Related papers: Solving Causal Stream Inclusions
We define representations of continuous functions on infinite streams of discrete values, both in the case of discrete-valued functions, and in the case of stream-valued functions. We define also an operation on the representations of two…
Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying…
We propose a novel formalism for describing Structural Causal Models (SCMs) as fixed-point problems on causally ordered variables, eliminating the need for Directed Acyclic Graphs (DAGs), and establish the weakest known conditions for their…
We develop a framework for causal inference with continuous spatiotemporal point-process outcomes under cell-level interventions and outcome spillover. Potential outcomes are indexed by full treatment allocations, and the observed…
Systems whose organization displays causal asymmetry constraints, from evolutionary trees to river basins or transport networks, can be often described in terms of directed paths (causal flows) on a discrete state space. Such a set of paths…
We propose a constraint-based algorithm, which automatically determines causal relevance thresholds, to infer causal networks from data. We call these topological thresholds. We present two methods for determining the threshold: the first…
In this study, we address causal inference when only observational data and a valid causal ordering from the causal graph are available. We introduce a set of flow models that can recover component-wise, invertible transformation of…
We propose a simple calculus for processing data streams (infinite flows of data series), represented by finite sets of equations built on stream operators. Furthermore, functions defining streams are regularly corecursive, that is, cyclic…
We introduce action-driven flows for causal variational principles, being a class of non-convex variational problems emanating from applications in fundamental physics. In the compact setting, H\"older continuous curves of measures are…
The main result is a doubly exponential decision procedure for the first-order equality theory of streams with both arithmetic and control-oriented stream operations. This stream logic is expressive for elementary problems of stream…
We investigate causal inference in the asymptotic regime as the number of variables approaches infinity using an information-theoretic framework. We define structural entropy of a causal model in terms of its description complexity measured…
Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. A core property is productivity: unfolding the equations produces the intended stream in the limit. In this…
We study rational streams (over a field) from a coalgebraic perspective. Exploiting the finality of the set of streams, we present an elementary and uniform proof of the equivalence of four notions of representability of rational streams:…
We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point…
Tree transductions are binary relations of finite trees. For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable. Adding origin semantics to…
Fixpoint operators are tools to reason on recursive programs and data types obtained by induction (e.g. lists, trees) or coinduction (e.g. streams). They were given a categorical treatment with the notion of categories with fixpoints. A…
Causal inference has traditionally focused on interventions at the unit level. In many applications, however, the central question concerns the causal effects of connections between units, such as transportation links, social relationships,…
Longstanding problems regarding the causality of the diffusion equation are resolved through a class of exact solutions. A universal differential solution for diffusive processes is derived that is causal and exact at any analytic point in…
Our aim in this paper is to prove some interesting fixed point theorems for the class of asymptotically $T$-regular mappings in the framework of preordered modular G-metric spaces. Our results are novel and generalizes several know results.…
We consider the integrable family of symmetric boundary-driven interacting particle systems that arise from the non-compact XXX Heisenberg model in one dimension with open boundaries. In contrast to the well-known symmetric exclusion…