相关论文: Parameter estimates for fractional autoregressive …

We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, $H$, or the fractional integration parameter, $d$, in long memory time series. We compare and contrast their performance on…

We consider an algorithm to approximate complex-valued periodic functions $f(e^{i\theta})$ as a matrix element of a product of $SU(2)$-valued functions, which underlies so-called quantum signal processing. We prove that the algorithm runs…

In this paper, we study robust estimators of the memory parameter d of a (possibly) non stationary Gaussian time series with generalized spectral density f. This generalized spectral density is characterized by the memory parameter d and by…

We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients satisfy a linear recurrence equation. We interpret this…

We introduce a broad class of models called semiparametric spatial point process for making inference between spatial point patterns and spatial covariates. These models feature an intensity function with both parametric and nonparametric…

In the paper, we discuss the reconstruction of scalar parameters in a linear diffusion equation with fractional in time differential operators and with additional nonlocal (convolution) terms, which incorporate memory effects in models.…

We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence.…

We make an observation that facilitates exact likelihood-based inference for the parameters of the popular ARFIMA model without requiring stationarity by allowing the upper bound $\bar{d}$ for the memory parameter $d$ to exceed $0.5$:…

This paper introduces a framework for approximate message passing (AMP) in dynamic settings where the data at each iteration is passed through a linear operator. This framework is motivated in part by applications in large-scale,…

Operator learning focuses on approximating mappings $\mathcal{G}^\dagger:\mathcal{U} \rightarrow\mathcal{V}$ between infinite-dimensional spaces of functions, such as $u: \Omega_u\rightarrow\mathbb{R}$ and $v:…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications…

Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…

Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the…

We propose a single chunk model of long-term memory that combines the basic features of the ACT-R theory and the multiple trace memory architecture. The pivot point of the developed theory is a mathematical description of the creation of…

In this article, we introduce a non Gaussian long memory process constructed by the aggregation of independent copies of a fractional L\'evy Ornstein-Uhlenbeck process with random coefficients. Several properties and a limit theorem are…

Contemporaneous aggregation of individual AR(1) random processes might lead to different properties of the limit aggregated time series, in particular, long memory (Granger, 1980). We provide a new characterization of the series of…

We study parameter estimation problem for diagonalizable stochastic partial differential equations driven by a multiplicative fractional noise with any Hurst parameter $H\in(0,1)$. Two classes of estimators are investigated: traditional…

We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…