scholarly journals Discriminating the Influence of Correlated Factors from Multivariate Observations: the Back-to-Back Regression

2020 ◽  
Author(s):  
Jean-Rémi King ◽  
François Charton ◽  
David Lopez-Paz ◽  
Maxime Oquab
Keyword(s):  
Least Squares ◽  
Linear Method ◽  
Simulated Data ◽  
Least Squares Regression ◽  
Brain Responses ◽  
Two Factors ◽  
Respective Contribution ◽  
Potential Factors ◽  
Cross Decomposition ◽  
Correlated Factors

AbstractIdentifying causes solely from observations can be particularly challenging when i) potential factors are difficult to manipulate independently and ii) observations are multi-dimensional. To address this issue, we introduce “Back-to-Back” regression (B2B), a linear method designed to efficiently measure, from a set of correlated factors, those that most plausibly account for multidimensional observations. First, we prove the consistency of B2B, its links to other linear approaches, and show how it provides a robust, unbiased and interpretable scalar estimate for each factor. Second, we use a variety of simulated data to show that B2B outperforms least-squares regression and cross-decomposition techniques (e.g. canonical correlation analysis and partial least squares) on causal identification when the factors and the observations are partially collinear. Finally, we apply B2B to magneto-encephalography of 102 subjects recorded during a reading task to test whether our method appropriately disentangles the respective contribution of word length and word frequency - two correlated factors known to cause early and late brain responses respectively. The results show that these two factors are better disentangled with B2B than with other standard techniques.

scholarly journals Robust Nonlinear Partial Least Squares Regression Using the BACON Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Abdelmounaim Kerkri ◽  
Jelloul Allal ◽  
Zoubir Zarrouk
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Latent Variables ◽  
Partial Least Squares Regression ◽  
Chemical Engineering ◽  
Simulated Data ◽  
Ordinary Least Squares ◽  
Least Squares Regression ◽  
Computationally Efficient ◽  
The Difference

Partial least squares regression (PLS regression) is used as an alternative for ordinary least squares regression in the presence of multicollinearity. This occurrence is common in chemical engineering problems. In addition to the linear form of PLS, there are other versions that are based on a nonlinear approach, such as the quadratic PLS (QPLS2). The difference between QPLS2 and the regular PLS algorithm is the use of quadratic regression instead of OLS regression in the calculations of latent variables. In this paper we propose a robust version of QPLS2 to overcome sensitivity to outliers using the Blocked Adaptive Computationally Efficient Outlier Nominators (BACON) algorithm. Our hybrid method is tested on both real and simulated data.

Application of Non-Linear Partial Least-Squares Regression in the Prediction of Carbonization Depth of Concrete

2011 ◽  
Vol 341-342 ◽  
pp. 53-57
Author(s):  
Jian Ping Jiang
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Exposure Time ◽  
Latent Variables ◽  
Linear Method ◽  
Forecast Model ◽  
Residual Value ◽  
Least Squares Regression ◽  
Multinomial Regression ◽  
Non Linear

Based on partial least-squares multinomial regression, this paper had a prediction on carbonization depth of conctete. Taking water-cement ratio (i.e. water-ash ratio), cement content (i.e. application amount of cement material), and exposure time of concrete as independent variables , and carbonization depth of conctete as dependent variable , the forecast model of carbonization depth of conctete was obtained. It was found that, Press residual value decreased with the increase of number of latent variables, and the number of latent variables were three by Press residual value versus number of latent variables. The normal regression coefficient of exposure time of concrete was the largest wiithin three influence factors, this indicated that the influence of exposure time of concrete was largest to conctete carbonization depth; The determination coefficient of forecast model obtained in this paper was 0.9940, the error of forecast model was . The following conclusion can be drawn that, the model is accurate and credible, and the partial least-squares multinomial regression is a eximious non-linear method, and it is worthy to spread its application in the forecast analysis of conctete carbonization depth.

Use of reflectance spectroscopy to estimate the organic carbon and CaCO3 contents of soils

2012 ◽  
Vol 61 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Ádám Csorba ◽  
Vince Láng ◽  
László Fenyvesi ◽  
Erika Michéli
Keyword(s):  
Organic Carbon ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Mean Squared Error ◽  
Reflectance Spectroscopy ◽  
Least Squares Regression ◽  
Root Mean Squared Error ◽  
Squared Error

