Related papers: Uniform error bounds for a continuous approximatio…
We consider a finite volume scheme with two-point flux approximation (TPFA) to approximate a Laplace problem when the solution exhibits no more regularity than belonging to $H^1_0(\Omega)$. We establish in this case some error bounds for…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…
In this paper, we improve upon our previous work[24,22] and establish convergence bounds on the objective function values of approximate proximal-gradient descent (AxPGD), approximate accelerated proximal-gradient descent (AxAPGD) and…
Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics. In this work, we consider the problem of estimating the…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The…
Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
This paper studies quantitative deviation bounds for statistical ensembles evolving under the one-parameter flow of a nearly integrable Hamiltonian system. Combining Nekhoroshev-type stability estimates with phase-mixing arguments, we…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
In this paper we provide a probabilistic representation of Lagrange's identity which we use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead to generalized sequences of weights which depend on an…
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…
We discuss the role of random basis function approximators in modeling and control. We analyze the published work on random basis function approximators and demonstrate that their favorable error rate of convergence O(1/n) is guaranteed…
A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or…
We obtain an error estimate between viscosity solutions and \delta-viscosity solutions of nonhomogeneous fully nonlinear uniformly elliptic equations. The main assumption, besides uniform ellipticity, is that the nonlinearity is…
We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and…
We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…
The local regularity of functional time series is studied under $L^p-m-$appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity…
We pose the approximation problem for scalar nonnegative input-output systems via impulse response convolutions of finite order, i.e. finite order moving averages, based on repeated observations of input/output signal pairs. The problem is…
In this paper we study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. We propose approximating a discrete time problem with a continuous time problem allowing us to apply developed…
Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical…