New ICA method improves on existing techniques.
problem Finding independent components in data.
method Multiple-weighted Independent Component Analysis (MWeICA) based on approximate diagonalization of weighted covariance matrices.
result MWeICA achieves better results than state-of-the-art ICA methods with similar computational time.
Paper shows how to use elementary triplets to simplify independence model operations.
problem Simplifying operations with independence models.
method Using elementary triplets to represent conditional independences.
result Elementary triplets help in various operations like finding dominant triplets and computing model unions/intersections.
New framework extends ICA for non-independent variables, identifying pairwise mean independence.
problem Non-independent variables complicating ICA recovery.
method Algebraic recovery algorithm based on least-squares optimization over the orthogonal group.
result Pairwise mean independence is identifiable, robust to independence constraints.
New strategy improves cluster ensemble accuracy using Independency and Diversity metrics.
problem Lack of control over basic clustering result accuracy in diversity-based ensemble selection.
method Introduces Independency metric alongside Diversity for cluster ensemble selection. Uses graph conversion heuristic for Independency calculation and CAIL modeling language. Introduces Uniformity for diversity evaluation.
result Significant improvement in final ensemble accuracy compared to other methods.
New algorithms find half-optimal independent sets in sparse graphs.
problem Finding large independent sets in sparse random graphs.
method Low-degree polynomial algorithms.
result Low-degree polynomial algorithms can find independent sets of half-optimal size.
Entropy regularized OT test assesses independence between samples.
problem Testing independence between two samples.
method Entropy regularized optimal transport.
result Non-asymptotic bounds for test statistic established.
Path-independent equilibrium models improve network performance on harder problems.
problem Improving network performance on harder problem instances.
method Investigated path-independent equilibrium models and their impact on network performance.
result Path independence correlates with better performance on harder problem instances.
Identifying components and estimating mixing weights in unlabeled finite mixtures under marginal independence.
problem Identifying components and estimating mixing weights in unlabeled finite mixtures.
method Proving structural results and extending them to observable mixtures.
result Identifying components and estimating mixing weights under marginal independence.
Paper optimizes approximating high-dimensional diffusions by independent coordinates.
problem Optimizing approximations of high-dimensional diffusions by independent coordinates.
method Introduces independent projection as optimal for two criteria.
result Independent projection is optimal for two criteria related to entropy and convergence.
New method exploits independence in instrumental variable models for better causal inference.
problem Identify causal functions in the presence of unobserved confounders.
method HSIC-X method that exploits independence between response, hidden confounders, and instruments.
result The method provides better finite sample results and is invariant to distributional shifts.
Derives derivatives and geometric framework for functions with non-independent variables.
problem Characterizing functions with non-independent variables in probabilistic models.
method Derives actual and dependent partial derivatives, dependent Jacobian matrix, and tensor metric.
result Derives gradient, Hessian, and Taylor expansion for functions with non-independent variables.
Improved sample complexity bounds for neural networks with depth independence.
problem Understanding the sample complexity of neural networks with depth and size independence.
method New bounds on Rademacher complexity with norm constraints on parameter matrices.
result Improved sample complexity bounds that are fully independent of network size under certain assumptions.
Method learns reward functions that are independently obtainable and sum to original reward.
problem Learning reward functions that are independent and meaningful.
method Defining independent obtainability and optimizing a novel objective function.
result Learned reward functions generalize well to modified environments and have optimal policies.
New knots have unique Whitehead doubles.
problem Understanding independence in knot concordance groups.
method Using 4-dimensional constructions and Whitehead doubles.
result Infinite families of knots with independent Whitehead doubles.
New knot invariants from covering involutions help deduce linear independence results.
problem Understanding the smooth concordance group of knots.
method Covering involutions and adapted ideas from previous research.
result Novel linear independence results in the smooth concordance group of knots.
This research designs a data-driven partition to test independence between continuous variables.
problem Testing independence between continuous random variables.
method Empirical log-likelihood statistic and data-driven tree-structured partition.
result Strongly consistent test of independence over probability families.
