We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $mathbf{X}^star$ from the (possibly noisy) observation of $|mathbf{Phi} mathbf{X}^star|$, in which $mathbf{Phi}$ is a matrix of size $m times n$. We consider a emph{high-dimensional} setting where $n,m to infty$ with $m/n = mathcal{O}(1)$, and a large class of (possibly correlated) random matrices $mathbf{Phi}$ and observation channels… Spectral methods are a powerful tool to obtain approximate observations of the signal $mathbf{X}^star$ which […]

Unveil the homophilic/heterophilic behaviors that characterize the wiring patterns of complex networks is an important task in social network analysis, often approached studying the assortative mixing of node attributes. Recent works underlined that a global measure to quantify node homophily necessarily provides a partial, often deceiving, picture of the reality… Moving from such literature, in this work, we propose a novel measure, namely Conformity, designed to overcome such limitation by providing a node-centric quantification of assortative mixing patterns. Differently from […]

We present a novel approach to video deblurring by fitting a deep network to the test video. One key observation is that some frames in a video with motion blur are much sharper than others, and thus we can transfer the texture information in those sharp frames to blurry frames… Our approach heuristically selects sharp frames from a video and then trains a convolutional neural network on these sharp frames. The trained network often absorbs enough details in the scene […]

Data mixing augmentation has proved effective in training deep models. Recent methods mix labels mainly based on the mixture proportion of image pixels… As the main discriminative information of a fine-grained image usually resides in subtle regions, methods along this line are prone to heavy label noise in fine-grained recognition. We propose in this paper a novel scheme, termed as Semantically Proportional Mixing (SnapMix), which exploits class activation map (CAM) to lessen the label noise in augmenting fine-grained data. SnapMix […]

We study the conditions under which input-output networks can dynamically attain competitive equilibrium, where markets clear and profits are zero. We endow a classical firm network model with simple dynamical rules that reduce supply/demand imbalances and excess profits… We show that the time needed to reach equilibrium diverges as the system approaches an instability point beyond which the Hawkins-Simons condition is violated and competitive equilibrium is no longer realisable. We argue that such slow dynamics is a source of excess […]

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems, especially in parameter retrieval… An addition to a predictive mean function, GPs come equipped with a useful property: the predictive variance function which provides confidence intervals for the predictions. The GP formulation usually assumes that there is no input noise in the training and […]

Recently, heatmap regression has been widely explored in facial landmark detection and obtained remarkable performance. However, most of the existing heatmap regression-based facial landmark detection methods neglect to explore the high-order feature correlations, which is very important to learn more representative features and enhance shape constraints… Moreover, no explicit global shape constraints have been added to the final predicted landmarks, which leads to a reduction in accuracy. To address these issues, in this paper, we propose a Multi-order Multi-constraint Deep […]

Noisy labels can impair the performance of deep neural networks. To tackle this problem, in this paper, we propose a new method for filtering label noise… Unlike most existing methods relying on the posterior probability of a noisy classifier, we focus on the much richer spatial behavior of data in the latent representational space. By leveraging the high-order topological information of data, we are able to collect most of the clean data and train a high-quality model. Theoretically we prove […]