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.
We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This …
FairICP addresses equalized odds fairness for multiple sensitive attributes.
problem Equalized odds fairness for multiple sensitive attributes.
method Adversarial learning with inverse conditional permutation.
result Promotes equalized odds under complex, multi-dimensional sensitive attributes.
PARD generates graphs efficiently and invariantly to node ordering.
problem Graph generation sensitivity to node ordering.
method Integrates autoregressive and diffusion models with a partial order for nodes and edges.
result PARD achieves state-of-the-art performance on molecular and non-molecular datasets.
Transformers for binary decisions are sensitive to evidence order, leading to unreliable outcomes.
problem Order sensitivity in Transformers for binary decisions leads to unreliable outcomes.
method Formalized an expectation-realization gap and developed QMV and EDFL bounds.
result Uniform permutation mixtures reduce dispersion and improve reliability.
Paper proposes a differentially private test for joint dependence among random vectors.
problem Detecting joint dependence among sensitive data while maintaining privacy.
method Differentially private permutation methodology for dHSIC test.
result Proposed test attains minimax optimal power across privacy regimes.
This paper introduces differentially private permutation tests for hypothesis testing.
problem Privacy concerns in sensitive data analysis.
method Differentially private permutation tests for kernel methods.
result Proposes dpMMD and dpHSIC for two-sample and independence testing, achieving optimal power.
Entity resolution seeks to merge databases as to remove duplicate entries where unique identifiers are typically unknown. We review modern blocking approaches for entity resolution, focusing on those based upon locality sensitive hashing (LSH). First, we introduce k-means locality sensitive hashing (KLSH), which is b…
The paper derives theoretical foundations for two common machine learning variable importance measures.
problem Understanding variable importance in machine learning problems.
method The paper derives closed-form expressions for Permute-and-Predict (PaP) and Leave-One-Covariate-Out (LOCO) methods.
result Theoretical derivations explain the behavior of PaP and LOCO under collinearity, linking them to coefficients and predictor variability.
To date, testing interactions in high dimensions has been a challenging task. Existing methods often have issues with sensitivity to modeling assumptions and heavily asymptotic nominal p-values. To help alleviate these issues, we propose a permutation-based method for testing marginal interactions with a binary respons…
Framework for sensitivity analysis in biomanufacturing processes.
problem High complexity and uncertainty in biomanufacturing processes.
method Shapley value estimation for linear and nonlinear pKG models, using quasi-Monte Carlo and antithetic sampling.
result Improved efficiency and accuracy in sensitivity analysis for biomanufacturing processes.
We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or permuted during the protocol. In this work, we propose a framework that treats the un…
Proposes a new method for variable importance using targeted learning.
problem Uncertainty quantification in variable importance metrics.
method Employing the targeted learning (TL) framework for conditional permutation variable importance.
result Improved accuracy in finite sample contexts compared to traditional methods.
New LCM aggregator improves GNN performance and efficiency.
problem Graph neural networks' sensitivity to aggregation function choice.
method Learnable commutative monoid for graph aggregation.
result LCM aggregator achieves performance competitive with recurrent aggregators.
A novel double-space tensor-product RKHS framework for hybrid uncertainty sensitivity analysis.
problem Quantifying the influence of hybrid aleatory and epistemic uncertainties on high-dimensional system responses.
method A novel double-space tensor-product RKHS framework for sensitivity analysis under hybrid uncertainty.
result Concurrent double Möbius inversion orthogonally decomposes global dependence measure into pure aleatory effects, pure epistemic effects, and their interaction contributions.
PEAR dynamically reconfigures agent roles to prevent persistent biases in multi-agent debates.
problem Persistent positional biases and sensitivity to role assignments in fixed topologies.
method Dynamic reconfiguration of agent roles and sparse topologies based on evolving agent states.
result Significantly improves average accuracy over debate baselines across multiple reasoning benchmarks.
Develops a scalable model for drug combination prediction in cancer.
problem Accurate prediction of drug combinations for cancer treatment.
method Permutation invariant multi-output Gaussian Processes with variational approximation and deep generative model.
result Model efficiently borrows information across drug combinations and provides uncertainty quantification.
