Structural Equation Modeling and simultaneous clustering through the Partial Least Squares algorithm

The identification of different homogeneous groups of observations and their appropriate analysis in PLS-SEM has become a critical issue in many appli- cation fields. Usually, both SEM and PLS-SEM assume the homogeneity of all units on which the model is estimated, and approaches of segmentation present in literature, consist in estimating separate models for each segments of statistical units, which have been obtained either by assigning the units to segments a priori defined. However, these approaches are not fully accept- able because no causal structure among the variables is postulated. In other words, a modeling approach should be used, where the obtained clusters are homogeneous with respect to the structural causal relationships. In this paper, a new methodology for simultaneous non-hierarchical clus- tering and PLS-SEM is proposed. This methodology is motivated by the fact that the sequential approach of applying first SEM or PLS-SEM and second the clustering algorithm such as K-means on the latent scores of the SEM/PLS-SEM may fail to find the correct clustering structure existing in the data. A simulation study and an application on real data are included to evaluate the performance of the proposed methodology

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible both due to significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world record determinations of critical exponents and correlation function coefficients in the Ising and $O(N)$ models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry.Comment: 81 pages, double column, 58 figures; v3: updated references, minor typos correcte

Partitioning predictors in multivariate regression models

A Multivariate Regression Model Based on the Optimal Partition of Predictors (MRBOP) useful in applications in the presence of strongly correlated predictors is presented. Such classes of predictors are synthesized by latent factors, which are obtained through an appropriate linear combination of the original variables and are forced to be weakly correlated. Specifically, the proposed model assumes that the latent factors are determined by subsets of predictors characterizing only one latent factor. MRBOP is formalized in a least squares framework optimizing a penalized quadratic objective function through an alternating least-squares (ALS) algorithm. The performance of the methodology is evaluated on simulated and real data sets. © 2013 Springer Science+Business Media New York

Bounds in 4D Conformal Field Theories with Global Symmetry

We explore the constraining power of OPE associativity in 4D Conformal Field Theory with a continuous global symmetry group. We give a general analysis of crossing symmetry constraints in the 4-point function , where Phi is a primary scalar operator in a given representation R. These constraints take the form of 'vectorial sum rules' for conformal blocks of operators whose representations appear in R x R and R x Rbar. The coefficients in these sum rules are related to the Fierz transformation matrices for the R x R x Rbar x Rbar invariant tensors. We show that the number of equations is always equal to the number of symmetry channels to be constrained. We also analyze in detail two cases - the fundamental of SO(N) and the fundamental of SU(N). We derive the vectorial sum rules explicitly, and use them to study the dimension of the lowest singlet scalar in the Phi x Phi* OPE. We prove the existence of an upper bound on the dimension of this scalar. The bound depends on the conformal dimension of Phi and approaches 2 in the limit dim(Phi)-->1. For several small groups, we compute the behavior of the bound at dim(Phi)>1. We discuss implications of our bound for the Conformal Technicolor scenario of electroweak symmetry breaking.Comment: 30 page

A composite indicator via hierarchical disjoint factor analysis for measuring the Italian football teams’ performances

In the last years, with the data revolution and the use of new technologies, phenomena are frequently described by a huge quantity of information useful for making strategical decisions. In the current ”big data” era, the interest of statistics into sports is increasing over the years, sportive and economic data are collected for all teams which use statistical analysis in order to improve their performances. For dealing with all this amount of information, an appropriate statistical analysis is needed. A priority is having statistical tools useful to synthesise the information arised from the data. Such tools are represented by composite indicators, that is, non-observable latent variables and linear combination of observed variables. The strategy of construction of a composite indicator used in this paper is based on a non-negative disjoint and hierarchical model for a set of quantitative variables. This is a factor model with a hierarchical struc- ture formed by factors associated to subsets of manifest variables with positive loadings. In this paper, a composite indicator for measuring the Italian football teams’ performances, in terms of sportive and economic variables, is proposed

Carving Out the Space of 4D CFTs

We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. Using our algorithm, we dramatically improve previous bounds on a number of CFT quantities, particularly for theories with global symmetries. In the case of SO(4) or SU(2) symmetry, our bounds severely constrain models of conformal technicolor. In N=1 superconformal theories, we place strong bounds on dim(Phi*Phi), where Phi is a chiral operator. These bounds asymptote to the line dim(Phi*Phi) <= 2 dim(Phi) near dim(Phi) ~ 1, forbidding positive anomalous dimensions in this region. We also place novel upper and lower bounds on OPE coefficients of protected operators in the Phi x Phi OPE. Finally, we find examples of lower bounds on central charges and flavor current two-point functions that scale with the size of global symmetry representations. In the case of N=1 theories with an SU(N) flavor symmetry, our bounds on current two-point functions lie within an O(1) factor of the values realized in supersymmetric QCD in the conformal window.Comment: 60 pages, 22 figure

The ABC (in any D) of Logarithmic CFT

Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our analysis is model-independent and holds for any spacetime dimension. Our results include a determination of the general form of correlation functions and conformal block decompositions, clearing the path for future bootstrap applications. Several examples are discussed in detail, including logarithmic generalized free fields, holographic models, self-avoiding random walks and critical percolation.Comment: 55 pages + appendice

Multi-mode partitioning for text clustering to reduce dimensionality and noises

Co-clustering in text mining has been proposed to partition words and documents simultaneously. Although the main advantage of this approach may improve interpretation of clusters on the data, there are still few proposals on these methods; while one-way partition is even now widely utilized for information retrieval. In contrast to structured information, textual data suffer of high dimensionality and sparse matrices, so it is strictly necessary to pre-process texts for applying clustering techniques. In this paper, we propose a new procedure to reduce high dimensionality of corpora and to remove the noises from the unstructured data. We test two different processes to treat data applying two co-clustering algorithms; based on the results we present the procedure that provides the best interpretation of the data