instruction:
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.
question:
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.
answer:
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.


question:
In this paper, we propose a novel kind of kernel, random forest kernel, to enhance the empirical performance of MMD GAN. Different from common forests with deterministic routings, a probabilistic routing variant is used in our innovated random-forest kernel, which is possible to merge with the CNN frameworks. Our proposed random-forest kernel has the following advantages: From the perspective of random forest, the output of GAN discriminator can be viewed as feature inputs to the forest, where each tree gets access to merely a fraction of the features, and thus the entire forest benefits from ensemble learning. In the aspect of kernel method, random-forest kernel is proved to be characteristic, and therefore suitable for the MMD structure. Besides, being an asymmetric kernel, our random-forest kernel is much more flexible, in terms of capturing the differences between distributions. Sharing the advantages of CNN, kernel method, and ensemble learning, our random-forest kernel based MMD GAN obtains desirable empirical performances on CIFAR-10, CelebA and LSUN bedroom data sets. Furthermore, for the sake of completeness, we also put forward comprehensive theoretical analysis to support our experimental results.
answer:
Equip MMD GANs with a new random-forest kernel.


question:
Rectified linear units, or ReLUs, have become a preferred activation function for artificial neural networks. In this paper we consider the problem of learning a generative model in the presence of nonlinearity (modeled by the ReLU functions). Given a set of signal vectors $\mathbf{y}^i \in \mathbb{R}^d, i =1, 2, \dots , n$, we  aim to learn the network parameters, i.e., the $d\times k$ matrix $A$, under the model $\mathbf{y}^i = \mathrm{ReLU}(A\mathbf{c}^i +\mathbf{b})$, where $\mathbf{b}\in \mathbb{R}^d$ is a random bias vector, and {$\mathbf{c}^i \in \mathbb{R}^k$ are arbitrary unknown latent vectors}. We show that it is possible to recover the column space of $A$ within an error of $O(d)$ (in Frobenius norm) under certain conditions on the  distribution of $\mathbf{b}$.
answer:

We show that it is possible to recover the parameters of a 1-layer ReLU generative model from looking at samples generated by it