Related papers: Variability of qualitative variables: A Hilbert sp…
In this paper, we present the general theory of embedding independence tests on Hilbert spaces that generalizes the concepts of distance covariance, distance multivariance and HSIC. This is done by defining new types of kernel on an $n$…
Composites, or linear combinations of variables, play an important role in multivariate behavioral research. They appear in the form of indices, inventories, formative constructs, parcels, and emergent variables. Although structural…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
Effect size measures and visualization techniques aimed at maximizing the interpretability and comparability of results from statistical models have long been of great importance and are recently again receiving increased attention in the…
We develop a new approach to solving classification problems, which is bases on the theory of coherent measures of risk and risk sharing ideas. The proposed approach aims at designing a risk-averse classifier. The new approach allows for…
We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…
A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category…
This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…
We introduce an algebraicity criteria. It has the following form: under certain conditions, an analytic subvariety of some algebriac variety over a global field $K$, if it contains many $K$-points, then it is algebraic over $K.$ This gives…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…
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…
Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on…
The assessment of binary classifier performance traditionally centers on discriminative ability using metrics, such as accuracy. However, these metrics often disregard the model's inherent uncertainty, especially when dealing with sensitive…
We present a new and feasible test proving quantum contextuality in four-dimensional Hiltbert space. In our scheme, a contradiction between quantum mechanics and noncontextual hidden variables is revealed through the measurement statistics…
Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces, which leverages the data's internal structure…
We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of bounded operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a…
Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…
Modeling and parameter estimation for neuronal dynamics are often challenging because many parameters can range over orders of magnitude and are difficult to measure experimentally. Moreover, selecting a suitable model complexity requires a…
The dilemma which remained unsolved using Rao-Stirling diversity, namely of how variety and balance can be combined into "dual concept diversity" (Stirling, 1998, pp. 48f.) can be clarified by using Nijssen et al.'s (1998) argument that the…