Robust Matrix Regression

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches incorporate the low-rank property to the model and achieve satisfactory performance for certain applications. These approaches all assume that both predictors and labels for each pair of data within the training set are accurate. However, in real-world applications, it is common to see the training data contaminated by noises, which can affect the robustness of these matrix regression methods. In this paper, we address this issue by introducing a novel robust matrix regression method. We also derive efficient proximal algorithms for model training. To evaluate the performance of our methods, we apply it to real world applications with comparative studies. Our method achieves the state-of-the-art performance, which shows the effectiveness and the practical value of our method.

Online Prediction of Dyadic Data with Heterogeneous Matrix Factorization

Dyadic Data Prediction (DDP) is an important problem in many research areas. This paper develops a novel fully Bayesian nonparametric framework which integrates two popular and complementary approaches, discrete mixed membership modeling and continuous latent factor modeling into a unified Heterogeneous Matrix Factorization~(HeMF) model, which can predict the unobserved dyadics accurately. The HeMF can determine the number of communities automatically and exploit the latent linear structure for each bicluster efficiently. We propose a Variational Bayesian method to estimate the parameters and missing data. We further develop a novel online learning approach for Variational inference and use it for the online learning of HeMF, which can efficiently cope with the important large-scale DDP problem. We evaluate the performance of our method on the EachMoive, MovieLens and Netflix Prize collaborative filtering datasets. The experiment shows that, our model outperforms state-of-the-art methods on all benchmarks. Compared with Stochastic Gradient Method (SGD), our online learning approach achieves significant improvement on the estimation accuracy and robustness.

Blind Image Denoising via Dependent Dirichlet Process Tree

Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This paper addresses this problem and proposes a novel blind image denoising algorithm to recover the clean image from noisy one with the unknown noise model. To model the empirical noise of an image, our method introduces the mixture of Gaussian distribution, which is flexible enough to approximate different continuous distributions. The problem of blind image denoising is reformulated as a learning problem. The procedure is to first build a two-layer structural model for noisy patches and consider the clean ones as latent variable. To control the complexity of the noisy patch model, this work proposes a novel Bayesian nonparametric prior called "Dependent Dirichlet Process Tree" to build the model. Then, this study derives a variational inference algorithm to estimate model parameters and recover clean patches. We apply our method on synthesis and real noisy images with different noise models. Comparing with previous approaches, ours achieves better performance. The experimental results indicate the efficiency of the proposed algorithm to cope with practical image denoising tasks.