Post-Regularization Inference for Time-Varying Nonparanormal Graphical Models

We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model, we develop statistical tests for presence of edges both locally at a fixed index value and globally over a range of values. The tests are developed for a high-dimensional regime, are robust to model selection mistakes and do not require commonly assumed minimum signal strength. The testing procedures are based on a high dimensional, debiasing-free moment estimator, which uses a novel kernel smoothed Kendall's tau correlation matrix as an input statistic. The estimator consistently estimates the latent inverse Pearson correlation matrix uniformly in both the index variable and kernel bandwidth. Its rate of convergence is shown to be minimax optimal. Our method is supported by thorough numerical simulations and an application to a neural imaging data set

PiCANet: Learning Pixel-wise Contextual Attention for Saliency Detection

Contexts play an important role in the saliency detection task. However, given a context region, not all contextual information is helpful for the final task. In this paper, we propose a novel pixel-wise contextual attention network, i.e., the PiCANet, to learn to selectively attend to informative context locations for each pixel. Specifically, for each pixel, it can generate an attention map in which each attention weight corresponds to the contextual relevance at each context location. An attended contextual feature can then be constructed by selectively aggregating the contextual information. We formulate the proposed PiCANet in both global and local forms to attend to global and local contexts, respectively. Both models are fully differentiable and can be embedded into CNNs for joint training. We also incorporate the proposed models with the U-Net architecture to detect salient objects. Extensive experiments show that the proposed PiCANets can consistently improve saliency detection performance. The global and local PiCANets facilitate learning global contrast and homogeneousness, respectively. As a result, our saliency model can detect salient objects more accurately and uniformly, thus performing favorably against the state-of-the-art methods

Provable Sparse Tensor Decomposition

We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family of high dimensional latent variable models, including high dimensional Gaussian mixture and mixtures of sparse regressions. A thorough theoretical investigation is further conducted. In particular, we show that the final decomposition estimator is guaranteed to achieve a local statistical rate, and further strengthen it to the global statistical rate by introducing a proper initialization procedure. In high dimensional regimes, the obtained statistical rate significantly improves those shown in the existing non-sparse decomposition methods. The empirical advantages of TTP are confirmed in extensive simulated results and two real applications of click-through rate prediction and high-dimensional gene clustering.Comment: To Appear in JRSS-