Graph Embedding methods are aimed at mapping each vertex into a low dimensional vector space, which preserves certain structural relationships among the vertices in the original graph. Recently, several works have been proposed to learn embeddings based on sampled paths from the graph, e.g., DeepWalk, Line, Node2Vec. However, their methods only preserve symmetric proximities, which could be insufficient in many applications, even the underlying graph is undirected. Besides, they lack of theoretical analysis of what exactly the relationships they preserve in their embedding space. In this paper, we propose an asymmetric proximity preserving (APP) graph embedding method via random walk with restart, which captures both asymmetric and high-order similarities between node pairs. We give theoretical analysis that our method implicitly preserves the Rooted PageRank score for any two vertices. We conduct extensive experiments on tasks of link prediction and node recommendation on open source datasets, as well as online recommendation services in Alibaba Group, in which the training graph has over 290 million vertices and 18 billion edges, showing our method to be highly scalable and effective.

Stochastic gradient descent (SGD) and its variants have attracted much attention in machine learning due to their efficiency and effectiveness for optimization. To handle large-scale problems, researchers have recently proposed several lock-free strategy based parallel SGD (LF-PSGD) methods for multi-core systems. However, existing works have only proved the convergence of these LF-PSGD methods for convex problems. To the best of our knowledge, no work has proved the convergence of the LF-PSGD methods for non-convex problems. In this paper, we provide the theoretical proof about the convergence of two representative LF-PSGD methods, Hogwild! and AsySVRG, for non-convex problems. Empirical results also show that both Hogwild! and AsySVRG are convergent on non-convex problems, which successfully verifies our theoretical results.

Multi-View Clustering (MVC) has garnered more attention recently since many real-world data are comprised of different representations or views. The key is to explore complementary information to benefit the clustering problem. In this paper, we present a deep matrix factorization framework for MVC, where semi-nonnegative matrix factorization is adopted to learn the hierarchical semantics of multi-view data in a layer-wise fashion. To maximize the mutual information from each view, we enforce the non-negative representation of each view in the final layer to be the same. Furthermore, to respect the intrinsic geometric structure in each view data, graph regularizers are introduced to couple the output representation of deep structures. As a non-trivial contribution, we provide the solution based on alternating minimization strategy, followed by a theoretical proof of convergence. The superior experimental results on three face benchmarks show the effectiveness of the proposed deep matrix factorization model.

This paper shows that simply prescribing "none of the above" labels to unlabeled data has a beneficial regularization effect to supervised learning. We call it universum prescription by the fact that the prescribed labels cannot be one of the supervised labels. In spite of its simplicity, universum prescription obtained competitive results in training deep convolutional networks for CIFAR-10, CIFAR-100, STL-10 and ImageNet datasets. A qualitative justification of these approaches using Rademacher complexity is presented. The effect of a regularization parameter — probability of sampling from unlabeled data — is also studied empirically.

Feature selection is a fundamental problem in machine learning and data mining. The majority of feature selection algorithms are designed for running on a single machine (centralized setting) and they are less applicable to very large datasets. Although there are some distributed methods to tackle this problem, most of them are distributing the data horizontally which are not suitable for datasets with a large number of features and few number of instances. Thus, in this paper, we introduce a novel vertically distributable feature selection method in order to speed up this process and be able to handle very large datasets in a scalable manner. In general, feature selection methods aim at selecting relevant and non-redundant features (Minimum Redundancy and Maximum Relevance). It is much harder to consider redundancy in a vertically distributed setting than a centralized setting since there is no global access to the whole data. To the best of our knowledge, this is the first attempt toward solving the feature selection problem with a vertically distributed filter method which handles the redundancy with consistently comparable results with centralized methods. In this paper, we formalize the feature selection problem as a diversity maximization problem by introducing a mutual-information-based metric distance on the features. We show the effectiveness of our method by performing an extensive empirical study. In particular, we show that our distributed method outperforms state-of-the-art centralized feature selection algorithms on a variety of datasets. From a theoretical point of view, we have proved that the used greedy algorithm in our method achieves an approximation factor of 1/4 for the diversity maximization problem in a distributed setting with high probability. Furthermore, we improve this to 8/25 expected approximation using multiplicity in our distribution.

