In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Input: Consider Input: Positive-unlabeled (PU) learning addresses the problem of learning a binary classifier from positive (P) and unlabeled (U) data. It is often applied to situations where negative (N) data are difficult to be fully labeled. However, collecting a non-representative N set that contains only a small portion of all possible N data can be much easier in many practical situations. This paper studies a novel classification framework which incorporates such biased N (bN) data in PU learning. The fact that the training N data are biased also makes our work very different from those of standard semi-supervised learning. We provide an empirical risk minimization-based method to address this PUbN classification problem. Our approach can be regarded as a variant of traditional example-reweighting algorithms, with the weight of each example computed through a preliminary step that draws inspiration from PU learning. We also derive an estimation error bound for the proposed method. Experimental results demonstrate the effectiveness of our algorithm in not only PUbN learning scenarios but also ordinary PU leaning scenarios on several benchmark datasets.

Output: This paper studied the PUbN classification problem, where we incorporate biased negative (bN) data, i.e., negative data that is not fully representative of the true underlying negative distribution, into positive-unlabeled (PU) learning.

Input: Consider Input: This paper presents a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size. MINE is back-propable and we prove that it is strongly consistent. We illustrate a handful of applications in which MINE is succesfully applied to enhance the property of generative models in both unsupervised and supervised settings. We apply our framework to estimate the information bottleneck, and apply it in tasks related to supervised classification problems. Our results demonstrate substantial added flexibility and improvement in these settings.

Output: A scalable in sample size and dimensions mutual information estimator.

Input: Consider Input: Optimal Transport (OT) naturally arises in many machine learning applications, where we need to handle cross-modality data from multiple sources. Yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approximate the optimal transport plan by a pushforward of a reference distribution, and cast the optimal transport problem into a minimax problem. We then can solve OT problems efficiently using primal dual stochastic gradient-type algorithms. We also show that we can recover the density of the optimal transport plan using neural ordinary differential equations. Numerical experiments on both synthetic and real datasets illustrate that SPOT is robust and has favorable convergence behavior. SPOT also allows us to efficiently sample from the optimal transport plan, which benefits downstream applications such as domain adaptation.
Output: Use GAN-based method to scalably solve optimal transport