Related papers: Hilbert Space Multi-dimensional Modeling
Classifying points in high dimensional spaces is a fundamental geometric problem in machine learning. In this paper, we address classifying points in the $d$-dimensional Hilbert polygonal metric. The Hilbert metric is a generalization of…
We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
We investigate the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. After describing a general framework to reformulate such models in terms of Hermitian Hamiltonians defined on the Hilbert space…
It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
The Constrained Minimal Supersymmetric Standard Model (CMSSM) is one of the simplest and most widely-studied supersymmetric extensions to the standard model of particle physics. Nevertheless, current data do not sufficiently constrain the…
Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed…
Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring a…
Repeated-measure designs allow comparisons within a group as well as between groups, and are commonly referred to as split-plot designs. While originating in agricultural experiments, they are now widely used in medical research,…
For statistical analysis of multiway contingency tables we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom…
Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert…
Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
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…
We propose a mixture of latent trait models with common slope parameters (MCLT) for model-based clustering of high-dimensional binary data, a data type for which few established methods exist. Recent work on clustering of binary data, based…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
In this article, a large dimensional performance analysis of kernel least squares support vector machines (LS-SVMs) is provided under the assumption of a two-class Gaussian mixture model for the input data. Building upon recent advances in…
We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator.…
High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…
Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office…