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prof.dr.sc. Siniša Opić

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LASSO and RIDGE Linear regressions & L1 and L2
regularizations - the impact of the penalty term (in publishing, author - Sinisa Opic

Summary - Lasso and Ridge regressions are useful enhancements to ordinary least squares (OLS) regression, utilizing L1 and L2 regularization techniques. The main idea behind these methods is to balance the simplicity of the model with its accuracy by adding a penalty term to the existing regression formula. This approach leads to a significant reduction in the regression coefficients, potentially reducing some to zero (in the case of L1 regularization). These enhancements improve accuracy, increase R², lower mean squared error (MSE), eliminate non-significant coefficients, address the issue of multicollinearity among predictors, and most importantly, help prevent overfitting. In the empirical section of the study, both L1 (LASSO) and L2 (RIDGE) regression analyses were conducted on a dataset comprising 156 samples. A cross-validation procedure was employed with λ values ranging from 1 to 20 (with λmax=20, λmin = 0.5, and λ intervals of 1), using 5 folds. The results indicated that the application of Ridge regression, when compared to OLS, led to a reduction in the Beta coefficient, an increase in R², and a decrease in the Mean Squared Error (MSE). Furthermore, no significant discrepancies were found between the R² values for the training and holdout datasets, suggesting that the model is robust. However, in comparison, L1 regularization (LASSO) was performed, and the values of all betas for all categories of predictor variables are zero (βstd=0; B=0);∑_(i=0,5)^20 β=0 which indicates the impossibility of interpreting the regression model (type 2 error). LASSO and RIDGE regressions are iterative procedures, and their results depend on randomization, the number of k-fold cross-validations and k-iterations, the percentage of training and testing data, and the value of lambda (although this is a minor problem), so you should be careful when using them.

Keywords: Lasso regression, L1, L2 regularization, MSE, overfitting, penalty term, Ridge regression, The sum of squared residuals,

in publishing - prof.dr.sc.Sinisa Opic

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Statističke obrade - Quant research Ltd
Najsloženije statističke obrade iz područja društvenih, tehničkih, medicinskih znanosti, STEM; supervizija međunarodnih projekata, data analysis znanstvenih radova; SPSS, Statistic, AMOS; R, Phyton... parametric/non-parametric test, robust; univariate/multivariate approaches; linear vs nonlinear; MANOVA (n way), ANOVA (factorial), Descriptive, CFA, EFA (PCA FA...), Regressions (OLS, Lasso, Ridge; regulations L1, L2), SEM (CFA, mediation, moderations/bootstrapping), bayesian (ML); Log-linear (qualitative data); ANCOVA (n way), Longitudinal Canonical Correlation Analysis (LCCA), MANCOVA (n way)... RASCH measurement theory, Cox regression (survival analysis, Proportional Hazards Model, Fratility), Testiranje hipoteza NHST, proširenje na Polystohastic statistical inference). Izrada mjernih instrumenata, testiranje metrijskih karakteristika, kontrola bias-a, related samples, determiniranje probabilističkih uzoraka...
Suradnici Quant Research d.o.o su sveučilišni profesori (statistics, quantitative methodology, data mining) s niza prestižnih sveučilišta u svijetu te eksperti, matematičari u području obrade podataka u gospodarstvu (gaming,aktuarska matematika).
Poseban dio odnosi se na SVMs, non-parametric Kernel regression, Neural Networks (CNN, GNN, RNN...) u području složenih prediktivnih modela)

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