This note shows how independent elliptical distributions minimize the Wasserstein distance.
problem Minimizing the Wasserstein distance between elliptical distributions.
method Analyzing the Wasserstein distance between independent elliptical distributions with the same density generators.
result Independent elliptical distributions minimize their Wasserstein distance from other elliptical distributions with the same density generators.
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by con…
This work investigates the intersection property of conditional independence. It states that for random variables A,B,C and X we have that X independent of A given B,C and X independent of B given A,C implies X independent of (A,B) given C. Under the assumption that the joint distribution has a co…
Deep learning models predict generalization gaps without specific task or architecture.
problem Predicting when deep learning works across different tasks and architectures.
method Created a dataset of 13,500 neural networks trained on various spiral datasets and parameters. Used this dataset to train predictors for generalization gaps.
result DNNs and RNNs outperform linear models in predicting generalization gaps, with RNNs achieving R2=0.584. New findings show independent subordination is not relevant for accurate option pricing.
problem Determining if independent subordination improves option pricing accuracy.
method Utilized a class of additive processes (ATS) to demonstrate that independent subordination is incompatible with market data and shows worse calibration performances.
result Independent subordination is not relevant for accurate option pricing, as shown by the ATS class of processes.
The paper characterizes measures preserving independence through planar web geometry.
problem Characterizing measures with preserved independence.
method Planar web geometry and inhomogeneous Abelian functional equations.
result The independence-preserving property is preserved by coordinatewise reparametrizations and forms a natural invariant.
New methods infer causal structure from data without hidden variables.
problem Inferring causal structure from observational data with hidden variables.
method Introduces alternative independence tests and conditionally-additive-noise models.
result Can infer causal relations without assumptions about equation form or hidden variables.
Estimates marginal independence structure of Bayesian networks from data.
problem Learning the marginal independence structure of Bayesian networks from observational data.
method Using Gröbner basis and MCMC method (GrUES) to connect and recover the true structure.
result GrUES recovers the true marginal independence structure at a higher rate than simple independence tests.
Greedy selection works well in a toy model of independent increments.
problem Iterative selection of maximum-value processes from i.i.d. stochastic processes.
method Fixed greedy selection at each stage.
result Optimal strategy is greedy selection under independent increments.
The paper analyzes counterfactual invariance and its relation to conditional independence.
problem Understanding the relationship between counterfactual invariance and conditional independence.
method Theoretical analysis of existing definitions, graphical implications, and mathematical proofs.
result Counterfactual invariance implies conditional independence, but not the other way around.
New model improves GP approximations by relaxing independence across resolutions.
problem Overfitting and non-smooth predictions in multiresolution GPs.
method Conditional independence among GPs across resolutions.
result Improved robustness against overfitting and smoother predictions.
Paper introduces a new test for conditional independence using weighted partial copulas.
problem Testing conditional independence between variables.
method The approach uses a weighted partial copula function and a bootstrap procedure to compute regions of rejection.
result The proposed test has competitive power compared to existing methods.
Paper extends nonparametric regression bounds for dependent β-mixing samples.
problem Analyzing error in nonparametric regression with dependent data.
method Extends uniform deviation inequalities from independent to dependent β-mixing samples. result Derives generalization bounds for nonparametric regression with dependent data.
First semi-device independent quantum money scheme introduced, proving unforgeability.
problem Creating secure quantum money without full device independence.
method Inspired by semi-device independent quantum key distribution, relaxes mint's cooperation assumption.
result First unforgeable quantum money scheme with partially relaxed device independence.
We present two algorithms for learning the structure of a Markov network from data: GSMN* and GSIMN. Both algorithms use statistical independence tests to infer the structure by successively constraining the set of structures consistent with the results of these tests. Until very recently, algorithms for structure lear…
Embeds Teichmüller space into geodesic currents, proving independence.
problem Embedding Teichmüller space into geodesic currents.
method Algebraic method for Teichmüller space, ergodic argument for negatively curved surfaces.
result Embedding is totally linearly independent.
