In the analysis and diagnosis of many diseases, such as the Alzheimer's disease (AD), two important and related tasks are usually required: i) selecting genetic and phenotypical markers for diagnosis, and ii) identifying associations between genetic and phenotypical features. While previous studies treat these two tasks separately, they are tightly coupled due to the same underlying biological basis. To harness their potential benefits for each other, we propose a new sparse Bayesian approach to jointly carry out the two important and related tasks. In our approach, we extract common latent features from different data sources by sparse projection matrices and then use the latent features to predict disease severity levels; in return, the disease status can guide the learning of sparse projection matrices, which not only reveal interactions between data sources but also select groups of related biomarkers. In order to boost the learning of sparse projection matrices, we further incorporate graph Laplacian priors encoding the valuable linkage disequilibrium (LD) information. To efficiently estimate the model, we develop a variational inference algorithm. Analysis on an imaging genetics dataset for AD study shows that our model discovers biologically meaningful associations between single nucleotide polymorphisms (SNPs) and magnetic resonance imaging (MRI) features, and achieves significantly higher accuracy for predicting ordinal AD stages than competitive methods.

Colorization aims at recovering the original color of a monochrome image from only a few color pixels. A state-of-the-art approach is based on matrix completion, which assumes that the target color image is low-rank. However, this low-rank assumption is often invalid on natural images. In this paper, we propose a patch-based approach that divides the image into patches and then imposes a low-rank structure only on groups of similar patches. Each local matrix completion problem is solved by an accelerated version of alternating direction method of multipliers (ADMM), and each AD-MM subproblem is solved efficiently by divide-and-conquer. Experiments on a number of benchmark images demonstrate that the proposed method outperforms existing approaches.

There has been an increasing interest in exploring signed networks with positive and negative links in that they contain more information than unsigned networks. As fundamental problems of signed network analysis, community detection and sign (or attitude) prediction are still primary challenges. To address them, we propose a generative Bayesian approach, in which 1) a signed stochastic blockmodel is proposed to characterize the community structure in context of signed networks, by means of explicitly formulating the distributions of both density and frustration of signed links from a stochastic perspective, and 2) a model learning algorithm is proposed by theoretically deriving a variational Bayes EM for parameter estimation and a variation based approximate evidence for model selection. Through the comparisons with state-of-the-art methods on synthetic and real-world networks, the proposed approach shows its superiority in both community detection and sign prediction for exploratory networks.

We examine the fundamental problem of background modeling which is to model the background scenes in video sequences and segment the moving objects from the background. A novel approach is proposed based on the Restricted Boltzmann Machine (RBM) while exploiting the temporal nature of the problem. In particular, we augment the standard RBM to take a window of sequential video frames as input and generate the background model while enforcing the background smoothly adapting to the temporal changes. As a result, the augmented temporally adaptive model can generate stable background given noisy inputs and adapt quickly to the changes in background while keeping all the advantages of RBMs including exact inference and effective learning procedure. Experimental results demonstrate the effectiveness of the proposed method in modeling the temporal nature in background.

In multi-task learning, multiple related tasks are considered simultaneously, with the goal to improve the generalization performance by utilizing the intrinsic sharing of information across tasks. This paper presents a multi-task learning approach by modeling the task-feature relationships. Specifically, instead of assuming that similar tasks have similar weights on all the features, we start with the motivation that the tasks should be related in terms of subsets of features, which implies a co-cluster structure. We design a novel regularization term to capture this task-feature co-cluster structure. A proximal algorithm is adopted to solve the optimization problem. Convincing experimental results demonstrate the effectiveness of the proposed algorithm and justify the idea of exploiting the task-feature relationships.

