Related papers: Analysis of Probabilistic and Parametric Reduced O…
Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry…
Metamodeling of complex numerical systems has recently attracted the interest of the mathematical programming community. Despite the progress in high performance computing, simulations remain costly, as a matter of fact, the assessment of…
In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…
This paper proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector…
Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…
Modeling has become a widespread, useful tool in mathematics applied to diverse fields, from physics to economics to biomedicine. Practitioners of modeling may use algebraic or differential equations, to the elements of which they attribute…
This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…
Quantum statistical models (i.e., families of normalized density matrices) and quantum measurements (i.e., positive operator-valued measures) can be regarded as linear maps: the former, mapping the space of effects to the space of…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
One of the major open problems in machine learning is to characterize generalization in the overparameterized regime, where most traditional generalization bounds become inconsistent even for overparameterized linear regression. In many…
The reduced-rank vector autoregressive (VAR) model can be interpreted as a supervised factor model, where two factor modelings are simultaneously applied to response and predictor spaces. This article introduces a new model, called vector…
Biased sampling designs can be highly efficient when studying rare (binary) or low variability (continuous) endpoints. We consider longitudinal data settings in which the probability of being sampled depends on a repeatedly measured…
We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some…