The derived group of a permutation representation, introduced by R.H. Crowell, unites many notions of knot theory. We survey Crowell's construction, and offer new applications. The twisted Alexander group of a knot is defined. Using it, we obtain twisted Alexander modules and polynomials. Also, we extend a well-known t…
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…
We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group G that acts discretely on the input and output of a standard neural network layer φW:ℜM→ℜN, we show that φW is equivariant with respect to G-action iff $\m…
Generative adversarial networks (GANs) have proven effective in modeling distributions of high-dimensional data. However, their training instability is a well-known hindrance to convergence, which results in practical challenges in their applications to novel data. Furthermore, even when convergence is reached, GANs ca…
Permutations linked to knots and links, with unknots counted by Schröder numbers.
problem Understanding permutations as knots and links.
method Using grid diagrams and Bennequin's inequality.
result Permutations corresponding to unknots and links are counted by Schröder numbers.
Regularizes RNNs to be invariant to input order.
problem Making RNNs invariant to input order.
method Stochastic regularization to enforce permutation invariance.
result Improves model performance on permutation invariant tasks.
We tackle permutation in linear regression with a new inference framework.
problem Statistical investigation of permutation in linear regression models.
method Localization step followed by conditional Monte Carlo test and coefficient inference.
result Valid statistical inference procedures for permutation and regression coefficients.
Permutability of surface transforms yields discrete analogs.
problem Discretization of smooth surfaces with specific properties.
method Permutability of transforms of smooth surfaces.
result Discrete surfaces with discrete analogs of original properties.
A new permutation method improves two-sample testing power.
problem Two-sample testing with improved power and validity.
method Structured block-restricted cross-swaps.
result Block-restricted permutations achieve higher power than full permutations.
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…
New link topology connects permutation discrepancies to Diaconis-Graham inequalities.
problem Characterize permutations for which Diaconis-Graham inequalities hold with equality.
method Relate permutation discrepancies to the Euler characteristic of their associated links.
result Permutation discrepancies are directly related to the Euler characteristic of their associated links.
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, …
We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non-Ga…
Survey on neural networks for set-based data.
problem Efficient processing of set-based inputs in machine learning.
method Exploration of Deep Sets and Transformers for set functions approximation.
result Deep Sets can be generalized by differences in aggregation function.
New sampling methods improve Shapley value estimation for machine learning models.
problem Approximating Shapley values for non-trivial models is computationally challenging.
method Investigates new quadrature techniques and quasi-Monte Carlo methods for permutation sampling.
result Significant improvements in Shapley value estimates over existing methods.
4-Legendrian permutation racks can't distinguish knots but recover classical invariants.
problem Distinguishing Legendrian knots using permutation racks.
method Study of 4-Legendrian racks and their effectiveness.
result 4-Legendrian permutation racks cannot distinguish knots but recover classical invariants.
A new protocol evaluates small machine learning improvements conservatively.
problem Uncertainty in small gains reported in machine learning papers.
method Paired bootstrap protocol with BCa confidence intervals and sign-flip permutation tests.
result Conservative evaluation reduces over-claiming of small improvements.
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.
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.
Testing two potentially multivariate variables for statistical dependence on the basis finite samples is a fundamental statistical challenge. Here we explore a family of tests that adapt to the complexity of the relationship between the variables, promising robust power across scenarios. Building on the distance correl…
Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of considered entities (n!). It makes the direct definition of a multinomial dist…
Resolving Schwartz's quadratic meander number conjecture
problem Meander number of cyclic permutations
method Constructing families of cyclic permutations
result Meander number is bounded above and below quadratically in n
New method for accurate permutation inference in CCA.
problem Inaccurate permutation inference in CCA.
method Proposed solutions for permutation inference in CCA, including transforming residuals and stepwise estimation.
result Valid permutation tests for CCA with and without nuisance variables.
A new knot invariant uses permutations to extend Jones polynomials.
problem Extending Jones polynomials to classical and virtual knots and links.
method Colorings by permutations of a finite set to define new knot invariants.
result Established properties and computed polynomials for small cases.
Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of threads. In this way, subgroups and quotients are easily visualized. The general i…
A new method reduces computational costs for testing RF variable importance measures.
problem Testing variable importance measures from random forests is computationally expensive and challenging.
method Sequential permutation testing and sequential p-value estimation to reduce computational costs.
result Theoretical properties of sequential tests are confirmed, maintaining type-I error and high power.
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.
A new sampling scheme based on DOE improves Shapley value estimation accuracy and speed.
problem Heavy computational burden of calculating Shapley values in large coalition games.
method Design of Experiments (DOE) order-of-addition experimental designs for sampling.
result DOE-based sampling scheme yields more accurate and sometimes deterministic estimates of Shapley values.