Maksim Kazanskii

Maksim Kazanskii

Dimensionality reduction methods such as t-SNE are designed to preserve local neighborhood structure but do not explicitly account for how probability mass is distributed, often leading to distortions of data density. We reformulate dimensionality reduction as the joint alignment of two components: (i) conditional structure, capturing local relationships, and (ii) relative density structure, captured via local density statistics. Based on this perspective, we introduce Density-Regularized SNE (DR-SNE), which augments the stochastic neighbor embedding objective with a density regularization term derived from normalized log-density estimates. Unlike prior approaches such as DensMAP and DenSNE, which rely on local scale consistency, DR-SNE directly aligns normalized density estimates, providing a simple and scale-invariant mechanism for preserving relative density variations. Empirically, DR-SNE improves density preservation while maintaining competitive neighborhood fidelity, and yields gains on density-sensitive tasks such as anomaly detection across multiple datasets. These results suggest that incorporating density information complements geometry-focused objectives in dimensionality reduction.

Maksim Kazanskii, Artem Kasianov

This paper investigates the impact of training data distribution on the performance of image classification models. By analyzing the embeddings of the training set, we propose a framework to understand the confidence of model predictions on unseen data without the need for retraining. Our approach filters out low-confidence predictions based on their distance from the training distribution in the embedding space, significantly improving classification accuracy. We demonstrate this on the example of several classification models, showing consistent performance gains across architectures. Furthermore, we show that using multiple embedding models to represent the training data enables a more robust estimation of confidence, as different embeddings capture complementary aspects of the data. Combining these embeddings allows for better detection and exclusion of out-of-distribution samples, resulting in further accuracy improvements. The proposed method is model-agnostic and generalizable, with potential applications beyond computer vision, including domains such as Natural Language Processing where prediction reliability is critical.