Related papers: Lower estimates for linear operators with smooth r…
The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which established sharp local…
We deal with the problem of gradient estimation for stochastic differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. Stochastic smoothing conventionally perturbs the input of a…
Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…
Quantum Computing offers a new paradigm for efficient computing and many AI applications could benefit from its potential boost in performance. However, the main limitation is the constraint to linear operations that hampers the…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
We construct a zeroth-order gradient estimator for a smooth function defined on the probability simplex. The proposed estimator queries the simplex only. We prove that projected gradient descent and the exponential weights algorithm, when…
The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The approximation problem in Frobenius norm admits a well-known…
In this paper, a $k$-th generalized modulus of smoothness is defined based on an asymmetric operator of generalized translation and a theorem is proved about the coincidence of class of functions defined by this modulus and a class of…
Approximative properties of linear summation methods of Fourier series are considered in the Orlicz type spaces ${\mathcal S}_{M}$. In particular, in terms of approximations by such methods, constructive characteristics are obtained for…
We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least…
It is known that convergence of l.s.b. closed symmetric sesquilinear forms implies norm resolvent convergence of the associated self-adjoint operators and this in turn convergence of discrete spectra. In this paper in both cases sharp…
We outline a general procedure on how to apply random positive linear operators in nonparametric estimation. As a consequence, we give explicit confidence bands and intervals for a distribution function $F$ concentrated on $[0,1]$ by means…
In this paper we investigate the gamma-relative differentiation by the motivation of amending the order of the weighted polynomial approximation on the semiaxis for certain functions. With the help of this we give some definitions of…
The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of…
In this paper, exact rate of approximation of functions by linear means of Fourier series and Fourier integrals and corresponding $K$-functionals are expressed via special moduli of smoothness. . Introduction is given in $\S 1$. In $\S2$…
Observational data are often accompanied by natural structural indices, such as time stamps or geographic locations, which are meaningful to prediction tasks but are often discarded. We leverage semantically meaningful indexing data while…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…
This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic bounds on the estimation error in terms of the sparsity level of…
This paper develops and implements a practical simulation-based method for estimating dynamic discrete choice models. The method, which can accommodate lagged dependent variables, serially correlated errors, unobserved variables, and many…