvex function.
result Determines sample complexity for efficient permutation recovery.
Method detects effects of synthesis parameters on plutonium oxide microstructure.
problem Detecting effects of synthesis parameters on material microstructure.
method Copula theory, high dimensional distribution distances, and permutational statistics.
result Effects of strike order and oxalic acid feed on plutonium oxide microstructure detected.
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they lift the original n×n-dimensional variable to an n2×n2-d…
A new method for efficient causal structure learning at scale.
problem Causal structure learning is computationally challenging at scale.
method Relaxed sparsest-permutation formulation with support-level relaxation and masked zero-fill incomplete Cholesky factorization.
result The method enables scalable comparison of candidate orderings and matches the accuracy of slower baselines.
HOoD detects near-out-of-distribution groups in correlated biomedical assays.
problem Detecting near-out-of-distribution cases in biased or incomplete data.
method Projects correlated measurements through a trained model and uses permutation-based hypothesis tests.
result HOoD reliably identifies OoD groups, outperforming other detectors.
Paper tackles sparse recovery with shuffled labels, establishing statistical and computational limits.
problem Sparse recovery with shuffled labels, focusing on permutation matrix and sparse signal reconstruction.
method Statistical and computational analysis, including minimax lower bounds and exhaustive-search based estimator.
result Established statistical and computational limits for correct recovery of permutation matrix and support set.
We consider the problem of consistently matching multiple sets of elements to each other, which is a common task in fields such as computer vision. To solve the underlying NP-hard objective, existing methods often relax or approximate it, but end up with unsatisfying empirical performance due to a misaligned objective.…
Electronic health records are an increasingly important resource for understanding the interactions between patient health, environment, and clinical decisions. In this paper we report an empirical study of predictive modeling of several patient outcomes using three state-of-the-art machine learning methods. Our primar…
Automated model tracks mouse behavior in home cages.
problem Confounding analysis in specialized arenas.
method Group Behaviour Model (GBM) using permutation matrix.
result Model captures individual and group behavior.
SoccerCPD detects tactical changes in soccer matches using spatiotemporal tracking data.
problem Detecting consistent team formations in fluid sports like soccer.
method Two-step change-point detection: formation and role changes.
result Accurately detects tactical changes and estimates formation and role assignments.
This paper improves model fusion by training-time neuron alignment, reducing barriers in multi-model fusion.
problem Diverse neuron permutations across different settings hinder model fusion performances.
method Training-time neuron alignment using fixed neuron anchors to reduce training-time permutations.
result Training-time neuron alignment improves fusion of pretrained models and federated learning performances.
We study the sample complexity of semi-supervised learning (SSL) and introduce new assumptions based on the mismatch between a mixture model learned from unlabeled data and the true mixture model induced by the (unknown) class conditional distributions. Under these assumptions, we establish an Ω(KlogK) labeled samp…
Cheap permutation tests speed up distribution testing without sacrificing accuracy.
problem Efficiently testing distribution differences and independence.
method Group datapoints into bins and permute only these bins, using stored sufficient statistics.
result Cheap permutation tests maintain the accuracy and optimality of standard tests but are significantly faster.
C-OPH improves One Permutation Hashing by using a shorter circulant permutation.
problem Improving the accuracy of One Permutation Hashing (OPH) for Jaccard similarity estimation.
method Develops a new densification method using a shorter circulant permutation.
result Achieves the smallest estimation variance for Jaccard similarity.
Random permutations can offer faster convergence than with-replacement sampling for some functions.
problem Understanding when and how random permutations outperform with-replacement sampling in SGD convergence.
method Analyzing convergence rates for different function classes (1D strongly convex, general strongly convex, quadratic strongly convex).
result The optimal convergence gap between random and permutation-based SGD varies from exponential to nonexistent, depending on the function class.
Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be further processed to learn a permutation-invariant representation of that set, avoid…
Synthetic augmentation improves financial machine learning performance in variance-dominant regimes.
problem Data scarcity in financial machine learning.
method Formalized synthetic augmentation, introduced size-matched null augmentation, and developed a non-parametric block permutation test.
result Synthetic augmentation is beneficial only in variance-dominant regimes, such as persistent volatility forecasting.
Paper tackles non-stationary kernelized bandits with near-optimal algorithm.
problem Minimizing regret in a time-varying reward function.
method Near-optimal algorithm with a novel restarting phased elimination with random permutation (R-PERP).
result Regret upper bound matches the lower bound, making the algorithm near-optimal.