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.
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…
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.
This study provides a new mathematical structure for Koopman eigenfunctions.
problem Understanding and representing nonlinear dynamics as linear.
method Theoretical, analytical, and numerical approaches to Koopman eigenfunction space.
result Equivalence of minimal generating set and maximal independent set, defining conditions for independence.
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.
To each unit complex number with positive imaginary part there is defined a Tristram-Levine knot signature function. The set of all such signature functions is linearly independent as a set of functions defined on the set of all knots. The set of averaged signature functions forms a linearly independent set of homomoro…
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.
Algorithm learns causal structures from low-order conditional independencies.
problem Estimating high-order conditional independencies from data is challenging.
method Proposes an algorithm to compute a faithful graphical representation from low-order conditional independencies.
result Algorithm successfully learns causal structures from zero- and first-order conditional independencies.
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.
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.
We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set map, from a given realization of a variable to a set of possible realizations of…
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…
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.
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.
This paper aims at justifying LWF and AMP chain graphs by showing that they do not represent arbitrary independence models. Specifically, we show that every chain graph is inclusion optimal wrt the intersection of the independence models represented by a set of directed and acyclic graphs under conditioning. This impli…
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…
New test detects independence in streaming data, adapting to data complexity.
problem Independence testing in streaming data with adaptive stopping.
method Sequential kernelized independence tests using betting principles.
result Valid inference in streaming data with improved power.
Develops a nonparametric graphical model for conditional independence.
problem Evaluation of conditional independence without distributional assumptions.
method Nonlinear sufficient dimension reduction techniques applied to a nonparametric graphical model.
result Method outperforms existing methods in non-Gaussian settings and high-dimensional data.
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.
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…
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.
We propose a new approach, called cooperative neural networks (CoNN), which uses a set of cooperatively trained neural networks to capture latent representations that exploit prior given independence structure. The model is more flexible than traditional graphical models based on exponential family distributions, but i…
A new algorithm for robust causal discovery in small sample sizes.
problem Limited data leads to weak conditional independence tests in causal discovery.
method Proposes a k-PC algorithm that bounds conditioning set size for robust causal discovery. result The k-PC algorithm enables more robust causal discovery in small sample sizes. Novel tests for genetic independence in high-dimensional data.
problem Testing independence in genetics studies with many variables.
method Defining premetric structures on genetic data support spaces.
result Solid theoretical framework and computationally-efficient implementations.
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.
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…
We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model to call options with discrete set of maturities but a continuum of strikes. In …
The independence clustering problem is considered in the following formulation: given a set S of random variables, it is required to find the finest partitioning {U1,…,Uk} of S into clusters such that the clusters U1,…,Uk are mutually independent. Since mutual independence is the target, pairwise …
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.
We introduce a new class of processes for the evaluation of multivariate equity derivatives. The proposed setting is well suited for the application of the standard copula function theory to processes, rather than variables, and easily enables to enforce the martingale pricing requirement. The martingale condition is i…
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…
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.
A new DRL scheme optimizes solving large graphs' maximum independent set problem.
problem Efficiently solving maximum independent set problems on large graphs.
method Learning what to defer (LwD) to adaptively control the number of stages.
result Significantly outperforms state-of-the-art DRL and conventional solvers.
AI methods often fail to outperform classical CPU-based solvers on Maximum Independent Set problems.
problem Comparing AI methods with classical CPU-based solvers on Maximum Independent Set problems.
method Comparison of AI methods (e.g., generative models, reinforcement learning) with classical CPU-based solvers (e.g., KaMIS) on Maximum Independent Set problem.
result AI-inspired methods are often outperformed by classical CPU-based solvers, even with post-processing techniques.
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 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.
New bounds for SGLD show error decreases with more data.
problem Establishing generalization error bounds for SGLD in non-convex settings.
method Using dissipativity, smoothness, and uniform stability, time-independent bounds are derived.
result Error bounds decay to zero as sample size increases.
Test for quasi-independence in ordered time data.
problem Determining dependence beyond temporal ordering.
method Nonparametric statistical test considering infinite alternatives.
result Better power and computational efficiency compared to existing methods.
IMA addresses non-identifiability in nonlinear ICA by assuming orthogonal Jacobian columns.
problem Non-identifiability in nonlinear ICA.
method IMA assumes orthogonal Jacobian columns and extends to manifold settings.
result IMA circumvents non-identifiability issues and can be beneficial for higher-dimensional observations.
Let X be the moduli space of SL(3,C) representations of a free group of rank r. In this paper we describe maximal algebraically independent subsets of certain minimal sets of coordinate functions on X. These subsets locally parametrize the moduli space.
New approach reveals causal and probabilistic relationships from equations.
problem Understanding causal and probabilistic relationships from sets of equations.
method Simon's causal ordering algorithm and Markov ordering graph construction.
result Implied conditional independences and causal relations without solving equations.
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.
In Ben-David et al.'s "Learnability Can Be Undecidable," they prove an independence result in theoretical machine learning. In particular, they define a new type of learnability, called Estimating The Maximum (EMX) learnability. They argue that this type of learnability fits in with other notions such as PAC learnabili…
CIRCE measures conditional independence for learning invariant features.
problem Learning invariant features while being conditionally independent of a distractor.
method CIRCE is a measure of conditional independence applied as a regularizer in feature learning.
result CIRCE provides a zero value if and only if features are conditionally independent of the distractor given the target.
Study of supervised learning from multiple non-independent sequences.
problem Efficient learning from many non-independent sequences.
method Generalizes conditions for efficient learning from independent examples and single auto-correlated sequences.
result Error rate changes from Θ(n/mT) to Ω(n2/m2T) as the number of trajectories increases. The paper develops a test for independence of selected Gaussian variables after thresholding correlations.
problem Testing independence of selected Gaussian variables after thresholding correlations.
method The approach involves conditioning on the selection event and using a new characterization of the conditioning event in terms of canonical correlation.
result The proposed test has higher power than a naive approach that ignores selection effects.
Yoshikawa moves were introduced at least quarter-century ago and are still actively used by researchers. For any marked graph diagram we will define its twisted diagram and its mirror cut surface. By using a surface-link group of a mirror cut surface of a twisted diagram we will prove the independence of Yoshikawa eigh…
Unified framework for structure learning via conditional independence testing.
problem Optimal structure learning and conditional independence testing.
method Established a fundamental connection and reduction between structure learning and conditional independence testing.
result Optimal rates for structure learning are determined by conditional independence testing rates.