iVPF: Numerical Invertible Volume Preserving Flow for Efficient Lossless Compression

It is nontrivial to store rapidly growing big data nowadays, which demands high-performance lossless compression techniques. Likelihood-based generative models have witnessed their success on lossless compression, where flow based models are desirable in allowing exact data likelihood optimisation with bijective mappings. However, common continuous flows are in contradiction with the discreteness of coding schemes, which requires either 1) imposing strict constraints on flow models that degrades the performance or 2) coding numerous bijective mapping errors which reduces the efficiency. In this paper, we investigate volume preserving flows for lossless compression and show that a bijective mapping without error is possible. We propose Numerical Invertible Volume Preserving Flow (iVPF) which is derived from the general volume preserving flows. By introducing novel computation algorithms on flow models, an exact bijective mapping is achieved without any numerical error. We also propose a lossless compression algorithm based on iVPF. Experiments on various datasets show that the algorithm based on iVPF achieves state-of-the-art compression ratio over lightweight compression algorithms.

Meta-Learning PAC-Bayes Priors in Model Averaging

Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a single final model via a model selection procedure to account for this model's uncertainty to improve reliability and accuracy of inferences. Here one main challenge is to learn the prior over the model set. To tackle this problem, we propose two data-based algorithms to get proper priors for model averaging. One is for meta-learner, the analysts should use historical similar tasks to extract the information about the prior. The other one is for base-learner, a subsampling method is used to deal with the data step by step. Theoretically, an upper bound of risk for our algorithm is presented to guarantee the performance of the worst situation. In practice, both methods perform well in simulations and real data studies, especially with poor quality data.