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The purpose of this paper is to propose a framework for data analytics where everything is grey in nature and the associated uncertainty is considered as an essential part in data collection, profiling, imputation, analysis and decision making.

A comparative study is conducted between the available uncertainty models and the feasibility of grey systems is highlighted. Furthermore, a general framework for the integration of grey systems and grey sets into data analytics is proposed.

Grey systems and grey sets are useful not only for small data, but also big data as well. It is complementary to other models and can play a significant role in data analytics.

The proposed framework brings a radical change in data analytics. It may bring a fundamental change in our way to deal with uncertainties.

The proposed model has the potential to avoid the mistake from a misleading data imputation.

The proposed model takes the philosophy of grey systems in recognising the limitation of our knowledge which has significant implications in our way to deal with our social life and relations.

This is the first time that the whole data analytics is considered from the point of view of grey systems.

The purpose of this paper is to alleviate the problem of poor robustness and over-fitting caused by large-scale data in collaborative filtering recommendation algorithms.

Interpreting user behavior from the probabilistic perspective of hidden variables is helpful to improve robustness and over-fitting problems. Constructing a recommendation network by variational inference can effectively solve the complex distribution calculation in the probabilistic recommendation model. Based on the aforementioned analysis, this paper uses variational auto-encoder to construct a generating network, which can restore user-rating data to solve the problem of poor robustness and over-fitting caused by large-scale data. Meanwhile, for the existing KL-vanishing problem in the variational inference deep learning model, this paper optimizes the model by the KL annealing and Free Bits methods.

The effect of the basic model is considerably improved after using the KL annealing or Free Bits method to solve KL vanishing. The proposed models evidently perform worse than competitors on small data sets, such as MovieLens 1 M. By contrast, they have better effects on large data sets such as MovieLens 10 M and MovieLens 20 M.

This paper presents the usage of the variational inference model for collaborative filtering recommendation and introduces the KL annealing and Free Bits methods to improve the basic model effect. Because the variational inference training denotes the probability distribution of the hidden vector, the problem of poor robustness and overfitting is alleviated. When the amount of data is relatively large in the actual application scenario, the probability distribution of the fitted actual data can better represent the user and the item. Therefore, using variational inference for collaborative filtering recommendation is of practical value.