Related papers: Conditional independence ideals with hidden variab…

Explaining artificial intelligence or machine learning models is increasingly important. To use such data-driven systems wisely we must understand how they interact with the world, including how they depend causally on data inputs. In this…

When a monomial ideal has linear quotients with respect to an admissible order of increasing support-degree, we provide two proofs of different flavors to show that it is componentwise support-linear. We also introduce the variable…

Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be…

We show that there can be no finite list of conditional independence relations which can be used to deduce all conditional independence implications among Gaussian random variables. To do this, we construct, for each $n> 3$ a family of $n$…

Typical Bayesian methods for models with latent variables (or random effects) involve directly sampling the latent variables along with the model parameters. In high-level software code for model definitions (using, e.g., BUGS, JAGS, Stan),…

There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…

We present an encoding of a polynomial system into vanishing and non-vanishing constraints on almost-principal minors of a symmetric, principally regular matrix, such that the solvability of the system over some field is equivalent to the…

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…

In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…

A seminal result in the ICA literature states that for $AY = \varepsilon$, if the components of $\varepsilon$ are independent and at most one is Gaussian, then $A$ is identified up to sign and permutation of its rows (Comon, 1994). In this…

Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…

The inference of causal relationships using observational data from partially observed multivariate systems with hidden variables is a fundamental question in many scientific domains. Methods extracting causal information from conditional…

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…

For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…

We consider inference on a scalar regression coefficient under a constraint on the magnitude of the control coefficients. A class of estimators based on a regularized propensity score regression is shown to exactly solve a tradeoff between…

Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…

Constraint-based causal discovery methods leverage conditional independence tests to infer causal relationships in a wide variety of applications. Just as the majority of machine learning methods, existing work focuses on studying…

This paper studies how violations of structural assumptions like expected utility and exponential discounting can be connected to basic rationality violations, even though these assumptions are typically regarded as independent building…

Testing a hypothesized causal model against observational data is a key prerequisite for many causal inference tasks. A natural approach is to test whether the conditional independence relations (CIs) assumed in the model hold in the data.…

Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…