The curse of dimensionality causes the well-known and widely discussed problems for machine learning methods. There is a hypothesis that using the Manhattan distance and even fractional $l_p$ quasinorms (for p less than 1) can help to overcome the curse of dimensionality in classification problems. In this study, we systematically test this hypothesis. It is illustrated that fractional quasinorms have a greater relative contrast and coefficient of variation than the Euclidean norm $l_2$, but it is shown that this difference decays with increasing space dimension. It has been demonstrated that the concentration of distances shows qualitatively the same behaviour for all tested norms and quasinorms. It is shown that a greater relative contrast does not mean a better classification quality. It was revealed that for different databases the best (worst) performance was achieved under different norms (quasinorms). A systematic comparison shows that the difference in the performance of kNN classifiers for $l_p$ at p = 0.5, 1, and 2 is statistically insignificant. Analysis of curse and blessing of dimensionality requires careful definition of data dimensionality that rarely coincides with the number of attributes. We systematically examined several intrinsic dimensions of the data.

Forecasting macroeconomic variables is essential to macroeconomics, financial economics, and monetary policy analysis. Due to the high dimensionality of the macroeconomic dataset, it is challenging to forecast efficiently and accurately. Thus, this study provides a comprehensive analysis of predicting macroeconomic variables by comparing various vector autoregressive models followed by different estimation techniques. To address this, this paper proposes a novel hybrid model based on a smoothly clipped absolute deviation estimation method and a vector autoregression model that combats the curse of dimensionality and simultaneously produces reliable forecasts. The proposed hybrid model is applied to the U.S. quarterly macroeconomic data from the first quarter of 1959 to the fourth quarter of 2023, yielding multi-step-ahead forecasts (one-, three-, and six-step ahead). The multi-step-ahead out-of-sample forecast results (root mean square error and mean absolute error) for the considered data suggest that the proposed hybrid model yields a highly accurate and efficient gain. Additionally, it is demonstrated that the proposed models outperform the baseline models. Finally, the authors believe the proposed hybrid model may be expanded to other countries to assess its efficacy and accuracy.

Skin cancer is a major global health concern and one of the deadliest forms of cancer. Early and accurate detection significantly increases the chances of survival. However, traditional visual inspection methods are time-consuming and prone to errors due to artifacts and noise in dermoscopic images. To address these challenges, this paper proposes an innovative deep learning-based framework that integrates an ensemble of two pre-trained convolutional neural networks (CNNs), SqueezeNet and InceptionResNet-V2, combined with an improved Whale Optimization Algorithm (WOA) for feature selection. The deep features extracted from both models are fused to create a comprehensive feature set, which is then optimized using the proposed enhanced WOA that employs a quadratic decay function for dynamic parameter tuning and an advanced mutation mechanism to prevent premature convergence. The optimized features are fed into machine learning classifiers to achieve robust classification performance. The effectiveness of the framework is evaluated on two benchmark datasets, PH2 and Med-Node, achieving state-of-the-art classification accuracies of 95.48% and 98.59%, respectively. Comparative analysis with existing optimization algorithms and skin cancer classification approaches demonstrates the superiority of the proposed method in terms of accuracy, robustness, and computational efficiency. Our method outperforms the genetic algorithm (GA), Particle Swarm Optimization (PSO), and the slime mould algorithm (SMA), as well as deep learning-based skin cancer classification models, which have reported accuracies of 87% to 94% in previous studies. A more effective feature selection methodology improves accuracy and reduces computational overhead while maintaining robust performance. Our enhanced deep learning ensemble and feature selection technique can improve early-stage skin cancer diagnosis, as shown by these data.

This paper proposes a novel two-stage ensemble framework combining Long Short-Term Memory (LSTM) and Bidirectional LSTM (BiLSTM) with randomized feature selection to enhance diabetes prediction accuracy and calibration. The method first trains multiple LSTM/BiLSTM base models on dynamically sampled feature subsets to promote diversity, followed by a meta-learner that integrates predictions into a final robust output. A systematic simulation study conducted reveals that feature selection proportion critically impacts generalization: mid-range values (0.5–0.8 for LSTM; 0.6–0.8 for BiLSTM) optimize performance, while values close to 1 induce overfitting. Furthermore, real-life data evaluation on three benchmark datasets—Pima Indian Diabetes, Diabetic Retinopathy Debrecen, and Early Stage Diabetes Risk Prediction—revealed that the framework achieves state-of-the-art results, surpassing conventional (random forest, support vector machine) and recent hybrid frameworks with an accuracy of up to 100%, AUC of 99.1–100%, and superior calibration (Brier score: 0.006–0.023). Notably, the BiLSTM variant consistently outperforms unidirectional LSTM in the proposed framework, particularly in sensitivity (98.4% vs. 97.0% on retinopathy data), highlighting its strength in capturing temporal dependencies.

Maintaining stable prices is one of the goals of monetary policy makers. Since its formation, inflation has been a key issue and priority for every Pakistani government; it is a fundamental macroeconomic variable that plays a significant role in a nation’s economic progress and development. This research investigates the predictive capabilities of different univariate and multivariate models. The study considers autoregressive models, autoregressive neural networks, autoregressive moving average models, and other nonparametric autoregressive models within the univariate category. In contrast, the multivariate models include factor models that utilize Minimax Concave Penalty, Elastic-Smoothly Clipped Absolute Deviation, Principal Component Analysis, and Partial Least Squares. We conducted an empirical analysis using a well-established macroeconomic dataset from Pakistan. This dataset covers the period from January 2013 to December 2020 and consists of 79 variables recorded at that frequency. To evaluate the forecasting accuracy of the models for multiple steps ahead in the post-sample period, an analysis was performed using data extracted from January 2013 to February 2019 for model estimation and then another set from March 2019 to December 2020. The predictability of the univariate models following the sample period is compared with that of the multivariate models using statistical accuracy measurements, specifically root mean square error and mean absolute error. Additionally, the Diebold–Mariano test has been employed to evaluate the accuracy of the average errors statistically. The results indicated that the factor approach based on Partial Least Squares delivers significantly more effective outcomes than its competing methods.

Count regression models, particularly negative binomial regression (NBR), are widely used in various fields, including biometrics, ecology, and insurance. Over-dispersion is likely when dealing with count data, and NBR has gained attention as an effective tool to address this challenge. However, multicollinearity among covariates and the presence of outliers can lead to inflated confidence intervals and inaccurate predictions in the model. This study proposes a comprehensive approach integrating robust and regularization techniques to handle the simultaneous impact of multicollinearity and outliers in the negative binomial regression model (NBRM). We investigate the estimators’ performance through extensive simulation studies and provide analytical comparisons. The simulation results and the theoretical comparisons demonstrate the superiority of the proposed robust hybrid KL estimator (M-NBKLE) with predictive accuracy and stability when multicollinearity and outliers exist. We illustrate the application of our methodology by analyzing a forestry dataset. Our findings complement and reinforce the simulation and theoretical results.