Related papers: The differential calculus of causal functions
Complex dynamical systems are prevalent in many scientific disciplines. In the analysis of such systems two aspects are of particular interest: 1) the temporal patterns along which they evolve and 2) the underlying causal mechanisms.…
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…
Algorithms for constraint-based causal discovery select graphical causal models among a space of possible candidates (e.g., all directed acyclic graphs) by executing a sequence of conditional independence tests. These may be used to inform…
In this paper we propose a causal analog to the purely observational Dynamic Bayesian Networks, which we call Dynamic Causal Networks. We provide a sound and complete algorithm for identification of Dynamic Causal Net- works, namely, for…
Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of…
Functional equations (FE) arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to…
Causal reasoning is a cornerstone of human intelligence and a critical capability for artificial systems aiming to achieve advanced understanding and decision-making. This thesis delves into various dimensions of causal reasoning and…
We provide estimates for the convolution product of an arbitrary number of "resurgent functions", that is holomorphic germs at the origin of $C$ that admit analytic continuation outside a closed discrete subset of $C$ which is stable under…
Causal inference, as a major research area in statistics and data science, plays a central role across diverse fields such as medicine, economics, education, and the social sciences. Design-based causal inference begins with randomized…
Causality is receiving increasing attention by the artificial intelligence and machine learning communities. This paper gives an example of modelling a recommender system problem using causal graphs. Specifically, we approached the causal…
Causal discovery is challenging in general dynamical systems because, without strong structural assumptions, the underlying causal graph may not be identifiable even from interventional data. However, many real-world systems exhibit…
Causal relationships among a set of variables are commonly represented by a directed acyclic graph. The orientations of some edges in the causal DAG can be discovered from observational/interventional data. Further edges can be oriented by…
Modern machine learning (ML) methods typically fail to adequately capture causal information. Consequently, such models do not handle data distributional shifts, are vulnerable to adversarial examples, and often learn spurious correlations.…
We introduce a new diagrammatic notation for representing the result of (algebraic) effectful computations. Our notation explicitly separates the effects produced during a computation from the possible values returned, this way simplifying…
Causal theory is now widely developed with many applications to medicine and public health. However within the discipline of reliability, although causation is a key concept in this field, there has been much less theoretical attention. In…
One of the defining features of living systems is their adaptability to changing environmental conditions. This requires organisms to extract temporal and spatial features of their environment, and use that information to compute the…
Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…
We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing, with a focus on functionals that arise in causal inference. We study the case where probability distributions are…
Deep neural networks can obtain impressive performance on various tasks under the assumption that their training domain is identical to their target domain. Performance can drop dramatically when this assumption does not hold. One…
Causal Graph Dynamics generalize Cellular Automata, extending them to bounded degree, time varying graphs. The dynamics rewrite the graph at each time step with respect to two physics-like symmetries: causality (bounded speed of…