arXiv research

Consider a noisy linear observation model with an unknown permutation, based on observing $y = Π^* A x^* + w$, where $x^* \in \mathbb{R}^d$ is an unknown vector, $Π^*$ is an unknown $n \times n$ permutation matrix, and $w \in \mathbb{R}^n$ is additive Gaussian noise. We analyze the problem of permutation recovery in a …

We tackle tensor denoising with unknown permutations, achieving optimal recovery with polynomial estimators.

Estimates isotonic functions under unknown permutations, achieving optimal statistical and computational efficiency.

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…

We shrink confidence sets for equivalent discrete distributions using permutation equivalence.

In "Unlabeled Sensing", one observes a set of linear measurements of an underlying signal with incomplete or missing information about their ordering, which can be modeled in terms of an unknown permutation. Previous work on the case of a single noisy measurement vector has exposed two main challenges: 1) a high requir…

We tackle permutation in linear regression with a new inference framework.

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…

Method estimates treatment effects in dyadic data with unknown confounders.

A new method resolves permutation issues in shuffled linear regression for large-scale applications.

Study aggregation of statistical evidence under unknown dependence using group-invariance.

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…

Study recovers spike order in noisy tensor estimation without SNR assumptions.

New method uses exponential family priors to handle shuffled data problems.

Active seriation recovers item order from noisy pairwise similarity measurements.

Matching correlated VAR time series databases by recovering matching permutations.

Many applications, including rank aggregation and crowd-labeling, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and columns. We consider the problem of estimating such a matrix based on noisy observations of a subset of its entries, and design and analyze a polynomi…

In this paper we study G-surfaces, a rather unknown surface class originally defined by Calapso, and show that the coordinate surfaces of a Guichard net are G-surfaces. Based on this observation, we present distinguished Combescure transformations that provide a duality for Guichard nets. Another class of special Combe…

New algorithm recovers matrices with unknown correspondences.

The paper explores how low-degree polynomials can detect shuffled linear regression models.

This paper addresses the general problem of modelling and learning rank data with ties. We propose a probabilistic generative model, that models the process as permutations over partitions. This results in super-exponential combinatorial state space with unknown numbers of partitions and unknown ordering among them. We…

Many machine learning problems can be characterized by mutual contamination models. In these problems, one observes several random samples from different convex combinations of a set of unknown base distributions. It is of interest to decontaminate mutual contamination models, i.e., to recover the base distributions ei…

Paper tackles sparse recovery with shuffled labels, establishing statistical and computational limits.

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…

Paper develops new conformal prediction methods for sum or average of unknown labels.

Paper studies vertex correspondence recovery in correlated graphs with node features.

Algorithm recovers permutations of high-dimensional Gaussian vectors with constant correlation.

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 $Ω(K\log K)$ labeled samp…

Paper tackles non-stationary kernelized bandits with near-optimal algorithm.

Cheap permutation tests speed up distribution testing without sacrificing accuracy.

C-OPH improves One Permutation Hashing by using a shorter circulant permutation.

Random permutations can offer faster convergence than with-replacement sampling for some functions.

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…

The paper improves Fisher-Pitman tests for Poisson mixtures, detecting autism-related genes.

Permutations linked to knots and links, with unknots counted by Schröder numbers.

Regularizes RNNs to be invariant to input order.

Permutability of surface transforms yields discrete analogs.

We solve continuous-time latent SDE identifiability using diffusion shifts.

Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in diverse domains such as computer vision, data mining, communications and biology.…

A new permutation method improves two-sample testing power.

The paper proposes an efficient estimator for linear regression with shuffled labels.

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.

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…

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 …

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, …

Given a knot complement X and its p-fold cyclic cover X_p, we identify twisted polynomials associated to 1-dimensional linear representations of the fundamental group of X_p with twisted polynomials associated to related p-dimensional linear representations of the fundamental group of X. This provides a simpler and fas…

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…