With the prosperity of cyber-intelligent services, massive data has been rapidly accumulated for training machine learning models to support application scenarios, which is treated as a computation-intensive task. Given this context, leveraging cloud services to manage massive datasets seems natural. Unfortunately, since the cloud is sometimes not entirely trustworthy, it may not be a proper choice for users who do not want to disclose their privacy, especially when the datasets contain sensitive information. To that end, in this paper, we propose a novel learning framework to mix real data instances with synthetic instances for model training tasks via cloud services. We also provide a PAC analysis of the generalization error of the model obtained by our framework. The experiments show that our learning framework is effective in practice. In the experiments, our framework often can help us save over 80 % local computation cost and hide more than 70 % real data from the cloud, while the model accuracy loss is less than 4 %.

A set of categorical items is a common data structure used in various applications, such as customer orders in online shopping. With the rise of big data and e-commerce, there is an increasing need to store such a large number of set data efficiently. This paper presents a novel lossless compression method that uses binary trees for set compression. The compressed code is generated by performing a depth-first search for items in the set on the binary tree. We prove that finding the optimal tree for minimizing the total code length for a given collection of sets is NP-hard, and the problem even remains NP-hard when we only need to assign items to the leaf nodes of a given tree. A heuristic algorithm is then proposed for building trees. To further improve the compression efficiency, we incorporate the entropy coding method into the coding process. Moreover, we reveal the underlying probabilistic expression of the binary tree model and present the conditional independence structure of the model. To validate the effectiveness of the proposed method, empirical studies are conducted on two real-world online e-commerce datasets. The results show that the proposed coding method significantly reduces the storage space required for set data and the tree structure for compressing sets can help identify conditional independent items.

In this paper, we propose a sequence-to-set method that can transform any sequence generative model based on maximum likelihood to a set generative model where we can evaluate the utility/probability of any set. An efficient importance sampling algorithm is devised to tackle the computational challenge of learning our sequence-to-set model. We present GRU2Set, which is an instance of our sequence-to-set method and employs the famous GRU model as the sequence generative model.To further obtain permutation invariant representation of sets, we devise the SetNN model which is also an instance of the sequence-to-set model. A direct application of our models is to learn an order/set distribution from a collection of e-commerce orders, which is an essential step in many important operational decisions such as inventory arrangement for fast delivery. Based on the intuition that small-sized sets are usually easier to learn than large sets, we propose a size-bias trick that can help learn better set distributions with respect to the $\ell_1$-distance evaluation metric. Two e-commerce order datasets, TMALL and HKTVMALL, are used to conduct extensive experiments to show the effectiveness of our models. The experimental results demonstrate that our models can learn better set/order distributions from order data than the baselines. Moreover, no matter what model we use, applying the size-bias trick can always improve the quality of the set distribution learned from data.