Related papers: A general definition of influence between stochast…
Moser and Tardos (2010) gave an algorithmic proof of the lopsided Lov\'asz local lemma (LLL) in the variable framework, where each of the undesirable events is assumed to depend on a subset of a collection of independent random variables.…
A fundamental problem of causal discovery is cause-effect inference, learning the correct causal direction between two random variables. Significant progress has been made through modelling the effect as a function of its cause and a noise…
We present a class of inequality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network, in which some of the variables remain unmeasured. We derive bounds on causal effects…
Classical graphical modeling of multivariate random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some…
Recently established, directed dependence measures for pairs $(X,Y)$ of random variables build upon the natural idea of comparing the conditional distributions of $Y$ given $X=x$ with the marginal distribution of $Y$. They assign pairs…
We introduce a maximal inequality for a local empirical process under strongly mixing data. Local empirical processes are defined as the (local) averages $\frac{1}{nh}\sum_{i=1}^n \mathbf{1}\{x - h \leq X_i \leq x+h\}f(Z_i)$, where $f$…
One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been…
Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal…
It is well-known that discrete-time finite-state Markov Chains, which are described by one-sided conditional probabilities which describe a dependence on the past as only dependent on the present, can also be described as one-dimensional…
In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…
In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…
This paper examines the interdependence generated between two parent nodes with a common instantiated child node, such as two hypotheses sharing common evidence. The relation so generated has been termed "intercausal." It is shown by…
An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and…
In unsupervised causal representation learning for sequential data with time-delayed latent causal influences, strong identifiability results for the disentanglement of causally-related latent variables have been established in stationary…
A standard assumption for causal inference from observational data is that one has measured a sufficiently rich set of covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values. Skepticism…
We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
The dynamical rules in auxiliary stochastic process that generates the biased ensemble of rare events are non-local. For the systems with one type of particle, it is shown that there are special cases for which the generators of effective…
The notion of a tensor product with projections or with inclusions is defined. It is shown that the definition of stochastic independence relies on such a structure and that independence can be defined in an arbitrary category with a tensor…
Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$…