Paper recovers multi-subspace matrices from permuted data.
problem Recovering a multi-subspace matrix from permuted data with corrupted columns.
method Four-stage algorithm pipeline: outlier identification, subspace reconstruction, outlier classification, unsupervised sensing.
result The pipeline provides theoretical guarantees for reliable multi-subspace matrix recovery.
New model improves matrix completion under noisy conditions.
problem Noisy matrix completion with structured matrices.
method Introduces permutation-rank model, analyzes SVD algorithm.
result Minimax rates equivalent to low-rank model, consistent estimator.
UPCA solves data matrix completion with permuted columns.
problem Data matrix completion with permuted columns.
method Algebraic geometry and two-stage algorithm.
result UPCA recovers the ground-truth matrix from corrupted data.
Permutation recovery in noisy linear models is studied with Gaussian noise and permutation matrix.
problem Permutation recovery in noisy linear models with unknown permutation and Gaussian noise.
method Random design setting with Gaussian matrix entries; NP-hardness of maximum likelihood estimation; polynomial time algorithm for d=1.
result Sharp conditions on SNR, sample size, and dimension for exact and approximate permutation recovery.
Polynomial-time algorithms improve on isotonic matrix estimation with unknown permutations.
problem Estimating a bivariate isotonic matrix with unknown permutations from noisy observations.
method Design and analysis of polynomial-time algorithms.
result Minimax optimal, computationally efficient estimation achievable in certain settings.
Dynamic systems linked to infinite permutation matrices.
problem Dynamic equivalence of control systems.
method Association of infinite permutation matrices.
result Relationship between dynamic equivalences and permutation matrices.
Faster rates achieved for estimating permutation-based matrices.
problem Estimating a bivariate isotonic matrix with unknown permutations.
method Polynomial-time algorithm for noisy observations of a subset of entries.
result Efficient estimation at rate O ~ ( n − 3 / 4 ) \widetilde{\mathcal O}(n^{-3/4}) O ( n − 3/4 ) . The paper models financial correlation matrices using permutation invariant Gaussian models and predicts market anomalies.
problem Modeling and predicting financial correlation matrices from high-frequency data.
method Constructing permutation invariant Gaussian matrix models with 4 parameters, using graph theory and polynomial functions.
result The permutation invariant Gaussian matrix model predicts the expectation values of cubic and quartic polynomials with strong evidence of fit.
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.
The paper examines when real matrix Schubert varieties are minimal submanifolds.
problem When are real matrix Schubert varieties minimal submanifolds?
method The authors establish minimality conditions using geometric arguments and partial permutations.
result The paper identifies specific conditions for real matrix Schubert varieties to be minimal submanifolds.
Develops a fast BMF approach for binary matrices.
problem Finding patterns in binary matrices for various applications.
method MEBF (Median Expansion for Boolean Factorization) using geometric segmentation and heuristic submatrix identification.
result Superior performance in reconstruction error and computational efficiency compared to existing methods.
RapidPT accelerates permutation testing in neuroimaging by reducing runtime.
problem Significant computational burden in voxel-wise analysis.
method Exploits low-rank structure of permutation testing matrix for efficient recovery.
result Achieves substantial speedups (1.5x - 1000x) over existing methods.
A new method reduces memory requirements for sorting high-dimensional data.
problem Efficiently sorting and organizing high-dimensional data with low memory usage.
method Iteratively shuffles N indices and applies SoftSort optimization steps.
result Significantly improves sorting quality for multidimensional data.
Deep models learn interactions across sets, achieving state-of-the-art performance.
problem Modeling interactions across multiple sets of objects.
method Permutation-equivariant parameter-sharing scheme for deep learning.
result State-of-the-art performance on matrix completion benchmarks and extrapolation tasks.
SQL-Rank improves recommendation systems by modeling user rankings as permutations.
problem Improving recommendation systems by better modeling user rankings.
method SQL-Rank uses a listwise approach based on a permutation model to construct user-specific rankings.
result SQL-Rank outperforms current state-of-the-art algorithms for implicit feedback and explicit feedback.
