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Extracting information from functional magnetic resonance (fMRI) images has been a major area of research for more than two decades. The goal of this work is to present a new method for the analysis of fMRI data sets, that is capable to…
Orthogonal Fractional Factorial Designs and in particular Orthogonal Arrays are frequently used in many fields of application, including medicine, engineering and agriculture. In this paper we present a methodology and an algorithm to find…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation…
Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than…
The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…
Selecting techniques is a crucial element of the business analysis approach planning in IT projects. Particular attention is paid to the choice of techniques for requirements elicitation. One of the promising methods for selecting…
A new differential-recurrence relation for the B-spline functions of the same degree is proved. From this relation, a recursive method of computing the coefficients of B-spline functions of degree $m$ in the Bernstein-B\'{e}zier form is…
Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications.…
Feature selection is an important task in many problems occurring in pattern recognition, bioinformatics, machine learning and data mining applications. The feature selection approach enables us to reduce the computation burden and the…
The Fast Fourier Transform (FFT) is widely used in applications such as MRI, CT, and interferometry; however, because of its dependence on uniformly sampled data, it requires the use of gridding techniques for practical implementation. The…
Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…
In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…
Local-to-global learning approach plays an essential role in Bayesian network (BN) structure learning. Existing local-to-global learning algorithms first construct the skeleton of a DAG (directed acyclic graph) by learning the MB (Markov…
Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from…
Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a…
We develop a fully automatic Bayesian Lasso via variational inference. This is a scalable procedure for approximating the posterior distribution. Special attention is driven to the knot selection in regression spline. In order to carry…
We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal…
We propose a Bayesian approach to estimating parameters in multiclass functional models. Unordered multinomial probit, ordered multinomial probit and multinomial logistic models are considered. We use finite random series priors based on a…