Statistics

2112 Submissions

[3] viXra:2112.0158 [pdf] replaced on 2022-07-17 10:28:12

An Exhaustive Variable Selection Study for Linear Models of Soundscape Emotions: Rankings and Gibbs Analysis

Authors: R. San Millán-Castillo, L. Martino, E. Morgado, F. Llorente
Comments: 26 Pages. (to appear)) IEEE Transactions on Audio, Speech and Language Processing

In the last years, soundscapes have become one of the most active topics in Acoustics, providing a holistic approach to the acoustic environment, which involves human perception and context. Soundscapes-elicited emotions are central and substantially subtle and unnoticed (compared to speech or music). Currently, soundscape emotion recognition is a hot topic in the literature. We provide an exhaustive variable selection study (i.e., a selection of the soundscapes indicators) to a well-known dataset (emo-soundscapes).We consider linear soundscape emotion models for two soundscapes descriptors: arousal and valence. Several ranking schemes and procedures for selecting the number of variables are applied. We have also performed an alternating optimization scheme for obtaining the best sequences keeping fixed a certain number of features. Furthermore, we have designed a novel technique based on Gibbs sampling, which provides a more complete and clear view of the relevance of each variable. Finally, we have also compared our results with the analysis obtained by the classical methods based on p-values. As a result of our study, we suggest two simple and parsimonious linear models of only 7 and 16 variables (within the 122 possible features) for the two outputs (arousal and valence), respectively. The suggested linear models provide very good and competitive performance, with R2 > 0.86 and R2 > 0.63 (values obtained after a cross-validation procedure), respectively.
Category: Statistics

[2] viXra:2112.0058 [pdf] submitted on 2021-12-12 20:44:49

An Ordered Sample Mean That's a Bit Like Simpson's Rule

Authors: D Williams
Comments: 2 Pages.

A "Simpson's Rule"-like Ordered Sample Mean is compared with the standard version. It appears to be better at least for small sample sizes. A related integral approximation is also given and tested against the Mid Point Rule. Other Types of Ordered Sample Means need investigating.
Category: Statistics

[1] viXra:2112.0013 [pdf] submitted on 2021-12-02 02:52:21

Minimum with Inequality Constraint Applied to Increasing Cubic, Logistic and Gomperz or Convex Quartic and Biexponential Regressions

Authors: Josef Bukac
Comments: 28 Pages.

We present a method of minimizing an objective function subject to an inequality constraint. It enables us to minimize the sum of squares of deviations in linear regression under inequality restrictions. We demonstrate how to calculate the coefficients of cubic function under the restriction that it is increasing, we also mention how to fit a convex quartic polynomial. We use such results for interpolation as a method for calculation of starting values for iterative methods of fitting some specific functions, such as four-parameter logistic, positive bi-exponential, or Gomperz functions. Curvature-driven interpolation enables such calculations for otherwise solutions to interpolation equations may not exist or may not be unique. We also present examples to illustrate how it works and compare our approach with that of Zhang (2020).
Category: Statistics