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.
In an independence model, the triplets that represent conditional independences between singletons are called elementary. It is known that the elementary triplets represent the independence model unambiguously under some conditions. In this paper, we show how this representation helps performing some operations with in…
Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impo…
A new method tests conditional independence by transforming it into an unconditional problem using transport maps.
problem Testing conditional independence between two random vectors given a third.
method Constructing transport maps to transform conditional independence into unconditional independence, estimating these maps from data using conditional continuous normalizing flow models.
result The proposed method is validated through simulations and real-data analysis, demonstrating practical effectiveness.
Topological Pontryagin classes are algebraically independent in high-dimensional spaces.
problem Algebraic independence of topological Pontryagin classes.
method Analyzing rationalised cohomology of BTop(d).
result Topological Pontryagin classes are algebraically independent.
Extracts the finest pattern of mutual independence from data.
problem Inferring the finest mutual independence pattern from data.
method Estimate the set of valid patterns of dichotomic independence and use their intersection to infer the finest pattern.
result The method can estimate the finest mutual independence pattern from i.i.d. realizations of a multivariate normal distribution.
The paper explores how semantic independence can be captured in text embeddings using partial orthogonality.
problem Capturing semantic independence in text embeddings.
method Developed a theory and methods based on partial orthogonality to demonstrate semantic independence.
result Partial orthogonality captures semantic independence in text embeddings.
Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. In this paper we present Multiple-weighted Independent Component Analysis (MWeICA) algorithm, a new ICA method which is based on approximate diagonalizat…
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.
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.
This work develops a non-parametric test for relational independence in non-i.i.d. data.
problem Testing independence in relational systems where data samples are not i.i.d.
method Kernel mean embedding for relational variables, consistent non-parametric scalable kernel test.
result Empirically validated effectiveness compared to state-of-the-art tests.
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.
We study 'meta-dependence' in conditional independence tests across different empirical distributions.
problem Understanding the breakdown of conditional independence properties in finite data.
method Geometric intuition and information projections to measure meta-dependence between conditional independences.
result We provide a measure of meta-dependence that consolidates findings across synthetic and real-world data.
Method discovers local independence in systems with continuous variables.
problem Applying Context-Specific Independence (CSI) to continuous variables is impractical.
method Neural contextual decomposition (NCD) learns partition of joint outcome space.
result NCD successfully discovers local independence in synthetic and real-world systems.
TCRI improves domain generalization by enforcing conditional independence constraints.
problem Limitations of existing domain generalization methods due to incomplete constraints.
method TCRI implements regularizers motivated by conditional independence constraints.
result TCRI achieves cross-domain stability and outperforms baselines in worst-domain accuracy.
Develops a new framework for conditional independence.
problem Generalizing previous notions of conditional independence.
method Introduces transition probability spaces and transitional random variables.
result Satisfies all desired relevance relations except symmetry.
New method recovers causal order from dependent data.
problem Causal discovery methods fail with shared volatility or common scale effects.
method Linear Mean-Independent Acyclic Model (LiMIAM) with mean-independence restrictions.
result Compatible causal order can be recovered from dependent disturbances.
In this article, we define an independence system for a classical knot diagram and prove that the independence system is a knot invariant for alternating knots. We also discuss the exchange property for minimal unknotting sets. Finally, we show that there are knot diagrams where the independence system is a matroid and…
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.
Measuring conditional independence is one of the important tasks in statistical inference and is fundamental in causal discovery, feature selection, dimensionality reduction, Bayesian network learning, and others. In this work, we explore the connection between conditional independence measures induced by distances on …
Learning the Markov network structure from data is a problem that has received considerable attention in machine learning, and in many other application fields. This work focuses on a particular approach for this purpose called independence-based learning. Such approach guarantees the learning of the correct structure …
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.
The independence of Central Banks is shown to be a myth.
problem The independence of Central Banks is questioned as a flawed concept.
method Analyzes the arguments for Central Bank independence and demonstrates their logical flaws.
result The independence of Central Banks is found to be a chimera.
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.
Neurosymbolic predictors fail to model uncertainty under independence assumption.
problem Neurosymbolic predictors' reliance on independence assumption limits their ability to model uncertainty.
method Formal analysis of NeSy predictors under independence assumption.
result Assuming independence among symbolic concepts prevents NeSy predictors from representing uncertainty.
New approach tackles nonidentifiability in nonlinear blind source separation.
problem Nonidentifiability in nonlinear blind source separation.
method Independent mechanism analysis, incorporating causal assumptions.
result Empirical and theoretical evidence shows improved identifiability.
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.
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional independence. We describe some conditional independencies through the conditions on t…
New knots show linear independence in slice concordance.
problem Understanding the structure of rationally slice knots.
method Provided an infinite family of knots that are linearly independent.
result Found knots that are linearly independent and infinite order.
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…
Constraint-based structure learning algorithms infer the causal structure of multivariate systems from observational data by determining an equivalent class of causal structures compatible with the conditional independencies in the data. Methods based on additive-noise (AN) models have been proposed to further discrimi…
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…
LCIT tests conditional independence using latent representations.
problem Detecting conditional independencies in statistical and machine learning tasks.
method Generative framework for learning latent representations of target variables X and Y, then testing for remaining dependencies.
result LCIT outperforms state-of-the-art baselines consistently under different metrics and settings.
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.
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.
New test for conditional independence using kernel embeddings.
problem Testing conditional independence in high-dimensional settings.
method Analytic kernel embeddings, asymptotic distribution.
result New test outperforms existing methods in high-dimensional settings.
The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion framework, that, surprisingly, some of the widely utilized risk measures cannot be used…
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.
Discusses MultiFIT for multivariate dependence, comparing it to HSIC tests.
problem Comparing Multiscale Fisher's Independence Test (MultiFIT) to HSIC tests for multivariate dependence.
method Compares MultiFIT to HSIC tests, highlighting exact level control and performance limitations.
result Observes performance limitations of MultiFIT in terms of test power.
Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art workflows suffer from the need for heuristic or subjective manual choices, high c…
Forré introduces a new conditional independence notion for mixed variables.
problem Unified framework for random and non-stochastic variables.
method Unified framework of transitional conditional independence and causal calculus for iDMGs.
result Unified framework connects conditional independencies to graphical separation criteria.
Constructs independent bases for cubic curve families using Hessian structures.
problem Finding independent bases for cubic curve families.
method Uses a Hessian structure to define a cost function for constructing bases.
result Constructs valuatively independent bases for H0(X,Lk). New method identifies causal structure in exchangeable data.
problem Existing causal discovery methods struggle with i.i.d. data.
method Exchangeable data provides richer conditional independence structure.
result Exchangeable data allows for unique causal structure identification.
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.
The paper develops robust tests for detecting independence in synchronous stochastic systems with finite sample guarantees.
problem Detecting independence in synchronous stochastic systems with finite sample guarantees.
method Combines confidence region estimates with permutation tests and dependence measures to detect nonlinear dependence.
result Consistent hypothesis tests for detecting independence under mild assumptions.
A new graphical model for discrete data without parametric restrictions.
problem Discrete data modeling with restrictions.
method Additive conditional independence and penalized estimation of precision operator.
result Consistency of the estimator in ultrahigh-dimensional settings.
Can we use deep learning to predict when deep learning works? Our results suggest the affirmative. We created a dataset by training 13,500 neural networks with different architectures, on different variations of spiral datasets, and using different optimization parameters. We used this dataset to train task-independent…