Related papers: Stochastic Integral Operator Model for IS, US and …
The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…
Motivated by the construction of the It\^o stochastic integral, we consider a step function method to discretize and simulate volatility modulated L\'evy semistationary processes. Moreover, we assess the accuracy of the method with a…
Instrumental variable regression is a foundational tool for causal analysis across the social and biomedical sciences. Recent advances use kernel methods to estimate nonparametric causal relationships, with general data types, while…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…
A general information transmission model, under independent and identically distributed Gaussian codebook and nearest neighbor decoding rule with processed channel output, is investigated using the performance metric of generalized mutual…
For a number of non-interacting identical particles entering a multi-channel scatterer in various wave packet states, we construct a generating function for the probabilities of various scattering outcomes. This is used to evaluate the mean…
We consider here convolution operators, in the Caputo sense, with non-singular kernels. We prove that the solutions to some integro-differential equations with such operators (acting on the space variable) coincide with the transition…
Irregular repetition slotted aloha (IRSA) is a distributed grant-free random access protocol where users transmit multiple replicas of their packets to a base station (BS). The BS recovers the packets using successive interference…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
We propose to model multivariate volatility processes based on the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrix-valued processes. It is flexible in the sense that…
We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as $t\to -\infty$ to asymptotic dynamics as $t\to +\infty$. The main novelty is the construction of modified…
The emerging 6G network envisions integrated sensing and communication (ISAC) as a promising solution to meet growing demand for native perception ability. To optimize and evaluate ISAC systems and techniques, it is crucial to have an…
This paper considers a large class of nonlinear integro-differential scalar equations which involve an anomalous diffusion (e.g. driven by a fractional Laplacian) and a non-local singular convolution kernel. Each of those singular equations…
A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously…
This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identites for these functions. The integrals are often used in…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…
A linear dispersive mechanism for error focusing in polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From…
This paper presents a nonparametric statistical modeling method for quantifying uncertainty in stochastic gradient systems with isotropic diffusion. The central idea is to apply the diffusion maps algorithm to a training data set to produce…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…