New method identifies latent sources from nonlinear mixtures without auxiliary variables.
problem Identifying latent sources from nonlinear mixtures without additional information.
method Structural Sparsity assumptions on the mixing process.
result Latent sources can be identified up to permutation and transformation.
Spectral Independence Criterion helps infer cause-effect relationships in time series.
problem Distinguishing cause from effect in time series data.
method Spectral Independence Criterion (SIC) based on PSD and frequency response.
result SIC provides a robust method for causal inference in time series data.
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that 2K projection vect…
New study shows limits of low-degree algorithms in finding large independent sets in sparse hypergraphs.
problem Finding large independent sets in sparse random hypergraphs.
method Low-degree polynomial algorithms are analyzed to determine their limits.
result Low-degree algorithms can find independent sets of density up to \(\left(\frac{\log d}{(r-1)d}
ight)^{1/(r-1)}\), but no larger.
Diagonal transformations preserve independence structures in non-Gaussian distributions.
problem Preserving independence structures in non-Gaussian distributions.
method Diagonal nonlinear transformations of multivariate normal variables.
result Independence structures are preserved in non-Gaussian distributions under diagonal transformations.
Fast nonparametric conditional independence testing via two-stage regression
problem Fast nonparametric conditional independence testing
method BLITZ (Broad-to-Local Independence Testing via residualiZation)
result Better null calibration than fast kernel, random-feature, and regression-based competitors
New framework relaxes independence assumption for graph-mixing dependencies.
problem Tackles limitations of existing generalization results for graph-mixing dependencies.
method Proposes a framework where dependencies decay with graph distance, derives generalization bounds leveraging online-to-PAC framework.
result Derives high-probability generalization guarantees that depend on mixing rate and graph's chromatic number.
New research challenges the independence assumption in neurosymbolic learning, leading to overconfident predictions and unrepresentable uncertainty.
problem The independence assumption in neurosymbolic learning systems can lead to overconfident predictions and hinder uncertainty quantification.
method The study proves the limitations of the independence assumption and introduces new loss functions that are non-convex and difficult to optimise.
result Neurosymbolic learning systems using the independence assumption are prone to overconfidence and cannot represent uncertainty over multiple valid options.
In this paper, we are interested in short homologically and homotopically independent loops based at the same point on Riemannian surfaces and metric graphs. First, we show that for every closed Riemannian surface of genus g≥2 and area normalized to g, there are at least $\ceil{\log(2g)+1}$ homotopically indep…
New bounds on random quadratic forms hold under dependence, useful for adaptive modeling.
problem Need for independence in bounds on random quadratic forms.
method Uniform bounds on random quadratic forms of conditionally independent and sub-Gaussian stochastic processes.
result Bounds hold under general dependencies and sequential design.
A new test for conditional independence in discretized data.
problem Testing conditional independence when only discretized observations are available.
method Proposes a conditional independence test designed for discretized observations, using bridge equations to recover latent variables' information.
result Demonstrates the effectiveness of the proposed test through theoretical and empirical validation.
The study examines the independence of GKM manifolds and symmetric spaces.
problem Understanding the independence of isotropy weights in GKM manifolds.
method Using weighted graphs and properties of symmetric spaces, the study analyzes the independence of isotropy weights.
result The maximal independence of G/H is 2, 3, or n=dimT, corresponding to symmetric spaces of rank >2. FIT is a fast nonparametric test for conditional independence.
problem Testing conditional independence for high-dimensional data.
method Based on the conditional independence principle, FIT assesses whether additional variables improve predictions.
result FIT is significantly faster and more accurate than existing methods for large datasets.
MISC finds multiple independent clusterings in different subspaces.
problem Difficulties in understanding diverse clusterings.
method Two-stage approach using independent subspace analysis and graph regularized semi-nonnegative matrix factorization.
result MISC discovers different clusterings from independent subspaces.
Coordinate-independent convolutions on manifolds avoid reference frame ambiguity.
problem Applying convolutions on non-Euclidean manifolds without reference frame ambiguity.
method Developed coordinate-independent and gauge-equivariant convolutions on Riemannian manifolds.
result Coordinate-independent convolutions are equivariant under local gauge transformations.
A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonp…