A new loss function for set reconstruction without order consideration.
problem Reconstructing sets of elements without considering their order.
method Set Cross Entropy, a permutation-invariant loss function.
result Natural information-theoretic interpretation and successful evaluations in tasks.
Study of financial time series and Brownian motion using order patterns and permutation entropy.
problem Analyzing order patterns and variation in financial time series and Brownian motion.
method Use of order patterns and permutation entropy to study financial data and Brownian motion, focusing on turning rate and up-down balance.
result For small lags, pattern frequencies in financial data remain constant. Up-down balance is better for change points in financial data.
This study analyzes oil market dynamics using information-theory metrics and finds geopolitical events impact market structure.
problem Analyzing informational efficiency of crude oil market during geopolitical events.
method Used information-theory-derived quantifiers (permutation entropy and permutation statistical complexity) to capture market dynamics.
result Geopolitical events impact the underlying dynamical structure of the oil market.
The paper analyzes Libor interest rates using Information Theory quantifiers and detects anomalous behavior.
problem Anomalous behavior in Libor interest rates across different maturities and currencies.
method Permutation Shannon entropy and Fisher information measure from Information Theory.
result Anomalous behavior detected in Libor interest rates, especially in 1, 2, and 3 months maturities.
The article uses complex system methods to predict cryptocurrency crises.
problem Predicting volatile cryptocurrency market crises.
method Recurrent analysis and permutation entropy of dynamic systems.
result Dynamic complexity measures can predict cryptocurrency crises.
Machine learning and complexity-entropy methods estimate liquid crystal properties from textures.
problem Extracting physical properties from liquid crystal textures.
method Combining permutation entropy, statistical complexity, and machine learning.
result Significant precision in predicting physical properties of liquid crystals.
Order-flow entropy predicts price magnitude without directionality.
problem Predicting price magnitude in financial markets.
method Real-time order-flow entropy computed from a 15-state Markov transition matrix.
result Order-flow entropy predicts the magnitude of intraday returns with high accuracy.
A new Bayesian multinomial regression model using permuted and augmented stick-breaking.
problem Modeling categorical response variables given covariates.
method Permuted and augmented stick-breaking (paSB) construction.
result Transforms multinomial regression into regression of stick-specific binary variables.
This study analyzes cryptocurrency price dynamics using complexity-entropy causality.
problem Understanding the price dynamics of cryptocurrencies during market booms and busts.
method Used permutation-information-theory quantifiers and complexity-entropy causality plane.
result Discerned three distinct dynamics in cryptocurrency price data.
Study uses new statistical tool to classify corporate bonds by informational efficiency, aligning with credit ratings.
problem Under scrutiny of credit rating agencies after subprime crisis, the study explores the relationship between credit ratings and informational efficiency.
method Used a permutation-information-theory analysis on a sample of corporate bonds using a complexity-entropy causality plane.
result The classification of bonds by informational efficiency agrees with their credit ratings, forming two clusters: investment and speculative grades.
This paper constructs pseudo-Anosov braids with small normalized entropies.
problem Finding pseudo-Anosov braids with minimal normalized entropies.
method Describes a structure of fibered cones and provides a constructive description of monodromies.
result Construction of many pseudo-Anosov braids with small normalized entropies.
Study non-negative curvature Markov chains, proving entropy contraction.
problem Prove entropy contraction for Markov chains with non-negative curvature.
method Prove 1-step contraction in Wasserstein distance implies 1-step contraction in relative entropy.
result Prove MLSI with constant equal to minimal rate increment for mean-field zero-range process.
Cryptocurrencies show varying levels of efficiency over time, forming clusters with younger ones mimicking older ones.
problem Determining the efficiency of cryptocurrencies over time.
method Permutation entropy and statistical complexity over sliding time-windows of price log returns.
result 37% of cryptocurrencies are efficient over 80% of the time, while 20% are efficient in less than 20% of the time.
Study shows stock market efficiency varies over time and can be networked.
problem Understanding the dynamic and collective aspects of stock market efficiency.
method Defined and calculated time-varying efficiency using permutation entropy of log-returns.
result Major world stock markets can be hierarchically classified into groups with similar efficiency profiles, but these rankings are unstable.
Bitcoin's price direction is better predicted without additional drivers during high volatility.
problem Predicting Bitcoin's price direction using various determinants.
method Continuous local transfer entropy for feature selection and deep learning classification model.
result Bitcoin's price direction can be better predicted without additional drivers during high volatility.
