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.
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.
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.
New algorithms test independence with fewer samples by using predictive information.
problem Testing independence of distributions with limited samples.
method Augmented distribution testing framework that incorporates predictive information.
result Optimal sample complexity achieved, matching lower bounds.
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.
Modeling financial returns as conditionally independent random variables explains power-law tails.
problem Understanding the distribution of financial returns and their relation to volatility.
method Assuming returns are conditionally independent given volatility, which varies randomly over time.
result Returns distribution can be described by the sum of conditionally independent random variables, showing scaling and power-law tails.
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 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.
Adversarial nets learn independent features from joint distributions.
problem Learning independent features from complex joint distributions.
method Adversarial objectives to optimize mutual information implicitly.
result Adversarial nets can solve both linear and non-linear ICA problems.
Novel methods transform correlated neutral vectors into independent variables.
problem Decorrelating correlated neutral vector variables that are not multivariate Gaussian distributed.
method Serial and parallel nonlinear transformations to achieve mutual independence.
result Highly negatively correlated neutral vectors can be transformed into mutually independent scalar variables.
Bayesian method finds patterns of mutual independence in data.
problem Investigating mutual independence in statistics.
method Bayesian model comparison using Markov chain Monte Carlo (MCMC).
result Automated search for patterns of mutual independence.
Sequential tests for two-sample and independence testing using betting strategies.
problem Testing sequential data for two-sample and independence without kernel selection issues.
method Prediction-based betting strategies that adaptively determine distribution and joint distribution.
result Prediction-based tests outperform kernel-based approaches in high-dimensional or structured data settings.
The upsilon distribution, the sum of independent chi random variates and a normal, is introduced. As a special case, the upsilon distribution includes Lecoutre's lambda-prime distribution. The upsilon distribution finds application in Frequentist inference on the Sharpe ratio, including hypothesis tests on independent …
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…
In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we consider the case in which the components are independently but not identically distri…
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.
New method allows generating independent data matrices from summary statistics.
problem Generating independent data matrices from summary statistics like mean and covariance.
method Thinning a Wishart random matrix based on sample mean and covariance.
result It is possible to generate two independent data matrices from summary statistics.
DPE embeds non-Euclidean objects into Hilbert space for independence testing.
problem Testing independence of non-Euclidean random objects.
method Distance Profile Embedding (DPE) maps objects into Hilbert space.
result Unified framework for marginal and conditional independence testing.
A new method splits data into independent mechanisms for better generative models.
problem Training a single model to capture the overall distribution of data.
method A competitive training procedure using mixtures of independent deep generative models and discriminators.
result The approach splits the training distribution in a sensible way and improves the quality of generated samples.
OT-ICA uses optimal transport to find independent components, outperforming traditional methods.
problem Finding independent components from linear mixtures of signals.
method OT-ICA uses the squared Wasserstein distance to maximize non-Gaussianity, optimizing projections via gradient descent.
result OT-ICA outperforms traditional proxy-based methods in various applications.
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a stochastically independent uniformly distributed unit vector. When the set of unit vectors …
The Freund family of distributions becomes a Riemannian 4-manifold with Fisher information as metric; we derive the induced α-geometry, i.e., the α-curvature, α-Ricci curvature with its eigenvales and eigenvectors, the α-scalar curvature etc. We show that the Freund manifold has a positive constant 0-scalar cur…
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.
Optimal transport is #P-hard when components are independent, even with approximate solutions.
problem Computational complexity of optimal transport with independent marginals.
method Proved #P-hardness and developed a pseudo-polynomial time approximation algorithm.
result Optimal transport is #P-hard even with independent components and approximate solutions.
The paper extends SARMA models by relaxing independence assumptions on error terms.
problem Testing adequacy of SARMA models with non-independent errors.
method Study of asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations under weak noise assumptions.
result Established asymptotic behavior of portmanteau tests for SARMA models.
Paper constructs unfaithful probability distributions in binary causal graphs.
problem Unfaithful probability distributions in binary causal graphs.
method Constructs unfaithful probability distributions in binary causal graphs.
result Examples of unfaithful probability distributions in binary causal graphs.
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full conditional independence between these two variables given all the other variables. In…
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.