MPDCompress compresses deep neural networks by rearranging their matrices for better hardware compatibility.
problem Large deep neural networks are hard to deploy on edge devices due to size and computational complexity.
method Matrix permutation decomposition via random mask generation to transform irregular matrices into structured blocks.
result Achieved up to 8x network compression with less than 1% accuracy loss on various datasets.
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.
Multiple hypothesis testing is a significant problem in nearly all neuroimaging studies. In order to correct for this phenomena, we require a reliable estimate of the Family-Wise Error Rate (FWER). The well known Bonferroni correction method, while simple to implement, is quite conservative, and can substantially under…
AutoShuffleNet learns permutation matrices in CNNs for improved accuracy.
problem Manual design of channel shuffling in ShuffleNet.
method Learning permutation matrices via an exact Lipschitz continuous penalty in deep learning.
result Improved classification accuracies on CIFAR-10 and ImageNet datasets.
Enhances GNNs by capturing node relationships, outperforming 2-WL test.
problem Inability of conventional GNNs to fully capture node relationships due to permutation invariance.
method Develops permutation-sensitive aggregation mechanism using permutation groups.
result Proves superior expressivity compared to 2-WL test and not less than 3-WL test.
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.
New basis for permutation equivariant layers reduces computation costs.
problem Efficiently computing permutation equivariant layers in neural networks.
method Generalized partition algebra basis with low-rank tensors.
result Low-rank tensors enable faster computation compared to orbit basis.
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.
Active seriation recovers item order from noisy pairwise similarity measurements.
problem Recovering an unknown item ordering from noisy pairwise similarity measurements.
method Proposes an active seriation algorithm that provably recovers the latent ordering with high probability.
result Establishes optimal performance guarantees for successful recovery under a uniform separation condition.
New model learns graph spectra accurately, outperforming existing methods.
problem Graph diffusion models struggle to distinguish certain graph families and their spectra.
method Leveraged random matrix theory to analytically extract spectral properties, introducing Dyson Diffusion Model.
result Dyson Diffusion Model learns graph spectra accurately and outperforms existing models.
Recently, the method of b-bit minwise hashing has been applied to large-scale linear learning and sublinear time near-neighbor search. The major drawback of minwise hashing is the expensive preprocessing cost, as the method requires applying (e.g.,) k=200 to 500 permutations on the data. The testing time can also be ex…
PiNet learns graph representations invariant to node permutations.
problem Graph classification and representation learning invariant to node permutations.
method Differentiable node attention pooling, permutation invariant graph neural network.
result Significant accuracy improvement in isomorphic graph classification with limited training data.
New method synchronizes partial permutations using non-negative factorizations.
problem Synchronizing partial multi-matchings in a cycle-consistent manner.
method Non-negative factorization approach with spectral relaxation and rotation scheme.
result Guaranteed cycle-consistent results compared to existing methods.
New method tightens convex relaxations for permutation matrix problems without lifting.
problem Optimizing quadratic problems over permutation matrices.
method Lifting-free convex relaxation approach.
result Proves at least as tight as existing methods and performs better experimentally.
Deep networks exhibit permutation saddles and valleys between equivalent minima.
problem Understanding the structure of loss landscapes in deep neural networks.
method Geometric approach to constructing paths between equivalent minima and saddle points.
result Existence of permutation saddles and valleys in deep neural networks.
Identifies latent actions and dynamics from offline data with diverse demonstrators.
problem Recovering latent actions and environment dynamics from action-free trajectories.
method Assumes distinct policies for each demonstrator, identifies latent transitions and policies via matrix factorization.
result Identifies latent transitions and demonstrator policies up to permutation.
Optimal statistical seriation method for noisy matrices.
problem Permuting a matrix to align columns with monotonicity or unimodality.
method Statistical approach using least squares estimator with adaptation to natural structure.
result Least squares estimator is optimal up to logarithmic factors and adapts to natural structure.
New framework reduces factorisation model run time by exploiting sparse vector geometry.
problem Inefficient inner product computations over large sparse vectors in real-time applications.
method Geometry-aware permutation maps on a tessellated unit sphere for sparse vector embeddings.
result Significant reduction in run time with minimal accuracy loss.
