scholarly journals Convergence rates of least squares regression estimators with heavy-tailed errors

2019 ◽  
Vol 47 (4) ◽  
pp. 2286-2319 ◽  
Author(s):  
Qiyang Han ◽  
Jon A. Wellner
Keyword(s):  
Least Squares ◽  
Convergence Rates ◽  
Least Squares Regression ◽  
Regression Estimators ◽  
Heavy Tailed

scholarly journals Robust Regression via Heuristic Hard Thresholding

2017 ◽  
Author(s):  
Xuchao Zhang ◽  
Liang Zhao ◽  
Arnold P. Boedihardjo ◽  
Chang-Tien Lu
Keyword(s):  
Least Squares ◽  
Robust Regression ◽  
Convergence Rates ◽  
State Of The Art ◽  
Fundamental Problem ◽  
Regression Coefficients ◽  
Least Squares Regression ◽  
Hard Thresholding ◽  
Robust Least Squares ◽  
Competitive Efficiency

The presence of data noise and corruptions recently invokes increasing attention on Robust Least Squares Regression (RLSR), which addresses the fundamental problem that learns reliable regression coefficients when response variables can be arbitrarily corrupted. Until now, several important challenges still cannot be handled concurrently: 1) exact recovery guarantee of regression coefficients 2) difficulty in estimating the corruption ratio parameter; and 3) scalability to massive dataset. This paper proposes a novel Robust Least squares regression algorithm via Heuristic Hard thresholding (RLHH), that concurrently addresses all the above challenges. Specifically, the algorithm alternately optimizes the regression coefficients and estimates the optimal uncorrupted set via heuristic hard thresholding without corruption ratio parameter until it converges. We also prove that our algorithm benefits from strong guarantees analogous to those of state-of-the-art methods in terms of convergence rates and recovery guarantees. We provide empirical evidence to demonstrate that the effectiveness of our new method is superior to that of existing methods in the recovery of both regression coefficients and uncorrupted sets, with very competitive efficiency.

scholarly journals Convergence rates of Kernel Conjugate Gradient for random design regression

2016 ◽  
Vol 14 (06) ◽  
pp. 763-794 ◽  
Author(s):  
Gilles Blanchard ◽  
Nicole Krämer
Keyword(s):  
Least Squares ◽  
Conjugate Gradient ◽  
Reproducing Kernel ◽  
Convergence Rates ◽  
Reproducing Kernel Hilbert Space ◽  
Regression Function ◽  
Rates Of Convergence ◽  
Least Squares Regression ◽  
Hilbert Norm ◽  
Effective Dimensionality

We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient (CG) algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called “fast convergence rates” depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the ℒ2 (prediction) norm as well as for the stronger Hilbert norm, if the true regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.

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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