Related papers: Causal Rate Distortion Function and Relations to F…

We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…

In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…

The causal set theory d'Alembertian has rational coefficients for which alternating expressions are known. Here, a combinatorial interpretation of these numbers is given.

This paper presents a simple generalization of causal consistency suited to any object defined by a sequential specification. As causality is captured by a partial order on the set of operations issued by the processes on shared objects…

In this work we establish and investigate connections between causes for query answers in databases, database repairs wrt. denial constraints, and consistency-based diagnosis. The first two are relatively new research areas in databases,…

The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…

Causal understanding is important in many disciplines of science and engineering, where we seek to understand how different factors in the system causally affect an experiment or situation and pave a pathway towards creating effective or…

Causal inference from observational data following the restricted structural causal model (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or nonlinearity.…

We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We…

In spite of the (correct) common-wisdom statement correlation does not imply causation, a proper employ of time correlations and of fluctuation-response theory allows to understand the causal relations between the variables of a…

Granger causal inference is a contentious but widespread method used in fields ranging from economics to neuroscience. The original definition addresses the notion of causality in time series by establishing functional dependence…

Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…

A common approach to mechanistic interpretability is to causally manipulate model representations via targeted interventions in order to understand what those representations encode. Here we ask whether such interventions create…

A fundamental challenge in causal inference with observational data is correct specification of a causal model. When there is model uncertainty, analysts may seek to use estimates from multiple candidate models that rely on distinct, and…

Classical rate-distortion theory requires knowledge of an elusive source distribution. Instead, we analyze rate-distortion properties of individual objects using the recently developed algorithmic rate-distortion theory. The latter is based…

In this exploratory article, we draw attention to the common formal ground among various estimators such as the belief functions of evidence theory and their relatives, approximation quality of rough set theory, and contextual probability.…

Counterfactual explanation is one branch of interpretable machine learning that produces a perturbation sample to change the model's original decision. The generated samples can act as a recommendation for end-users to achieve their desired…

The goal of algorithmic recourse is to reverse unfavorable decisions (e.g., from loan denial to approval) under automated decision making by suggesting actionable feature changes (e.g., reduce the number of credit cards). To generate…

Causality analysis is an important problem lying at the heart of science, and is of particular importance in data science and machine learning. An endeavor during the past 16 years viewing causality as real physical notion so as to…

Causal inference from observational data following the restricted structural causal models (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or…