Related papers: Inferring Kernel $\epsilon$-Machines: Discovering …

We develop a novel identification strategy as well as a new estimator for context-dependent causal inference in non-parametric triangular models with non-separable disturbances. Departing from the common practice, our analysis does not rely…

We consider the problem of causal discovery (structure learning) from heterogeneous observational data. Most existing methods assume a homogeneous sampling scheme, which leads to misleading conclusions when violated in many applications. To…

We probe the foundations of causal structure inference experimentally. The causal structure concerns which events influence other events. We probe whether causal structure can be determined without intervention in quantum systems.…

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…

This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent…

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 many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

In this study, a scalable online kernel learning framework is proposed for estimating bidirectional causal effects in systems characterized by mutual dependence and heteroskedasticity. Traditional causal inference often focuses on…

We give a derivation of the non-Markovian quantum state diffusion equation of Di{\'o}si and Strunz starting from a model of a quantum mechanical system coupled to a bosonic bath. We show that the complex trajectories arises as a consequence…

Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…

Causal discovery, beyond the inference of a network as a collection of connected dots, offers a crucial functionality in scientific discovery using artificial intelligence. The questions that arise in multiple domains, such as physics,…

Structural causal models describe how the components of a robotic system interact. They provide both structural and functional information about the relationships that are present in the system. The structural information outlines the…

Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in…

Inferring causal relationships from observational data is rarely straightforward, but the problem is especially difficult in high dimensions. For these applications, causal discovery algorithms typically require parametric restrictions or…

Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number…

Kernel classifiers and regressors designed for structured data, such as sequences, trees and graphs, have significantly advanced a number of interdisciplinary areas such as computational biology and drug design. Typically, kernels are…

This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…

Reasoning based on causality, instead of association has been considered as a key ingredient towards real machine intelligence. However, it is a challenging task to infer causal relationship/structure among variables. In recent years, an…

Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed…

The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical…