We develop statistical models to learn latent (one-layer or multiple-layer, aka deep) representations for data analysis tasks, ranging from the simple tasks of classification and regression, to the slightly more complex problems of multi-modal data fusion and multi-task learning, and to the even more complex problems of social network data analsysis and web recommendation. We are particularly focusing on solving some important problems for representation learning, including

• model complexity inference by developing nonparametric Bayesian methods
• max-margin latent variable models for learning predictive representations
• learning sparse representations with sparse regularization techniques
• scalable algorithms on CPU and GPU clusters
• The cool thing is that we found many interesting interplays between these topics, e.g., Bayesian nonparametrics and max-margin learning are no longer isolated from each other in our RegBayes framework, and sparse coding can discover hierarchical topic representations with effective sparsity control. I also address the fundamental challenges of scaling up our techniques to large-scale applications by developing efficient Monte Carlo and variational inference algorithms.