arXiv subjects

Ilya Ivanov

Publications and source records attributed to Ilya Ivanov.

4 recordsLinked to original sources

arXiv2026

Bradley-Terry Rankings for Recommender Systems Across Dataset Taxonomies

The ranking of recommendation algorithms is a challenging problem since model performance is sensitive to dataset characteristics such as sparsity, sequential structure, and scale. This drives a demand for a proper methodology for fair comparison between algorithms. Naive aggregation of performance metrics (e.g., averaging NDCG over benchmarks) can yield misleading rankings, undermining practical selection. To address this problem, we introduce a novel, data-driven ranking methodology based on Bradley-Terry (BT) model. We demonstrate that the obtained ranking depends on key dataset statistics. Additionally, we propose a novel metric for evaluating ranking consistency and demonstrate robustness of our ranking to incomplete data. Finally, we introduce a dataset-specific methodology for ranking algorithms on unseen datasets without running the models, relying on extensions of the Bradley-Terry framework, including BT trees and BT models with covariates.

cs.IR↗

arXiv2022

RDRN: Recursively Defined Residual Network for Image Super-Resolution

Deep convolutional neural networks (CNNs) have obtained remarkable performance in single image super-resolution (SISR). However, very deep networks can suffer from training difficulty and hardly achieve further performance gain. There are two main trends to solve that problem: improving the network architecture for better propagation of features through large number of layers and designing an attention mechanism for selecting most informative features. Recent SISR solutions propose advanced attention and self-attention mechanisms. However, constructing a network to use an attention block in the most efficient way is a challenging problem. To address this issue, we propose a general recursively defined residual block (RDRB) for better feature extraction and propagation through network layers. Based on RDRB we designed recursively defined residual network (RDRN), a novel network architecture which utilizes attention blocks efficiently. Extensive experiments show that the proposed model achieves state-of-the-art results on several popular super-resolution benchmarks and outperforms previous methods by up to 0.43 dB.

eess.IV↗

arXiv2022

Illuminating spiky balls and cap bodies

The convex hull of a ball with an exterior point is called a spike (or cap). A union of finitely many spikes of a ball is called a spiky ball. If a spiky ball is convex, then we call it a cap body. In this note we upper bound the illumination numbers of $2$-illuminable spiky balls as well as centrally symmetric cap bodies. In particular, we prove the Illumination Conjecture for centrally symmetric cap bodies in sufficiently large dimensions by showing that any $d$-dimensional centrally symmetric cap body can be illuminated by $<2^d$ directions in Euclidean $d$-space for all $d\geq 20$. Furthermore, we strengthen the latter result for $1$-unconditionally symmetric cap bodies.

math.MG↗

arXiv2020

On the illumination of centrally symmetric cap bodies in small dimensions

The illumination number $I(K)$ of a convex body $K$ in Euclidean space $\mathbb{E}^d$ is the smallest number of directions that completely illuminate the boundary of a convex body. A cap body $K_c$ of a ball is the convex hull of a Euclidean ball and a countable set of points outside the ball under the condition that each segment connecting two of these points intersects the ball. The main results of this paper are the sharp estimates $I(K_c)\leq6$ for centrally symmetric cap bodies of a ball in $\mathbb{E}^3$, and $I(K_c)\leq 8$ for unconditionally symmetric cap bodies of a ball in $\mathbb{E}^4$.

math.MG↗