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The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we…

We propose a novel method for testing serial independence of object-valued time series in metric spaces, which is more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters, and can…

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…

The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some {known} graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity…

We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the…

Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…

It is difficult to extract reliable criteria for causal locality from the limited ingredients found in textbook quantum theory. In the end, Bell humbly warned that his eponymous theorem was based on criteria that "should be viewed with the…

We show how two level atoms can be used to determine the local time dependent spectrum. The method is applied to a one dimensional cavity. The spectrum obtained is compared with the mode spectrum determined using spatially filtered second…

We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These…

In ordinary Quantum Mechanics only ideally instantaneous observations of a quantity or a set of compatible quantities are usually considered. In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of…

This paper presents theoretical advances in the application of the Stochastic Partial Differential Equation (SPDE) approach in geostatistics. We show a general approach to construct stationary models related to a wide class of linear SPDEs,…

The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…

Granger causality has been employed to investigate causality relations between components of stationary multiple time series. We generalize this concept by developing statistical inference for local Granger causality for multivariate…

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints…

In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If…

For stationary time series, it is common to use the plots of partial autocorrelation function (PACF) or PACF-based tests to explore the temporal dependence structure of such processes. To our best knowledge, such analogs for non-stationary…

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on…

Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…

We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally…