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.
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…
We study petal diagrams of knots, which provide a method of describing knots in terms of permutations in a symmetric group S2n+1. We define two classes of moves on such permutations, called trivial petal additions and crossing exchanges, which do not change the isotopy class of the underlying knot. We prove that a…
Unlabeled sensing is a linear inverse problem where the measurements are scrambled under an unknown permutation leading to loss of correspondence between the measurements and the rows of the sensing matrix. Motivated by practical tasks such as mobile sensor networks, target tracking and the pose and correspondence esti…
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming that the underlying matrix has low rank, or is well-approximated by a low rank matr…
Improves full conformal prediction for stochastic non-conformity measures.
problem Inability of existing conditions to guarantee full conformal prediction validity under stochastic settings.
method Introduces a new sufficient condition: Conditional Independence & Permutation Invariance in Distribution.
result Corrects the insufficient condition and provides a new sufficient condition for full conformal prediction validity.
Generative model for set-valued data using permutation invariant flows.
problem Modeling set-valued data with conditional generative models.
method Conditional generative probabilistic model using continuous normalizing flows with permutation equivariant dynamics.
result Significantly outperforms non-permutation invariant baselines in log likelihood and domain-specific metrics.
New methods reduce extrapolation errors in feature importance.
problem Flawed feature importance methods using unrestricted permutations lead to extrapolation errors.
method Three new approaches: conditional model reliance, Knockoffs with Gaussian transformation, and restricted ALE plot designs.
result Theoretical and numerical results show our strategies reduce/eliminate extrapolation.
CPI overcomes limitations of permutation importance by providing accurate variable selection.
problem Misidentification of unimportant variables in complex models due to covariate correlations.
method Developed a model agnostic and computationally lean Conditional Permutation Importance (CPI) approach.
result CPI provides accurate type-I error control and more parsimonious variable selection.
Paper connects GLM and LRM for better classification performance.
problem Improving classification performance using statistical inference.
method Derives a statistical test based on SVM and permutation analysis.
result MLE-based inference provides better parameter estimation.
P. Berglund, T. Hübsch, and M. Henningson proposed a method to construct mirror symmetric Calabi-Yau manifolds. They considered a pair consisting of an invertible polynomial and of a finite (abelian) group of its diagonal symmetries together with a dual pair. A. Takahashi suggested a method to generalize this construct…
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.
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.
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.
Novel neural GP kernels learn stable, flexible covariance structures.
problem Scalable and flexible covariance kernels for Gaussian processes.
method Directly learn kriging coefficients and conditional standard deviations using deep neural architectures exploiting permutation-equivariant structure.
result Improved training stability and data efficiency with expressive, non-stationary kernels.
CIT and CIF improve feature selection for downstream prediction.
problem Feature selection bias in machine learning models.
method Conditional inference trees and forests with Bonferroni correction.
result CIF ranks top 3 among 18 regression methods and top 4 among 17 classification methods.
Permutation-equivariant neural networks improve auction mechanisms by reducing regret and sample complexity.
problem Designing optimal auction mechanisms that balance revenue and bidders' regret.
method Introduced permutation-equivariant neural networks to auction mechanisms.
result Permutation-equivariant neural networks decrease expected ex-post regret and improve model generalizability.
The paper examines properties of GW optimal transport plans, showing they can be sparse and permutation-supported.
problem Properties of Gromov-Wasserstein optimal transport plans.
method Exploration of sparsity, permutation support, and cyclical monotonicity properties.
result GW optimal plans can be sparse and permutation-supported under certain conditions.
Proposes PEMI for online selective conformal prediction with asymmetric rules.
problem Challenges of handling asymmetric selection mechanisms in online selective conformal prediction.
method PEMI: permutation-based framework for selective conformal prediction with arbitrary asymmetric selection rules.
result Achieves exact selection-conditional coverage for any asymmetric selection mechanism and any prediction model.
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.
Consider a noisy linear observation model with an unknown permutation, based on observing y=Π∗Ax∗+w, where x∗∈Rd is an unknown vector, Π∗ is an unknown n×n permutation matrix, and w∈Rn is additive Gaussian noise. We analyze the problem of permutation recovery in a …
Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel conditional independence test in a predictive setting, and show that it achieves bet…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional mutual information combined with a local permutation scheme …
We study the problem of designing models for machine learning tasks defined on \emph{sets}. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of populati…
New method for nonlinear Granger causality improves predictive relationships.
problem Challenges in applying Granger causality to nonlinear data.
method Permutation of covariate set, artificial neural networks, consistent variance estimation.
result Permutation method outperforms other techniques in predicting nonlinear relationships.
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 …
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.
New method for estimating parameters in inverse problems using double robustness.
problem Estimating parameters defined as linear functionals of solutions to linear inverse problems.
method Source condition double robust inference method that uses iterated Tikhonov regularized adversarial estimators.
result Asymptotic normality of the parameter of interest as long as either the primal or dual inverse problem is sufficiently well-posed.
Permutation testing is a non-parametric method for obtaining the max null distribution used to compute corrected p-values that provide strong control of false positives. In neuroimaging, however, the computational burden of running such an algorithm can be significant. We find that by viewing the permutation testing …
New method improves transfer and robustness of supervised contrastive learning.
problem Class collapse in supervised contrastive learning leads to poor representation quality.
method Adding a weighted class-conditional InfoNCE loss and a class-conditional autoencoder.
result Improves transfer and robustness on 5 standard datasets and 3 worst-group robustness datasets.
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.
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.
EquivCNP learns group symmetries for conditional data.
problem Learning conditional models with data symmetries.
method Group equivariant decomposition and Lie group convolutional layers.
result EquivCNP achieves comparable performance and zero-shot generalization.
Choice models, which capture popular preferences over objects of interest, play a key role in making decisions whose eventual outcome is impacted by human choice behavior. In most scenarios, the choice model, which can effectively be viewed as a distribution over permutations, must be learned from observed data. The ob…
Proves existence of proper solutions for inverse mean curvature flow.
problem Existence of proper solutions for inverse mean curvature flow.
method Proves existence theorem assuming non-degeneracy conditions on isoperimetric profile.
result No curvature assumption in existence theorem.
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.
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.
We obtain the following version of Lidskii theorem. Let L, M, N be p-dimensional subspaces in R^n. Let ψ_j be the angles between L and M, let φ_j be the angles between M and N, and let θ_j be the angles between L and N. Consider the orbit of the vector ψwith respect to permutations of coordinates and inversions of axis…
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…
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.
New method uses exponential family priors to handle shuffled data problems.
problem Handling mismatch errors in record linkage of two data files.
method Flexible exponential family prior on the permutation group for regularization.
result The proposed method outperforms competing methods in synthetic and real data.
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…
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.
Efficiently solves inverse problems with diffusion and flow models in just a few steps.
problem Solving inverse problems like super-resolution, inpainting, or deblurring using diffusion or flow models.
method Conditional Conjugate Integrators framework that projects inverse problem dynamics into a more amenable space for sampling.
result Generates high-quality samples in as few as 5 conditional sampling steps, outperforming competing methods.
Paper introduces new importance metrics for machine learning models, linking them to CATE.
problem Interpreting black-box models' importance metrics due to data dependence and non-parametric nature.
method Introduces MVIM and CVIM, proposing permutation-based estimation and bias-variance decomposition.
result MVIM and CVIM have a quadratic relationship with CATE, addressing bias in correlated predictors.
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.