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

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

Most semi-supervised learning (SSL) models entail complex structures and iterative training processes as well as face difficulties in interpreting their predictions to users. To address these issues, this paper proposes a new interpretable SSL model using the supervised and unsupervised Adaptive Resonance Theory (ART) family of networks, which is denoted as SSL-ART. Firstly, SSL-ART adopts an unsupervised fuzzy ART network to create a number of prototype nodes using unlabeled samples. Then, it leverages a supervised fuzzy ARTMAP structure to map the established prototype nodes to the target classes using labeled samples. Specifically, a one-to-many (OtM) mapping scheme is devised to associate a prototype node with more than one class label. The main advantages of SSL-ART include the capability of: (i) performing online learning, (ii) reducing the number of redundant prototype nodes through the OtM mapping scheme and minimizing the effects of noisy samples, and (iii) providing an explanation facility for users to interpret the predicted outcomes. In addition, a weighted voting strategy is introduced to form an ensemble SSL-ART model, which is denoted as WESSL-ART. Every ensemble member, i.e., SSL-ART, assigns {\color{black}a different weight} to each class based on its performance pertaining to the corresponding class. The aim is to mitigate the effects of training data sequences on all SSL-ART members and improve the overall performance of WESSL-ART. The experimental results on eighteen benchmark data sets, three artificially generated data sets, and a real-world case study indicate the benefits of the proposed SSL-ART and WESSL-ART models for tackling pattern classification problems.

This paper studies the estimation of large-scale optimal transport maps (OTM), which is a well-known challenging problem owing to the curse of dimensionality. Existing literature approximates the large-scale OTM by a series of one-dimensional OTM problems through iterative random projection. Such methods, however, suffer from slow or none convergence in practice due to the nature of randomly selected projection directions. Instead, we propose an estimation method of large-scale OTM by combining the idea of projection pursuit regression and sufficient dimension reduction. The proposed method, named projection pursuit Monge map (PPMM), adaptively selects the most ``informative'' projection direction in each iteration. We theoretically show the proposed dimension reduction method can consistently estimate the most ``informative'' projection direction in each iteration. Furthermore, the PPMM algorithm weakly convergences to the target large-scale OTM in a reasonable number of steps. Empirically, PPMM is computationally easy and converges fast. We assess its finite sample performance through the applications of Wasserstein distance estimation and generative models.

Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable node-wise scorers, have attracted a lot of interests in tackling this challenge due to their logarithmic computational complexity in both training and testing. Tree-based deep models (TDMs) and probabilistic label trees (PLTs) are two representative kinds of them. Though achieving many practical successes, existing tree models suffer from the training-testing discrepancy, where the retrieval performance deterioration caused by beam search in testing is not considered in training. This leads to an intrinsic gap between the most relevant targets and those retrieved by beam search with even the optimally trained node-wise scorers. We take a first step towards understanding and analyzing this problem theoretically, and develop the concept of Bayes optimality under beam search and calibration under beam search as general analyzing tools for this purpose. Moreover, to eliminate the discrepancy, we propose a novel algorithm for learning optimal tree models under beam search. Experiments on both synthetic and real data verify the rationality of our theoretical analysis and demonstrate the superiority of our algorithm compared to state-of-the-art methods.