On multi-view learning with additive models

In many scientific settings data can be naturally partitioned into variable groupings called views. Common examples include environmental (1st view) and genetic information (2nd view) in ecological applications, chemical (1st view) and biological (2nd view) data in drug discovery. Multi-view data also occur in text analysis and proteomics applications where one view consists of a graph with observations as the vertices and a weighted measure of pairwise similarity between observations as the edges. Further, in several of these applications the observations can be partitioned into two sets, one where the response is observed (labeled) and the other where the response is not (unlabeled). The problem for simultaneously addressing viewed data and incorporating unlabeled observations in training is referred to as multi-view transductive learning. In this work we introduce and study a comprehensive generalized fixed point additive modeling framework for multi-view transductive learning, where any view is represented by a linear smoother. The problem of view selection is discussed using a generalized Akaike Information Criterion, which provides an approach for testing the contribution of each view. An efficient implementation is provided for fitting these models with both backfitting and local-scoring type algorithms adjusted to semi-supervised graph-based learning. The proposed technique is assessed on both synthetic and real data sets and is shown to be competitive to state-of-the-art co-training and graph-based techniques.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS202 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Generalized Zero Range Potentials and Multi-Channel Electron-Molecule Scattering

A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges is considered. Spherical functions basis expansion of the potentials introduces partial amplitudes and corresponding radial functions. The approach is generalized to multi-channel case by a matrix formulation in which a state vector component is associated with a scattering channel. The zero-range potentials naturally enter the scheme when the class of operators of multiplication is widen to distributions. %Analog of multipolar expansion is treated. Spin variables, o Oscillations and rotations are incorporated into the scheme.Comment: 11 pages, 1 figure, CEPAS2 con

Context-Aware Deep Sequence Learning with Multi-View Factor Pooling for Time Series Classification

In this paper, we propose an effective, multi-view, multivariate deep classification model for time-series data. Multi-view methods show promise in their ability to learn correlation and exclusivity properties across different independent information resources. However, most current multi-view integration schemes employ only a linear model and, therefore, do not extensively utilize the relationships observed across different view-specific representations. Moreover, the majority of these methods rely exclusively on sophisticated, handcrafted features to capture local data patterns and, thus, depend heavily on large collections of labeled data. The multi-view, multivariate deep classification model for time-series data proposed in this paper makes important contributions to address these limitations. The proposed model derives a LSTM-based, deep feature descriptor to model both the view-specific data characteristics and cross-view interaction in an integrated deep architecture while driving the learning phase in a data-driven manner. The proposed model employs a compact context descriptor to exploit view-specific affinity information to design a more insightful context representation. Finally, the model uses a multi-view factor-pooling scheme for a context-driven attention learning strategy to weigh the most relevant feature dimensions while eliminating noise from the resulting fused descriptor. As shown by experiments, compared to the existing multi-view methods, the proposed multi-view deep sequential learning approach improves classification performance by roughly 4% in the UCI multi-view activity recognition dataset, while also showing significantly robust generalized representation capacity against its single-view counterparts, in classifying several large-scale multi-view light curve collections

Multi-Class Learning: Simplex Coding And Relaxation Error

We study multi-category classification in the framework of computational learning theory. We show how a relaxation approach, which is commonly used in binary classification, can be generalized to the multi-class setting. We propose a vector coding, namely the simplex coding, that allows to introduce a new notion of multi-class margin and cast multi-category classification into a vector valued regression problem. The analysis of the relaxation error be quantified and the binary case is recovered as a special case of our theory. From a computational point of view we can show that using the simplex coding we can design regularized learning algorithms for multi-category classification that can be trained at a complexity which is independent to the number of classes

