Search results for "interpolointi"
showing 10 items of 11 documents
Minimal Learning Machine: Theoretical Results and Clustering-Based Reference Point Selection
2019
The Minimal Learning Machine (MLM) is a nonlinear supervised approach based on learning a linear mapping between distance matrices computed in the input and output data spaces, where distances are calculated using a subset of points called reference points. Its simple formulation has attracted several recent works on extensions and applications. In this paper, we aim to address some open questions related to the MLM. First, we detail theoretical aspects that assure the interpolation and universal approximation capabilities of the MLM, which were previously only empirically verified. Second, we identify the task of selecting reference points as having major importance for the MLM's generaliz…
Malliavin smoothness on the Lévy space with Hölder continuous or BV functionals
2020
We consider Malliavin smoothness of random variables f(X1), where X is a purejump Lévy process and the functionfis either bounded and Hölder continuousor of bounded variation. We show that Malliavin differentiability and fractional differentiability off (X1) depend both on the regularity offand the Blumenthal-Getoor index of the Lévy measure. peerReviewed
A note on Malliavin smoothness on the Lévy space
2017
We consider Malliavin calculus based on the Itô chaos decomposition of square integrable random variables on the Lévy space. We show that when a random variable satisfies a certain measurability condition, its differentiability and fractional differentiability can be determined by weighted Lebesgue spaces. The measurability condition is satisfied for all random variables if the underlying Lévy process is a compound Poisson process on a finite time interval. peerReviewed
Poincaré Type Inequalities for Vector Functions with Zero Mean Normal Traces on the Boundary and Applications to Interpolation Methods
2019
We consider inequalities of the Poincaré–Steklov type for subspaces of H1 -functions defined in a bounded domain Ω∈Rd with Lipschitz boundary ∂Ω . For scalar valued functions, the subspaces are defined by zero mean condition on ∂Ω or on a part of ∂Ω having positive d−1 measure. For vector valued functions, zero mean conditions are applied to normal components on plane faces of ∂Ω (or to averaged normal components on curvilinear faces). We find explicit and simply computable bounds of constants in the respective Poincaré type inequalities for domains typically used in finite element methods (triangles, quadrilaterals, tetrahedrons, prisms, pyramids, and domains composed of them). The second …
CLUSTERING INCOMPLETE SPECTRAL DATA WITH ROBUST METHODS
2018
Abstract. Missing value imputation is a common approach for preprocessing incomplete data sets. In case of data clustering, imputation methods may cause unexpected bias because they may change the underlying structure of the data. In order to avoid prior imputation of missing values the computational operations must be projected on the available data values. In this paper, we apply a robust nan-K-spatmed algorithm to the clustering problem on hyperspectral image data. Robust statistics, such as multivariate medians, are more insensitive to outliers than classical statistics relying on the Gaussian assumptions. They are, however, computationally more intractable due to the lack of closed-for…
Generalized solutions of a system of differential equations of the first order and elliptic type with discontinuous coefficients
2009
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus
2022
AbstractWe present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given a simplicial mesh, we first refine the mesh into smaller simplices which can be used to define higher order Whitney forms. Cochains on this refined mesh can then be interpolated using higher order Whitney forms. Hence, when the refined mesh is used with methods based on discrete exterior calculus, the solution can be expressed as a higher order Whitney form. We present algorithms for the three required steps: refining the mesh, solving the coefficients of the interpolant, and evaluating the interpolant at a given point. With our algorithms, the order of…
Rakennusteknisten, geologisten ja ilmastollisten tekijöiden vaikutus asuntojen sisäilman radonpitoisuuteen
2008
Estimating aggregated nutrient fluxes in four Finnish rivers via Gaussian state space models
2013
Reliable estimates of the nutrient fluxes carried by rivers from land-based sources to the sea are needed for efficient abatement of marine eutrophication. Although nutrient concentrations in rivers generally display large temporal variation, sampling and analysis for nutrients, unlike flow measurements, are rarely performed on a daily basis. The infrequent data calls for ways to reliably estimate the nutrient concentrations of the missing days. Here, we use the Gaussian state space models with daily water flow as a predictor variable to predict missing nutrient concentrations for four agriculturally impacted Finnish rivers. Via simulation of Gaussian state space models, we are able to esti…