Recently, Stein's unbiased risk estimator (SURE) has been applied to unsupervised training of deep neural network Gaussian denoisers that outperformed classical non-deep learning based denoisers and yielded comparable performance to those trained with ground truth. While SURE requires only one noise realization per image for training, it does not take advantage of having multiple noise realizations per image when they are available (e.g., two uncorrelated noise realizations per image for Noise2Noise). Here, we propose an extended SURE (eSURE) to train deep denoisers with correlated pairs of noise realizations per image and applied it to the case with two uncorrelated realizations per image to achieve better performance than SURE based method and comparable results to Noise2Noise. Then, we further investigated the case with imperfect ground truth (i.e., mild noise in ground truth) that may be obtained considering painstaking, time-consuming, and even expensive processes of collecting ground truth images with multiple noisy images. For the case of generating noisy training data by adding synthetic noise to imperfect ground truth to yield correlated pairs of images, our proposed eSURE based training method outperformed conventional SURE based method as well as Noise2Noise.

This paper studies the problem of learning with augmented classes (LAC), where augmented classes unobserved in the training data might emerge in the testing phase. Previous studies generally attempt to discover augmented classes by exploiting geometric properties, achieving inspiring empirical performance yet lacking theoretical understandings particularly on the generalization ability. In this paper we show that, by using unlabeled training data to approximate the potential distribution of augmented classes, an unbiased risk estimator of the testing distribution can be established for the LAC problem under mild assumptions, which paves a way to develop a sound approach with theoretical guarantees. Moreover, the proposed approach can adapt to complex changing environments where augmented classes may appear and the prior of known classes may change simultaneously. Extensive experiments confirm the effectiveness of our proposed approach.

Neural Information Processing Systems http://nips.cc/

Weakly supervised learning often operates with coarse aggregate signals rather than instance labels. We study a setting where each training example is an $n$-tuple containing exactly m positives, while only the count m per tuple is observed. This NTMP (N-tuple with M positives) supervision arises in, e.g., image classification with region proposals and multi-instance measurements. We show that tuple counts admit a trainable unbiased risk estimator (URE) by linking the tuple-generation process to latent instance marginals. Starting from fixed (n,m), we derive a closed-form URE and extend it to variable tuple sizes, variable counts, and their combination. Identification holds whenever the effective mixing rate is separated from the class prior. We establish generalization bounds via Rademacher complexity and prove statistical consistency with standard rates under mild regularity assumptions. To improve finite-sample stability, we introduce simple ReLU corrections to the URE that preserve asymptotic correctness. Across benchmarks converted to NTMP tasks, the approach consistently outperforms representative weak-supervision baselines and yields favorable precision-recall and F1 trade-offs. It remains robust under class-prior imbalance and across diverse tuple configurations, demonstrating that count-only supervision can be exploited effectively through a theoretically grounded and practically stable objective.

The main challenge of the LAC problem lies in how to depict relationships between known and augmented classes.

We address your concern as follows. This clearly shows the advantage of our method. We answer your main questions as follows. Q1:"Do we need to commit ourselves to the OVR loss?...considering a loss function such as softmax cross entropy Y ou are absolutely correct! If convexity is not required (e.g., NN implementation), we can use more flexible multiclass loss and binary We will make this clear in the revision. Q2:"How to use the non-negative risk estimator in this problem?" We will add more elaborations about the formulation in the revision. Q3:"My question is have you tried different loss functions?" However, it does not converge in experiments. So we instead use sigmoid loss following Kiryo et al. [24]. Theorem 1 serves as a guide to choose binary loss for OVR scheme. Thus, a consistency guarantee (Theorem 1) is necessary. Thanks for the detailed review and helpful comments. We address your main concerns as follows. For the other minor issues, we will discuss in the paper and revise the paper according to your suggestions. We would like to revise the terminology in the revision if it is allowed. Q2:"Some of the claims made about prior work are not accurate.