FIRAL is a recently proposed deterministic active learning algorithm for multiclass classification using logistic regression. It was shown to outperform the state-of-the-art in terms of accuracy and robustness and comes with theoretical performance guarantees. However, its scalability suffers when dealing with datasets featuring a large number of points n, dimensions d, and classes c, due to its $\mathcal{O}\left(c^{2} d^{2}+n c^{2} d\right)$ storage and $\mathcal{O}\left(c^{3}\left(n d^{2}+b d^{3}+b n\right)\right)$ computational complexity where b is the number of points to select in active learning. To address these challenges, we propose an approximate algorithm with storage requirements reduced to $\mathcal{O}\left(n(d+c)+c d^{2}\right)$ and a computational complexity of $\mathcal{O}\left(b n c d^{2}\right)$. Additionally, we present a parallel implementation on GPUs. We demonstrate the accuracy and scalability of our approach using MNIST, CIFAR-10, Caltech101, and ImageNet. The accuracy tests reveal no deterioration in accuracy compared to FIRAL. We report strong and weak scaling tests on up to 12 GPUs, for three million point synthetic dataset.

We investigate theory and algorithms for pool-based active learning for multiclass classification using multinomial logistic regression. Using finite sample analysis, we prove that the Fisher Information Ratio (FIR) lower and upper bounds the excess risk. Based on our theoretical analysis, we propose an active learning algorithm that employs regret minimization to minimize the FIR. To verify our derived excess risk bounds, we conduct experiments on synthetic datasets. Furthermore, we compare FIRAL with five other methods and found that our scheme outperforms them: it consistently produces the smallest classification error in the multiclass logistic regression setting, as demonstrated through experiments on MNIST, CIFAR-10, and 50-class ImageNet.

Recently, most methods proposed for multi-label image retrieval focus on using hashing functions to improve retrieval efficiency. However, hashing functions may reduce retrieval accuracy and be sub-optimal for some scenarios where accuracy is more important than efficiency. In this paper, we propose a deep feature descriptor without hashing for multi-label image retrieval. We use Faster R-CNN with FPN to perform object detection on images and extract feature maps. Especially, we propose Regional-Confidence Weight, which can evaluate the importance of different regions, to generate more powerful feature maps. Additionally, GeM pooling is used to produce compact feature vectors from feature maps for retrieval. Extensive experiments demonstrate that our approach significantly outperforms several state-of-the-art methods with higher retrieval accuracy for multi-label image retrieval.