Cluster analysis is a widely applied machine learning technique to understand the existing patterns in the population of gamma-ray bursts (GRBs), in order to explore their physical sources. In the present scenario, the number of clusters corresponding to differentiable groups is still under conflict, in spite of numerous attempts with the state-of-the-art clustering procedures. This crucial unknown parameter needs to be evaluated, either directly or indirectly in terms of other tuning parameters, to produce the clusters in GRBs through implementation of an appropriate clustering algorithm. While most of the applied algorithms reached two physically explained groups of merger and collapsar predominated by the short and long bursts respectively, other statistical approaches violated this binary partition. However, physical establishment of any additional cluster(s) is not yet confirmed. Therefore, we propose a new algorithm, from a different stream of clustering referred to as `completely parameter-free', which carries out the classification of GRBs in a manner that has not been tried so far. It indicates two main groups, of short and long duration bursts from the BATSE sample, compatible with the merger-collapsar theory.

The paper applies a new, nonparametric, interpoint distance-based measure to confirm the inherent groups prevailing in the brightest source of light in the universe: gamma-ray bursts. Our effective metric, in association with clustering methods like Gaussian-mixture model-based and $K$-means algorithms, resolves the conflict regarding the possibility about existence of more than binary clusters in the gamma-ray burst population. Here we carry out multiple nonparametric statistical tests of hypotheses, as many as the number of bursts available from the `BATSE' catalog. An integrated $p$-value achieved from the aforesaid dependent tests solves our concern confirming two groups of short and long bursts.

Predicting future vehicle purchases among existing owners presents a critical challenge due to extreme class imbalance (<0.5% positive rate) and complex behavioral patterns. We propose REMEDI (Relative feature Enhanced Meta-learning with Distillation for Imbalanced prediction), a novel multi-stage framework addressing these challenges. REMEDI first trains diverse base models to capture complementary aspects of user behavior. Second, inspired by comparative op-timization techniques, we introduce relative performance meta-features (deviation from ensemble mean, rank among peers) for effective model fusion through a hybrid-expert architecture. Third, we distill the ensemble's knowledge into a single efficient model via supervised fine-tuning with MSE loss, enabling practical deployment. Evaluated on approximately 800,000 vehicle owners, REMEDI significantly outperforms baseline approaches, achieving the business target of identifying ~50% of actual buyers within the top 60,000 recommendations at ~10% precision. The distilled model preserves the ensemble's predictive power while maintaining deployment efficiency, demonstrating REMEDI's effectiveness for imbalanced prediction in industry settings.

In recent years, the rapid development of deep learning has led to a wide range of applications in medical image classification. The variants of neural network models with ever-increasing performance share some commonalities: to try to mitigate overfitting, improve generalization, avoid gradient vanishing and exploding, etc. AlexNet first utilizes the dropout technique to ease overfitting and the ReLU activation function to prevent vanishing gradient. Therefore, we focus on AlexNet, which initially contributed significantly to Convolutional Neural Networks (CNNs) research in 2012. After reviewing over 100 papers, including those from journals and conferences, we give a narrative on the technical details, advantages, and application areas of AlexNet.