A new method learns DAGs from Gaussian data without verifying acyclicity.
problem Learning DAGs from Gaussian data without verifying acyclicity.
method Relaxation technique for permutation matrix estimation and cyclic coordinatewise descent for sparse Cholesky factor estimation.
result The method recovers DAGs without verifying acyclicity constraints.
Enhances graph neural networks with structural message-passing for better generalization.
problem Limited representation power and inability to learn basic graph topological properties.
method Proposes a framework that includes a one-hot encoding of nodes and parametrized message and update functions ensuring permutation equivariance.
result Achieves state-of-the-art results on molecular graph regression on the ZINC dataset.
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.
New insights into when NMF decompositions are not unique.
problem Non-identifiability of NMF decompositions.
method Characterization of non-identifiability conditions.
result Characterized when and how non-uniqueness can occur in NMF.
New framework controls FDR for grouped features in sequential models.
problem FDR control for grouped features in sequential models.
method Grouped-feature FDR control framework for sequential and grouped models using mirror statistics and Permutation SHAP.
result FDR control for low- and high-dimensional grouped linear models and improved power under correlated signals.
The paper explores how low-degree polynomials can detect shuffled linear regression models.
problem Detecting multivariate shuffled linear regression models from independent Gaussian random matrices.
method Investigates the effectiveness of low-degree polynomial algorithms for distinguishing the model from independent Gaussian random matrices.
result Establishes a phase transition phenomenon in the performance of low-degree polynomial algorithms for distinguishing the model.
Non-Negative Matrix Factorization, NMF, attempts to find a number of archetypal response profiles, or parts, such that any sample profile in the dataset can be approximated by a close profile among these archetypes or a linear combination of these profiles. The non-negativity constraint is imposed while estimating arch…
DeepTMR reorders matrices without prior knowledge of structural patterns.
problem Matrix reordering without prior structural knowledge.
method DeepTMR uses a neural network to automatically extract features and reorder matrices.
result Trained network produces denoised mean matrix for visualization.
π-GNN learns soft permutations for graph representations, improving graph classification and regression.
problem Limitations of MPNNs in graph neural networks.
method Proposes π-GNN, which learns a soft permutation matrix for each graph, projecting graphs into a common vector space.
result π-GNN achieves performance competitive with state-of-the-art models on graph classification and regression tasks.
The column group is a subgroup of the symmetric group on the elements of a finite blackboard birack generated by the column permutations in the birack matrix. We use subgroups of the column group associated to birack homomorphisms to define an enhancement of the integral birack counting invariant and give examples whic…
MOB-dS uses permutation to correct for dependency in discrete survival data.
problem Identifying subgroups in discrete event time data with potential spurious results.
method Model-based recursive partitioning (MOB) with modified data matrix and permutation test.
result MOB-dS controls type I error rate better than standard MOB for discrete survival data.
Kaleidoscope matrices improve model quality and inference speed.
problem Choosing structured linear transformations for efficiency and accuracy.
method Introduce kaleidoscope matrices that can capture any structured matrix with near-optimal space and time complexity. Learn these matrices automatically within end-to-end pipelines.
result Kaleidoscope matrices can improve model quality and inference speed.
New method constructs equivariant neural networks for arbitrary matrix groups.
problem Challenges in constructing equivariant neural networks for complex groups.
method Completely general algorithm for solving equivariant layers of matrix groups.
result Constructs multilayer perceptrons equivariant to multiple groups including O(1,3), O(5), Sp(n), and Rubik's cube group.
A new test validates ensemble models against the null hypothesis.
problem Validating ensemble models against the null hypothesis of a constant response.
method Randomized permutation test on SVEM model predictions.
result The test maintains Type I error rate even with more parameters than observations.
Improved method for estimating precision matrices without knowing variable order.
problem Estimating precision matrices without knowing the order of variables.
method Combining multiple permutations and thresholding for sparse structure.
result Consistent property established under weak conditions, superior performance in simulations and real data.