Study tests adequacy of FARIMA models with uncorrelated but non-independent errors.
problem Testing adequacy of FARIMA models with specific error characteristics.
method Derive asymptotic distributions of residual autocovariances and autocorrelations, propose self-normalization approach.
result Asymptotic distributions of modified portmanteau statistics for weak FARIMA models.
SPQR improves Q-ensemble diversity in reinforcement learning.
problem Overestimation bias in Q-learning for complex tasks.
method Introduces SPQR for Q-ensemble independence regularization.
result SPQR outperforms baseline algorithms in online and offline RL benchmarks.
This paper tackles target-dependent label complexity gap in active learning.
problem Target-dependent label complexity gap in Agnostic Active Learning.
method Introduces a novel distribution-splitting strategy based on number density to reduce label complexity and error rate.
result Provides theoretical guarantees and practical advantages for reducing label complexity and error rate.
Efficiently compares independence structures in log-linear models.
problem Limited direct measures for comparing log-linear model independence structures.
method Direct comparison method based on independence structure, efficient computation.
result First metric for direct comparison of log-linear model independence structures.
Algorithm learns halfspaces robust to Massart noise without distribution knowledge.
problem Learning halfspaces in noisy data with arbitrary marginal distribution.
method Poly-time algorithm for distribution-independent PAC learning.
result Achieves misclassification error of η+ε with poly(d, 1/ε) time complexity.
New metrics for high-dimensional data improve on energy distance.
problem Testing equality of distributions and independence in high dimensions.
method Proposed new metrics inheriting properties of energy distance and others.
result Improved metrics detect homogeneity and independence in high dimensions.
The article explains the probabilistic method of default probability estimation by Pluto and Tasche.
problem Estimating default probabilities for portfolios with low default rates.
method Detailed derivation and explanation of the Pluto-Tasche method, including assumptions and inequalities.
result Clarification of borrower independence, conditional independence, and interaction between probability distributions.
The paper shows how to infer conditional independence from non-Gaussian data.
problem Inferring conditional independence from non-Gaussian distributions.
method Developed a method to recover conditional independence structure from the precision matrix of generalized nonparanormal data.
result The conditional independence structure can be inferred from the precision matrix of generalized nonparanormal data.
CoNN uses cooperative neural networks to leverage prior independence structure for improved text classification.
problem Improving text classification accuracy by exploiting prior independence structure.
method CoNN employs a set of cooperatively trained neural networks to capture latent representations based on prior independence structure.
result Demonstrated a 23% reduction in error on the MultiSent dataset compared to state-of-the-art methods.
We study the statistics of the number of records R_{n,N} for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We co…
A new process-level model explains how humans detect dependencies quickly.
problem Understanding how humans handle probabilistic independence relations efficiently.
method Developed a rational, distributed, message-passing model called D*.
result D* shows a tendency to quickly detect dependencies, outperforming other algorithms.
The paper explores tensor product kernels and their characteristic properties.
problem Understanding when HSIC characterizes independence and MMD with tensor product kernel discriminates probability distributions.
method Study of various notions of characteristic property of tensor product kernels.
result The paper answers questions about the characteristic and universal properties of tensor product kernels.
We show how to estimate a model's test error from unlabeled data, on distributions very different from the training distribution, while assuming only that certain conditional independencies are preserved between train and test. We do not need to assume that the optimal predictor is the same between train and test, or t…
Cycles in causal learning cause feedback loops under intervention.
problem Cyclic causal structures lead to feedback loops in causal inference.
method Theoretical observations about self-referential distributions and their factorizations.
result Cyclic causal dependence can exist even when observational data suggest independence.
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 …
We study the wealth distribution of the Bouchaud--Mézard (BM) model on complex networks. It has been known that this distribution depends on the topology of network by numerical simulations, however, no one have succeeded to explain it. Using "adiabatic" and "independent" assumptions along with the central-limit theore…
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.
IST trains neural networks locally, reducing memory and communication costs.
problem Challenges in distributed learning due to mandatory data separation.
method Independent subnet training (IST) decomposes the network into narrow subnetworks.
result IST reduces training times compared to common distributed learning approaches.
A new method, FactorVAE, learns disentangled representations from independent factors.
problem Unsupervised learning of disentangled representations from independent factors.
method FactorVAE encourages factorial distribution of representations to be independent across dimensions.
result FactorVAE improves disentanglement over β-VAE by better balancing disentanglement and reconstruction quality. 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.