Related papers: Reasoning about Independence in Probabilistic Mode…
Spirtes, Glymour and Scheines formulated a Conjecture that a direct dependence test and a head-to-head meeting test would suffice to construe directed acyclic graph decompositions of a joint probability distribution (Bayesian network) for…
Real causal processes may contain feedback loops and change over time. In this paper, we model cycles and non-stationary distributions using a mixture of directed acyclic graphs (DAGs). We then study the conditional independence (CI)…
The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting…
We develop a mathematical and interpretative foundation for the enterprise of decision-theoretic statistical causality (DT), which is a straightforward way of representing and addressing causal questions. DT reframes causal inference as…
Instead of requiring a domain expert to specify the probabilistic dependencies of the data, in this work we present an approach that uses the relational DB schema to automatically construct a Bayesian graphical model for a database. This…
Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific…
This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Polya tree priors on spaces of…
Disentanglement via mechanism sparsity was introduced recently as a principled approach to extract latent factors without supervision when the causal graph relating them in time is sparse, and/or when actions are observed and affect them…
In many scientific contexts, different investigators experiment with or observe different variables with data from a domain in which the distinct variable sets might well be related. This sort of fragmentation sometimes occurs in molecular…
Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For…
Two known results on the relationship between conditional and unconditional independence are obtained as a consequence of the main result of this paper, a theorem that uses independence of Markov kernels to obtain a minimal condition which…
We develop the theory linking 'E-separation' in directed mixed graphs (DMGs) with conditional independence relations among coordinate processes in stochastic differential equations (SDEs), where causal relationships are determined by "which…
It is inconceivable how chaotic the world would look to humans, faced with innumerable decisions a day to be made under uncertainty, had they been lacking the capacity to distinguish the relevant from the irrelevant---a capacity which…
Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof.…
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. For decomposable…
This paper develops the sufficiency principle suitable for data reduction in decentralized inference systems. Both parallel and tandem networks are studied and we focus on the cases where observations at decentralized nodes are…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of…