In classical machine learning, regression is treated as a black box process of identifying a suitable function from a hypothesis set without attempting to gain insight into the mechanism connecting inputs and outputs. In the natural sciences, however, finding an interpretable function for a phenomenon is the prime goal as it allows to understand and generalize results. This paper proposes a nov...

We propose and analyze a Multilevel Richardson-Romberg (ML2R) estimator which combines the higher order bias cancellation of the Multistep Richardson-Romberg method introduced in [Pag07] and the variance control resulting from the stratification introduced in the Multilevel Monte Carlo (MLMC) method (see [Gil08, Hei01]). Thus, in standard frameworks like discretization schemes of diffusion proc...

To a strongly continuous semigroup ? T(t) t0 on a Banach space X we will associate semigroups ? T n (t) t0 on new Banach spaces X n for each n 2 Z. This construction is inspired by the classical Sobolev spaces and, due to its simplicity, of great help in understanding abstract and concrete semigroups. We start with a strongly continuous semigroup ? T(t) t0 on a Banach space X for which we assum...

Mining evolving datastreams raises the question how to extrapolate trends in the evolution of densities over time. While approaches for change diagnosis work well for interpolating spatio-temporal densities, they are not designed for extrapolation tasks. This work studies the temporal density extrapolation problem and sketches two approaches that addresses it. Both use a set of pseudo-points in...

Debra P. C. Peters and Jeffrey E. Herrick, USDA ARS, Jornada Experimental Range, Box 30003, MSC 3JER, NMSU, Las Cruces, NM 88003-0003, USA ([email protected]). / Dean L. Urban, Nicholas School of the Environment and Earth Sciences, Duke Univ., Durham, NC 27708-0328, USA. / Robert H. Gardner, Appalachian Laboratory, Univ. of Maryland Center for Environmental Science, Frostburg, MD 21532, USA. / ...

A full independent drug development programme to demonstrate efficacy may not be ethical and/or feasible in small populations such as paediatric populations or orphan indications. Different levels of extrapolation from a larger population to smaller target populations are widely used for supporting decisions in this situation. There are guidance documents in drug regulation, where a weakening o...

Extrapolation methods for the solution of partial diierentialequations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, in the contrast, is based on applying extrapolation indirectly, by using it on quantities like the residual. In the context of multigrid methods, a special technique of this type is known as-extrapolation. For nite e...

A novel technique for extrapolation of transient response using early-time and low-frequency data is proposed in this paper. An improved extrapolation scheme using approximate prolate series is presented to obtain a transient electromagnetic response. The approximate prolate series, which has an approximately band-limited and sub-domain nature, is a better choice for extrapolating the timedomai...

Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by generating a model of the signal to be extrapolated as weighted superposition of basis functions. Unfortunately, this algorithm is computationally very expensive...

A novel technique for accelerating the convergence rate of the iterative power method for solving eigenvalue problems is presented. Smoothed Residual Acceleration (SRA) is based on a modification to the well known fixed-parameter extrapolation method for power iterations. In SRA the residual vector is passed through a low-pass filter before the extrapolation step. Filtering limits the extrapola...