Related papers: Spatial Depth-Based Classification for Functional …
Inhomogeneities in real-world data, e.g., due to changes in the observation noise level or variations in the structural complexity of the source function, pose a unique set of challenges for statistical inference. Accounting for them can…
Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…
We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is…
Data depth proves successful in the analysis of multivariate data sets, in particular deriving an overall center and assigning ranks to the observed units. Two key features are: the directions of the ordering, from the center towards the…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
Orbital-free density functional theory promises to deliver linear-scaling electronic structure calculations. This requires the knowledge of the non-interacting kinetic-energy density functional (KEDF), which should be accurate and must…
Synthetic data generation has become a key ingredient for training machine learning procedures, addressing tasks such as data augmentation, analysing privacy-sensitive data, or visualising representative samples. Assessing the quality of…
Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…
Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…
We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…
Complex models are often used to understand interactions and drivers of human-induced and/or natural phenomena. It is worth identifying the input variables that drive the model output(s) in a given domain and/or govern specific model…
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…
Embedded Feature Selection (FS) is a classical approach for interpretable machine learning, aiming to identify the most relevant features of a dataset while simultaneously training the model. We consider an approach based on a hard…
Dynamic feature selection (DFS) is a machine learning framework in which features are acquired sequentially for individual samples under budget constraints. The exponential growth in the number of possible feature acquisition paths forces a…
This paper presents a close form solution in Reproducing Kernel Hilbert Space (RKHS) for the famed Wiener filter, which we called the functional Wiener filter(FWF). Instead of using the Wiener-Hopf factorization theory, here we define a new…
In this study, a new Stacked Generalization technique called Fuzzy Stacked Generalization (FSG) is proposed to minimize the difference between N -sample and large-sample classification error of the Nearest Neighbor classifier. The proposed…