Image-to-image regression is an important computer vision task. In this paper, we propose a novel image-to-image regression model following the recent trend in generative modeling that employs Stochastic Differential Equations (SDEs) and score matching. We first apply diffusion processes to regression data using designed SDEs, and then perform inference by gradually reversing the processes. In particular, our method uses synchronized diffusion, which simultaneously applies diffusion to both input and response images to stabilize diffusion and subsequent parameter learning. Furthermore, based on the Expectation-Maximization (EM) algorithm, we develop an effective algorithm for prediction. We implement a conditional U-Net architecture with pre-trained DenseNet encoder for our proposed model and refer to it as DenseSocre. Our new model is able to generate diverse outcomes for image colorization, and the proposed prediction algorithm is able to achieve close to state-of-art performance on high-resolution monocular depth estimation.

Image to image regression is an essential machine learning problem that is commonly encountered in computer vision tasks. Previous research works have been concentrating on task-dependent end-to-end regression models. Although such a discriminative approach has shown its proficiency in producing precise predictions, its architecture is usually overly complicated for interpretation and unable to provide uncertainty quantification for prediction. We propose a general image to image regression framework named CSMNet which is based on conditional score matching and Langevin dynamics. The proposed framework is generative and emphasize on the probabilistic perspective of general image to image regression. Discriminative models are also involved as sufficient feature extractors to complement the generative modeling of the distribution of the target image conditioned an input image. The proposed model is trained by multi-level denoising score matching. Subsequently, the learned model is used for sampling from the conditional distribution via annealed Langevin dynamics. We introduce a grid selection procedure of Langevin sampling which can produce robust prediction. Comprehensive experiments are conducted on diverse image to image regression problems. The proposed model surpasses other purely generative models and achieves comparable performance to some end-to-end regression methods. Our method also demonstrates remarkable generalization ability which further demonstrates the advantage of the proposed conditional score matching framework.

Activity data of individual users on social media are easily accessible in this big data era. However, proper modeling strategies for user profiles have not been well developed in the literature. Existing methods or models usually have two limitations. The first limitation is that most methods target the population rather than individual users, and the second is that they cannot model non-stationary time-varying patterns. Different users in general demonstrate different activity modes on social media. Therefore, one population model may fail to characterize activities of individual users. Furthermore, online social media are dynamic and ever evolving, so are users' activities. Dynamic models are needed to properly model users' activities. In this paper, we introduce a non-parametric hidden Markov model to characterize the time-varying activities of social media users. An EM algorithm has been developed to estimate the parameters of the proposed model. In addition, based on the proposed model, we develop a clustering method to group users with similar activity patterns.

MOTIVATION: Identification of transcription factor binding motifs (TFBMs) is a crucial first step towards the understanding of regulatory circuitries controlling the expression of genes. In this paper, we propose a novel procedure called regularized sliced inverse regression (RSIR) for identifying TFBMs. RSIR follows a recent trend to combine information contained in both gene expression measurements and genes' promoter sequences. Compared with existing methods, RSIR is efficient in computation, very stable for data with high dimensionality and high collinearity, and improves motif detection sensitivities and specificities by avoiding inappropriate model specification. RESULTS: We compare RSIR with SIR and stepwise regression based on simulated data and find that RSIR has a lower false positive rate. We also demonstrate an excellent performance of RSIR by applying it to the yeast amino acid starvation data and cell cycle data. AVAILABILITY: Matlab programs are available upon request from the authors.

Randomization is an economical and efficient approach for privacy preserving data mining (PPDM). In order to guarantee the performance of data mining and the protection of individual privacy, optimal randomization schemes need to be employed. This paper demonstrates the construction of optimal randomization schemes for privacy preserving density estimation. We propose a general framework for randomization using mixture models. The impact of randomization on data mining is quantified by performance degradation and mutual information loss, while privacy and privacy loss are quantified by interval-based metrics. Two different types of problems are defined to identify optimal randomization for PPDM. Illustrative examples and simulation results are reported.