Napjainkban egyre nagyobb igény mutatkozik olyan technológiák és módszerek kidolgozására és alkalmazására, melyek lehetővé teszik a gyors, költséghatékony és környezetbarát talajadat-felvételezést és kiértékelést. Ezeknek az igényeknek felel meg a reflektancia spektroszkópia, mely az elektromágneses spektrum látható (VIS) és közeli infravörös (NIR) tartományában (350–2500 nm) végzett reflektancia-mérésekre épül. Figyelembe véve, hogy a talajokról felvett reflektancia spektrum információban nagyon gazdag, és a vizsgált tartományban számos talajalkotó rendelkezik karakterisztikus spektrális „ujjlenyomattal”, egyetlen görbéből lehetővé válik nagyszámú, kulcsfontosságú talajparaméter egyidejű meghatározása. Dolgozatunkban, a reflektancia spektroszkópia alapjaira helyezett, a talajok ösz-szetételének meghatározását célzó módszertani fejlesztés első lépéseit mutatjuk be. Munkánk során talajok szervesszén- és CaCO3-tartalmának megbecslését lehetővé tévő többváltozós matematikai-statisztikai módszerekre (részleges legkisebb négyzetek módszere, partial least squares regression – PLSR) épülő prediktív modellek létrehozását és tesztelését végeztük el. A létrehozott modellek tesztelése során megállapítottuk, hogy az eljárás mindkét talajparaméter esetében magas R2értéket [R2(szerves szén) = 0,815; R2(CaCO3) = 0,907] adott. A becslés pontosságát jelző közepes négyzetes eltérés (root mean squared error – RMSE) érték mindkét paraméter esetében közepesnek mondható [RMSE (szerves szén) = 0,467; RMSE (CaCO3) = 3,508], mely a reflektancia mérési előírások standardizálásával jelentősen javítható. Vizsgálataink alapján arra a következtetésre jutottunk, hogy a reflektancia spektroszkópia és a többváltozós kemometriai eljárások együttes alkalmazásával, gyors és költséghatékony adatfelvételezési és -értékelési módszerhez juthatunk.

Speech Emotion Recognition Based on Sparse Representation

2013 ◽  
Vol 38 (4) ◽  
pp. 465-470 ◽  
Author(s):  
Jingjie Yan ◽  
Xiaolan Wang ◽  
Weiyi Gu ◽  
LiLi Ma
Keyword(s):  
Dimensionality Reduction ◽  
Emotion Recognition ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Speech Emotion Recognition ◽  
Least Squares Regression ◽  
Computer Science Pedagogy ◽  
Reduction Methods ◽  
Analysis Computer

Abstract Speech emotion recognition is deemed to be a meaningful and intractable issue among a number of do- mains comprising sentiment analysis, computer science, pedagogy, and so on. In this study, we investigate speech emotion recognition based on sparse partial least squares regression (SPLSR) approach in depth. We make use of the sparse partial least squares regression method to implement the feature selection and dimensionality reduction on the whole acquired speech emotion features. By the means of exploiting the SPLSR method, the component parts of those redundant and meaningless speech emotion features are lessened to zero while those serviceable and informative speech emotion features are maintained and selected to the following classification step. A number of tests on Berlin database reveal that the recogni- tion rate of the SPLSR method can reach up to 79.23% and is superior to other compared dimensionality reduction methods.

An Approach of the Madeira Wine Chemistry

Beverages ◽  
2020 ◽  
Vol 6 (1) ◽  
pp. 12 ◽  
Author(s):  
Rosa Perestrelo ◽  
Catarina Silva ◽  
Carolina Gonçalves ◽  
Mariangie Castillo ◽  
José S. Câmara
Keyword(s):  
Mass Spectrometry ◽  
Gas Chromatography ◽  
Least Squares ◽  
Partial Least Squares ◽  
Chemical Reactions ◽  
Ageing Process ◽  
Gas Chromatography Mass Spectrometry ◽  
Wine Aroma ◽  
Least Squares Regression ◽  
Volatile Composition

Madeira wine is a fortified Portuguese wine, which has a crucial impact on the Madeira Island economy. The particular properties of Madeira wine result from the unique and specific winemaking and ageing processes that promote the occurrence of chemical reactions among acids, sugars, alcohols, and polyphenols, which are important to the extraordinary quality of the wine. These chemical reactions contribute to the appearance of novel compounds and/or the transformation of others, consequently promoting changes in qualitative and quantitative volatile and non-volatile composition. The current review comprises an overview of Madeira wines related to volatile (e.g., terpenes, norisoprenoids, alcohols, esters, fatty acids) and non-volatile composition (e.g., polyphenols, organic acids, amino acids, biogenic amines, and metals). Moreover, types of aroma compounds, the contribution of volatile organic compounds (VOCs) to the overall Madeira wine aroma, the change of their content during the ageing process, as well as the establishment of the potential ageing markers will also be reviewed. The viability of several analytical methods (e.g., gas chromatography-mass spectrometry (GC-MS), two-dimensional gas chromatography and time-of-flight mass spectrometry (GC×GC-ToFMS)) combined with chemometrics tools (e.g., partial least squares regression (PLS-R), partial least squares discriminant analysis (PLS-DA) was investigated to establish potential ageing markers to guarantee the Madeira wine authenticity. Acetals, furanic compounds, and lactones are the chemical families most commonly related with the ageing process.

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