Electronic Structure Calculations with LDA+DMFT

The LDA+DMFT method is a very powerful tool for gaining insight into the physics of strongly correlated materials. It combines traditional ab-initio density-functional techniques with the dynamical mean-field theory. The core aspects of the method are (i) building material-specific Hubbard-like many-body models and (ii) solving them in the dynamical mean-field approximation. Step (i) requires the construction of a localized one-electron basis, typically a set of Wannier functions. It also involves a number of approximations, such as the choice of the degrees of freedom for which many-body effects are explicitly taken into account, the scheme to account for screening effects, or the form of the double-counting correction. Step (ii) requires the dynamical mean-field solution of multi-orbital generalized Hubbard models. Here central is the quantum-impurity solver, which is also the computationally most demanding part of the full LDA+DMFT approach. In this chapter I will introduce the core aspects of the LDA+DMFT method and present a prototypical application.Comment: 21 pages, 7 figures. Chapter of "Many-Electron Approaches in Physics, Chemistry and Mathematics: A Multidisciplinary View", eds. V. Bach and L. Delle Site, Springer 201

Construction of a new family of Fubini-type polynomials and its applications

This paper gives an overview of systematic and analytic approach of operational technique involves to study multi-variable special functions significant in both mathematical and applied framework and to introduce new families of special polynomials. Motivation of this paper is to construct a new class of generalized Fubini-type polynomials of the parametric kind via operational view point. The generating functions, differential equations, and other properties for these polynomials are established within the context of the monomiality principle. Using the generating functions, various interesting identities and relations related to the generalized Fubini-type polynomials are derived. Further, we obtain certain partial derivative formulas including the generalized Fubini-type polynomials. In addition, certain members belonging to the aforementioned general class of polynomials are considered. The numerical results to calculate the zeros and approximate solutions of these polynomials are given and their graphical representation are shown. © 2021, The Author(s)

Mathematical modeling, simulation, and optimization of loading schemes for isometric resistance training

In this thesis, we present a novel mathematical model-based approach to optimize loading schemes of isometric resistance training (RT) sessions for different training goals. To this end, we develop a nonlinear ordinary differential equation model of the time course of maximum voluntary isometric (MVIC) force under external isometric loading. To validate the model, we set up multi-experiment parameter estimation problems using a comprehensive dataset from the literature. We solve these problems numerically via direct multiple shooting and the generalized Gauss-Newton method. Moreover, we use the proposed model to examine hypotheses about fatigue and recovery of MVIC force. Then, we mathematically formulate key performance indicators and optimality criteria for loading schemes of isometric RT sessions identified in sports science and incorporate these into multi-stage optimal control problems. We solve these problems numerically via direct multiple shooting and structure-exploiting sequential quadratic programming. We discuss the results from a numerical and sports scientific point of view. Based on the proposed model, we additionally formulate the estimation of critical torque as a nonlinear program. This allows us to reduce the experimental effort compared to conventional testing when estimating these quantities. Furthermore, we formulate multi-stage optimum experimental design problems to reduce the statistical uncertainty of the parameter estimates when calibrating the model. We solve these problems numerically via direct single shooting and sequential quadratic programming. We discuss the solutions from a numerical and physiological point of view. For our approach, a small amount of data obtained in a single testing session is sufficient. Our approach can be extended to more elaborate physiological models and other forms of resistance training once suitable models become available

Inter-Band GSNR Degradations and Leading Impairments in C+L Band 400G Transmission

Wideband optical transmission presents an appealing solution to network throughput and capacity requirements, improving existing network architectures with minimally invasive upgrades. This framework provides new perspectives into quality of transmission (QoT) management as a result of inter-band effects; the QoT is commonly given by the generalized signal-to-noise ratio (GSNR). In this study we address the leading impairments in multi-band nonlinear transmission in a C+L scenario from an operational point of view, supported by mathematical models and simulations. From this approach we identify that stimulated Raman scattering (SRS) is the main contributor to inter-band effects and causes the main variation in the GSNR degradation; correspondingly, we show that the inter-band nonlinear interference (NLI) can be neglected in a C+L scenario