arXiv research

A new graphical model for discrete data without parametric restrictions.

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…

New method identifies causal relationships in presence of hidden variables.

Sequential Kernel-based Conditional Independence Testing via Adaptive Betting

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…

Paper introduces a nonparametric functional graphical model for random functions.

Equilibrium pricing has been proven to underlie the rational Insured expectancy of premia additivity for composition of policies fully covering independent risks.

This work identifies redundant tests in conditional-independence-based discovery that can improve graphical model accuracy.

In two recent papers necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not independent and prove a stronger result accordingly.

We consider a 3-dimensional Riemannian manifold with additional structure q. We find a condition that the affine structure q is parallel with respect to the Riamannian connection.We prove the sectional curvatures of three 2-sections formed linearly independent vectors are equal among them.

Simple conditions for comonotonic additive risk measures from acceptance sets.

New algorithm reduces conditional independence tests needed for causal discovery.

Thompson Sampling with bilateral uncertainty improves performance in Bayesian Optimization.

As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known effect Z, i.e., E(Y|X, Z) = E(Y|Z). Assuming that E(Y|Z) and Z are linearly related, …

Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has also been shown to be a generalization of Hotelling's canonical correlation analysis. In this paper, we provide the ident…

New method tests conditional independence using spectral representations.

Much recent work has concerned sparse approximations to speed up the Gaussian process regression from the unfavorable O(n3) scaling in computational time to O(nm2). Thus far, work has concentrated on models with one covariance function. However, in many practical situations additive models with multiple covariance func…

Develops a test for conditional local independence of counting processes.

Let $S$ be any closed hyperbolic surface and let $λ$ be a maximal geodesic lamination on $S$. The amount of bending of an abstract pleated surface (homeomorphic to $S$) with the pleating locus $λ$ is completely determined by an $(\mathbb{R}/2π\mathbb{Z})$-valued finitely additive transverse cocycle $β$ to the geodesic …

Most existing works on disentangled representation learning are solely built upon an marginal independence assumption: all factors in disentangled representations should be statistically independent. This assumption is necessary but definitely not sufficient for the disentangled representations without additional induc…

FMCIT accelerates CI tests for causal discovery, maintaining power and efficiency.

We propose a method for inferring the existence of a latent common cause ('confounder') of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus independent, additive noise. We discuss under which conditions the model is identi…

In this paper, we prove that if an asymptotically Euclidean manifold $(M^n,g)$ under the condition that $R \ge 0$ has long time existence of Ricci flow, the mass of $(M^n,g)$ is nonnegative. In addition, we give an independent proof of positive mass theorem in dimension $3$.

Study shows simplicial volume is superadditive under specific conditions.

New model captures time and mark inter-dependence in TPPs.

We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments, from which data are often not available. We show that if the observational distribution follows a structural equation model with an …

Additive decoders tackle latent variables and image generation.

The ability to adequately model risks is crucial for insurance companies. The method of "Copula-based hierarchical risk aggregation" by Arbenz et al. offers a flexible way in doing so and has attracted much attention recently. We briefly introduce the aggregation tree model as well as the sampling algorithm proposed by…

It is natural to ask: what kinds of matrices satisfy the Restricted Eigenvalue (RE) condition? In this paper, we associate the RE condition (Bickel-Ritov-Tsybakov 09) with the complexity of a subset of the sphere in $\R^p$, where $p$ is the dimensionality of the data, and show that a class of random matrices with indep…

New method uses sufficient statistics to infer causal relationships from observational data.

Deep CITs test conditional independence in images, improving brain MRI scan analysis.

Efficiently estimates SAGE values using causal structure learning.

Estimates marginal independence structure of Bayesian networks from data.

New findings show independent subordination is not relevant for accurate option pricing.

New PCstar algorithm discovers causal structure of max-linear Bayesian networks.

Generalizes Hoeffding's decomposition for dependent inputs under mild conditions.

Reframed GES uses a neural conditional dependence measure for consistent causal structure learning.

A new algorithm reduces CI tests for causal graph recovery.

A RL-based method adds conditional controls to pre-trained diffusion models.

We consider the stochastic contextual bandit problem with additional regularization. The motivation comes from problems where the policy of the agent must be close to some baseline policy which is known to perform well on the task. To tackle this problem we use a nonparametric model and propose an algorithm splitting t…

A new method tests conditional independence by transforming it into an unconditional problem using transport maps.

This work aims at a deeper understanding of the mathematical implications of the economically-sound condition of absence of arbitrages of the first kind in a financial market. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP), it is shown here that absence of arbitrages of the first kind in the market is…

Missing data are ubiquitous in many domains including healthcare. When these data entries are not missing completely at random, the (conditional) independence relations in the observed data may be different from those in the complete data generated by the underlying causal process. Consequently, simply applying existin…

We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks …

The study examines how including additional call option prices affects model-independent price bounds for exotic derivatives.

We study 'meta-dependence' in conditional independence tests across different empirical distributions.

TGD improves conditional sampling by concentrating computation on promising trajectories.