The paper extends explainability methods to uncertainty-aware models, revealing feature impacts on predictive entropy and likelihood.
problem Understanding the factors contributing to uncertainty in probabilistic models.
method Adapting permutation feature importance, partial dependence plots, and individual conditional expectation plots to measure feature impacts on predictive entropy and likelihood.
result Novel insights into model behaviour and feature impacts on uncertainty are obtained.
EDD uses entropy of distance distributions to cluster unlabeled data.
problem Challenges in clustering unlabeled high-dimensional data.
method EDD employs Shannon entropy to quantify distance distribution peaks.
result EDD detects varying degrees of clustering sensitivity.
TSSC images enhance chaotic signal classification using ConvNets.
problem Classifying chaotic signals accurately and robustly.
method Triad State Space Construction (TSSC) for image encoding, Convolutional Neural Network (ConvNet) for classification.
result TSSC-ConvNet achieves high accuracy and robustness in chaotic signal classification.
Model learns set representations through optimized permutations.
problem Challenges in learning set representations due to permutation-invariance.
method Proposes a Permutation-Optimisation module to learn set permutations.
result Achieves state-of-the-art results on various set learning tasks.
We prove that any smooth action of Zm−1,m≥3 on an m-dimensional manifold that preserves a measure such that all non-identity elements of the suspension have positive entropy is essentially algebraic, i.e. isomorphic up to a finite permutation to an affine action on the torus or its factor by $\pm\Id$…
The existence of forbidden patterns, i.e., certain missing sequences in a given time series, is a recently proposed instrument of potential application in the study of time series. Forbidden patterns are related to the permutation entropy, which has the basic properties of classic chaos indicators, thus allowing to sep…
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.
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.
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.
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.
This work extends implicit bias analysis to multiclass classification using a new loss framework.
problem The implicit bias of gradient descent on multiclass data without explicit regularization.
method Employing the PERM framework to introduce a multiclass extension of the exponential tail property.
result Extended implicit bias result to multiclass classification using a new loss framework.
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.
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.
Study on writhe of permutations and random knots, with non-Gaussian distribution.
problem Understanding the writhe of permutations and its relation to random knots.
method Introduced writhe of permutations, studied asymptotics of random permutations, described model for random framed knots.
result Obtained a non-Gaussian limit distribution for the writhe of random permutations.
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.
Janossy pooling averages permutation-sensitive functions over all sequences to create invariant functions.
problem Creating deep, invariant functions for variable-size inputs.
method Janossy pooling: average permutation-sensitive functions over all reorderings.
result Improved performance over state-of-the-art methods.
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.
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.
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.
The paper uses permutation representations to visualize group extensions and subgroups.
problem Visualizing and understanding group extensions and subgroups.
method Developing metaphoric rope-thread diagrams to represent semi-direct products and their constituents.
result Injective homomorphisms into semi-direct products are established.
A theorem connects knot permutations with specific moves.
problem Understanding isotopy classes of knots through permutations.
method Defines and studies petal diagrams and two types of moves.
result Any isotopic knots can be transformed into each other via defined moves.
Paper addresses regression with permuted data, proposing robust methods.
problem Regression with permuted data, where response and predictor variables are mismatched.
method Proposes robust regression methods to handle inconsistent least squares estimators.
result Robust regression methods can recover permutation and estimate regression parameters.
New kernels for permutations improve accuracy in ranking tasks.
problem Improving ranking accuracy in permutation-based tasks.
method Introduced weighted Kendall kernel, supervised learning for weights, and higher-order permutation kernels.
result Supervised learning of weights enhances kernel performance for permutation tasks.
SPG learns policies on permutation matrices using Sinkhorn layers.
problem Optimizing permutations for tasks like sorting, ranking, and matching.
method Introduces Sinkhorn Policy Gradient (SPG) algorithm with a temperature-controlled Sinkhorn layer.
result SPG agents perform competitively and are more data-efficient than baseline methods on matching tasks.
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.
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.
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.
The Pontryagin dual of the twisted Alexander module for a d-component link and GL(N,Z) representation is an algebraic dynamical system with an elementary description in terms of colorings of a diagram. In the case of a knot, its associated topological entropy is the logarithmic growth rate of the number of torsion elem…
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.
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.