Machine learning algorithms have been applied to predict agent behaviors in real-world dynamic systems, such as advertiser behaviors in sponsored search and worker behaviors in crowdsourcing. Behavior data in these systems are generated by live agents: once systems change due to adoption of prediction models learnt from behavior data, agents will observe and respond to these changes by changing their own behaviors accordingly. Therefore, the evolving behavior data will not be identically and independently distributed, posing great challenges to theoretical analysis. To tackle this challenge, in this paper, we propose to use Markov Chain in Random Environments (MCRE) to describe the behavior data, and perform generalization analysis of machine learning algorithms on its basis. We propose a novel technique that transforms the original time-variant MCRE into a higher-dimensional time-homogeneous Markov chain, which is easier to deal with. We prove the convergence of the new Markov chain when time approaches infinity. Then we obtain a generalization bound for the machine learning algorithms on the behavior data generated by the new Markov chain. To the best of our knowledge, this is the first work that performs the generalization analysis on data generated by complex processes in real-world dynamic systems.

We present a novel approach to low-level vision problems that combines sparse coding and deep networks pre-trained with denoising auto-encoder (DA). We propose an alternative training scheme that successfully adapts DA, originally designed for unsupervised feature learning, to the tasks of image denoising and blind inpainting. Our method achieves state-of-the-art performance in the image denoising task. More importantly, in blind image inpainting task, the proposed method provides solutions to some complex problems that have not been tackled before. Specifically, we can automatically remove complex patterns like superimposed text from an image, rather than simple patterns like pixels missing at random. Moreover, the proposed method does not need the information regarding the region that requires inpainting to be given a priori. Experimental results demonstrate the effectiveness of the proposed method in the tasks of image denoising and blind inpainting. We also show that our new training scheme for DA is more effective and can improve the performance of unsupervised feature learning.