In many applications such as recommender systems and multi-label learning the task is to complete a partially observed binary matrix. Such PU learning (positive-unlabeled) problems can be solved by one-class matrix factorization (MF). In practice side information such as user or item features in recommender systems are often available besides the observed positive user-item connections. In this work we consider a generalization of one-class MF so that two types of side information are incorporated and a general convex loss function can be used. The resulting optimization problem is very challenging, but we derive an efficient and effective alternating minimization procedure. Experiments on large-scale multi-label learning and one-class recommender systems demonstrate the effectiveness of our proposed approach.

With the better availability of healthcare data, such as Electronic Health Records (EHR), more and more data analytics methodologies are developed aiming at digging insights from them to improve the quality of care delivery. There are many challenges on analyzing EHR, such as high dimensionality and event sparsity. Moreover, different from other application domains, the EHR analysis algorithms need to be highly interpretable to make them clinically useful. This makes representation learning from EHRs of key importance. In this paper, we propose an algorithm called Predictive Task Guided Tensor Decomposition (TaGiTeD), to analyze EHRs. Specifically, TaGiTeD learns event interaction patterns that are highly predictive for certain tasks from EHRs with supervised tensor decomposition. Compared with unsupervised methods, TaGiTeD can learn effective EHR representations in a more focused way. This is crucial because most of the medical problems have very limited patient samples, which are not enough for unsupervised algorithms to learn meaningful representations form. We apply TaGiTeD on real world EHR data warehouse and demonstrate that TaGiTeD can learn representations that are both interpretable and predictive.

A challenge for mining large-scale streaming data overlooked by most existing studies on online learning is the skew-distribution of examples over different classes. Many previous works have considered cost-sensitive approaches in an online setting for streaming data, where fixed costs are assigned to different classes, or ad-hoc costs are adapted based on the distribution of data received so far. However, it is not necessary for them to achieve optimal performance in terms of the measures suited for imbalanced data, such as F-measure, area under ROC curve (AUROC), area under precision and recall curve (AUPRC). This work proposes a general framework for online learning with imbalanced streaming data, where examples are coming sequentially and models are updated accordingly on-the-fly. By simultaneously learning multiple classifiers with different cost vectors, the proposed method can be adopted for different target measures for imbalanced data, including F-measure, AUROC and AUPRC. Moreover, we present a rigorous theoretical justification of the proposed framework for the F-measure maximization. Our empirical studies demonstrate the competitive if not better performance of the proposed method compared to previous cost-sensitive and resampling based online learning algorithms and those that are designed for optimizing certain measures.

In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling high-dimensionality challenge in machine learning. Recently, various non-oblivious randomized reduction methods have been developed and deployed for solving many numerical problems such as matrix product approximation, low-rank matrix approximation, etc. However, they are less explored for the machine learning tasks, e.g., classification. More seriously, the theoretical analysis of excess risk bounds for risk minimization, an important measure of generalization performance, has not been established for non-oblivious randomized reduction methods. It therefore remains an open problem what is the benefit of using them over previous oblivious random projection based approaches. To tackle these challenges, we propose an algorithmic framework for employing non-oblivious randomized reduction method for general empirical risk minimizing in machine learning tasks, where the original high-dimensional features are projected onto a random subspace that is derived from the data with a small matrix approximation error. We then derive the first excess risk bound for the proposed non-oblivious randomized reduction approach without requiring strong assumptions on the training data. The established excess risk bound exhibits that the proposed approach provides much better generalization performance and it also sheds more insights about different randomized reduction approaches. Finally, we conduct extensive experiments on both synthetic and real-world benchmark datasets, whose dimension scales to O(10^7), to demonstrate the efficacy of our proposed approach.

In standard machine learning and regression setting feature values are used to predict some desired information. The privacy challenge considered here is to prevent an adversary from using available feature values to predict confidential information that one wishes to keep secret. We show that this can sometimes be achieved with almost no effect on the qual- ity of predicting desired information. We describe two algorithms aimed at providing such privacy when the predictors have a linear operator in the first stage. The desired effect can be achieved by zeroing out feature components in the approximate null space of the linear operator.