Related papers: A general definition of influence between stochast…

We propose a novel approach for learning causal response representations. Our method aims to extract directions in which a multidimensional outcome is most directly caused by a treatment variable. By bridging conditional independence…

Using the method of Krylov's estimates, we prove the existence of weak solutions of stochastic differential equations driven by purely discontinuous Levy processes satisfying an additional assumption. The diffusion coefficient is assumed to…

Causal Learning has emerged as a major theme of research in statistics and machine learning in recent years, promising specific computational techniques to apply to datasets that reveal the true nature of cause and effect in a number of…

We study the weak convergence of conditional empirical copula processes, when the conditioning event has a nonzero probability. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general -…

Several instance-based explainability methods for finding influential training examples for test-time decisions have been proposed recently, including Influence Functions, TraceIn, Representer Point Selection, Grad-Dot, and Grad-Cos.…

A point process is R-dependent, if it behaves independently beyond the minimum distance R. This work investigates uniform positive lower bounds on the avoidance functions of R-dependent simple point processes with a common intensity.…

Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some…

Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…

In this paper we consider the influences of variables on Boolean functions in general product spaces. Unlike the case of functions on the discrete cube where there is a clear definition of influence, in the general case at least three…

The stochastic system approach to causality is applied to situations where the risk of death is not negligible. This approach grounds causality on physical laws, distinguishes system and observation and represents the system by multivariate…

We study the task of learning from non-i.i.d. data. In particular, we aim at learning predictors that minimize the conditional risk for a stochastic process, i.e. the expected loss of the predictor on the next point conditioned on the set…

The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…

We address causal reasoning in multivariate time series data generated by stochastic processes. Existing approaches are largely restricted to static settings, ignoring the continuity and emission of variations across time. In contrast, we…

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…

One of the common obstacles for learning causal models from data is that high-order conditional independence (CI) relationships between random variables are difficult to estimate. Since CI tests with conditioning sets of low order can be…

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the…

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…

In longitudinal studies where units are embedded in space or a social network, interference may arise, meaning that a unit's outcome can depend on treatment histories of others. The presence of interference poses significant challenges for…

We consider the problem of estimating the causal effect of a treatment on an outcome in linear structural causal models (SCM) with latent confounders when we have access to a single proxy variable. Several methods (such as…

The concept of causal nonseparability has been recently introduced, in opposition to that of causal separability, to qualify physical processes that locally abide by the laws of quantum theory, but cannot be embedded in a well-defined…