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

This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…

It is well-known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here, we study qualitative limitations on causal structures and correlations…

A data science task can be deemed as making sense of the data or testing a hypothesis about it. The conclusions inferred from data can greatly guide us to make informative decisions. Big data has enabled us to carry out countless prediction…

We provide a rigorous definition of the visual cause of a behavior that is broadly applicable to the visually driven behavior in humans, animals, neurons, robots and other perceiving systems. Our framework generalizes standard accounts of…

The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…

We consider the problem of function estimation in the case where an underlying causal model can be inferred. This has implications for popular scenarios such as covariate shift, concept drift, transfer learning and semi-supervised learning.…

This paper presents a new foundational approach to information theory based on the concept of the information efficiency of a recursive function, which is defined as the difference between the information in the input and the output. The…

This paper examines two related problems that are central to developing an autonomous decision-making agent, such as a robot. Both problems require generating structured representafions from a database of unstructured declarative knowledge…

The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…

We prove achievability of the recently characterized quadratic Gaussian rate-distortion function (RDF) subject to the constraint that the distortion is uncorrelated to the source. This result is based on shaped dithered lattice quantization…

Computational analysis of time-course data with an underlying causal structure is needed in a variety of domains, including neural spike trains, stock price movements, and gene expression levels. However, it can be challenging to determine…

This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…

Causality has the potential to truly transform the way we solve a large number of real-world problems. Yet, so far, its potential largely remains to be unlocked as causality often requires crucial assumptions which cannot be tested in…

A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…

Explainability plays an increasingly important role in machine learning. Furthermore, humans view the world through a causal lens and thus prefer causal explanations over associational ones. Therefore, in this paper, we develop a causal…

We consider a remote source coding problem subject to a {distortion function}. Contrary to the use of the classical separable distortion criterion, herein we consider the more general, $f$-separable distortion measure and study its…

As a pivotal component to attaining generalizable solutions in human intelligence, reasoning provides great potential for reinforcement learning (RL) agents' generalization towards varied goals by summarizing part-to-whole arguments and…

We extend the definition of the marginal causal effect to the continuous treatment setting and develop a novel characterization of causal bias in the framework of structural causal models. We prove that our derived bias expression is zero…

Causal reasoning is the main learning and explanation tool used by humans. AI systems should possess causal reasoning capabilities to be deployed in the real world with trust and reliability. Introducing the ideas of causality to machine…

Our evolution as a species made a huge step forward when we understood the relationships between causes and effects. These associations may be trivial for some events, but they are not in complex scenarios. To rigorously prove that some…