Related papers: The differential calculus of causal functions

The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…

Reversible computation is key in developing new, energy-efficient paradigms, but also in providing forward-only concepts with broader definitions and finer frames of study.Among other fields, the algebraic specification and representation…

Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…

We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variables are partially available, and we use recurrent neural…

We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…

The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…

We derive a set of causal deep neural networks whose architectures are a consequence of tensor (multilinear) factor analysis, a framework that facilitates causal inference. Forward causal questions are addressed with a neural network…

Noncommutative rational functions appeared in many contexts in system theory and control, from the theory of finite automata and formal languages to robust control and LMIs. We survey the construction of noncommutative rational functions,…

Causal inference, estimating causal effects from observational data, is a fundamental tool in many disciplines. Of particular importance across a variety of domains is the continuous treatment setting, where the variable of intervention has…

The calculus of finite differences is a solid foundation for the development of operations such as the derivative and the integral for infinite sequences. Here we showed a way to extend it for finite sequences. We could then define…

Much of our experiments are designed to uncover the cause(s) and effect(s) behind a data generating mechanism (i.e., phenomenon) we happen to be interested in. Uncovering such relationships allows us to identify the true working of a…

Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We…

The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i)\}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i…

Causal discovery aims to infer causal relationships among variables from observational data, typically represented by a directed acyclic graph (DAG). Most existing methods assume independent and identically distributed observations, an…

Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from…

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…

Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…

The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was…

In distributed systems where strong consistency is costly when not impossible, causal consistency provides a valuable abstraction to represent program executions as partial orders. In addition to the sequential program order of each…