In multi-label learning, an example is represented by a descriptive feature associated with several labels. Simply considering labels as independent or correlated is crude; it would be beneficial to define and exploit the causality between multiple labels. For example, an image label 'lake' implies the label 'water', but not vice versa. Since the original features are a disorderly mixture of the properties originating from different labels, it is intuitive to factorize these raw features to clearly represent each individual label and its causality relationship.Following the large-margin principle, we propose an effective approach to discover the causal features of multiple labels, thus revealing the causality between labels from the perspective of feature. We show theoretically that the proposed approach is a tight approximation of the empirical multi-label classification error, and the causality revealed strengthens the consistency of the algorithm. Extensive experimentations using synthetic and real-world data demonstrate that the proposed algorithm effectively discovers label causality, generates causal features, and improves multi-label learning.

Accurate road speed predictions can help drivers in smart route planning. Although the issue has been studied previously, most existing work focus on arterial roads only, where sensors are configured closely for collecting complete real-time data. For collector roads where sensors sparsly cover, however, speed predictions are often ignored. With GPS-equipped floating car signals being available nowadays, we aim at forecasting collector road speeds by utilizing these signals. The main challenge compared with arterial roads comes from the missing data. In a time slot of the real case, over 90% of collector roads cannot be covered by enough floating cars. Thus most traditional approaches for arterial roads, relying on complete historical data, cannot be employed directly. Aiming at solving this problem, we propose a multi-view road speed prediction framework. In the first view, temporal patterns are modeled by a layered hidden Markov model; and in the second view, spatial patterns are modeled by a collective matrix factorization model. The two models are learned and inferred simultaneously in a co-regularized manner. Experiments conducted in the Beijing road network, based on 10K taxi signals in 2 years, have demonstrated that the approach outperforms traditional approaches by 10% in MAE and RMSE.

Neuroimage analysis usually involves learning thousands or even millions of variables using only a limited number of samples. In this regard, sparse models, e.g. the lasso, are applied to select the optimal features and achieve high diagnosis accuracy. The lasso, however, usually results in independent unstable features. Stability, a manifest of reproducibility of statistical results subject to reasonable perturbations to data and the model (Yu 2013), is an important focus in statistics, especially in the analysis of high dimensional data. In this paper, we explore a nonnegative generalized fused lasso model for stable feature selection in the diagnosis of Alzheimer's disease. In addition to sparsity, our model incorporates two important pathological priors: the spatial cohesion of lesion voxels and the positive correlation between the features and the disease labels. To optimize the model, we propose an efficient algorithm by proving a novel link between total variation and fast network flow algorithms via conic duality. Experiments show that the proposed nonnegative model performs much better in exploring the intrinsic structure of data via selecting stable features compared with other state-of-the-arts.

Personal photos are enjoying explosive growth with the popularity of photo-taking devices and social media. The vast amount of online photos largely exhibit users' interests, emotion and opinions. Mining user interests from personal photos can boost a number of utilities, such as advertising, interest based community detection and photo recommendation. In this paper, we study the problem of user interests mining from personal photos. We propose a User Image Latent Space Model to jointly model user interests and image contents. User interests are modeled as latent factors and each user is assumed to have a distribution over them. By inferring the latent factors and users' distributions, we can discover what the users are interested in. We model image contents with a four-level hierarchical structure where the layers correspond to themes, semantic regions, visual words and pixels respectively. Users' latent interests are embedded in the theme layer. Given image contents, users' interests can be discovered by doing posterior inference. We use variational inference to approximate the posteriors of latent variables and learn model parameters. Experiments on 180K Flickr photos demonstrate the effectiveness of our model.

Motivated by problems such as molecular energy prediction, we derive an (improper) kernel between geometric inputs, that is able to capture the relevant rotational and translation invariances in geometric data. Since many physical simulations based upon geometric data produce derivatives of the output quantity with respect to the input positions, we derive an approach that incorporates derivative information into our kernel learning. We further show how to exploit the low rank structure of the resulting kernel matrices to speed up learning. Finally, we evaluated the method in the context of molecular energy prediction, showing good performance for modeling previously unseen molecular configurations. Integrating the approach into a Bayesian optimization, we show substantial improvement over the state of the art in molecular energy optimization.