Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

We propose a pool-based non-parametric active learning algorithm for general metric spaces, called MArgin Regularized Metric Active Nearest Neighbor (MARMANN), which outputs a nearest-neighbor classifier. We give prediction error guarantees that depend on the noisy-margin properties of the input sample, and are competitive with those obtained by previously proposed passive learners. We prove that the label complexity of MARMANN is significantly lower than that of any passive learner with similar error guarantees. Our algorithm is based on a generalized sample compression scheme and a new label-efficient active model-selection procedure.

In this paper, we propose a very deep fully convolutional encoding-decoding framework for image restoration such as denoising and super-resolution. The network is composed of multiple layers of convolution and deconvolution operators, learning end-to-end mappings from corrupted images to the original ones. The convolutional layers act as the feature extractor, which capture the abstraction of image contents while eliminating noises/corruptions. Deconvolutional layers are then used to recover the image details. We propose to symmetrically link convolutional and deconvolutional layers with skip-layer connections, with which the training converges much faster and attains a higher-quality local optimum. First, the skip connections allow the signal to be back-propagated to bottom layers directly, and thus tackles the problem of gradient vanishing, making training deep networks easier and achieving restoration performance gains consequently. Second, these skip connections pass image details from convolutional layers to deconvolutional layers, which is beneficial in recovering the original image. Significantly, with the large capacity, we can handle different levels of noises using a single model. Experimental results show that our network achieves better performance than recent state-of-the-art methods.

Bayesian nonparametric methods based on the Dirichlet Process (DP), gamma process and beta process, have proven effective in capturing aspects of various datasets arising in machine learning. However, it is now recognized that such processes have their limitations in terms of the ability to capture power law behavior. As such there is now considerable interest in models based on the Stable Processs (SP), Generalized Gamma process (GGP) and Stable-Beta Process (SBP).

We consider a crowdsourcing model in which nworkers are asked to rate the quality of nitems previously generated by other workers. An unknown set of αnworkers generate reliable ratings, while the remaining workers may behave arbitrarily and possibly adversarially. The manager of the experiment can also manually evaluate the quality of a small number of items, and wishes to curate together almost all of the high-quality items with at most anfraction of low-quality items.

Neural Information Processing Systems http://nips.cc/

Patriot missile involved in Bahrain blast likely U.S.-operated, analysis finds Smoke rises following a strike on the Bapco Oil Refinery, amid the U.S.-Israeli conflict with Iran, on Sitra Island Bahrain, on March 9. | REUTERS An American-operated Patriot air defense battery likely fired the interceptor missile involved in a pre-dawn explosion that injured dozens of civilians and tore through homes in U.S.-ally Bahrain 10 days into the war on Iran, according to an analysis by academic researchers examined by Reuters. Both Bahrain and Washington have blamed an Iranian drone attack for the March 9 blast, which the Gulf kingdom said injured 32 people including children, some seriously. Commenting on the day of the attack, U.S. Central Command said on X that an Iranian drone struck a residential neighborhood in Bahrain. In response to questions, Bahrain on Saturday acknowledged for the first time that a Patriot missile was involved in the explosion over the Mahazza neighborhood on Sitra island, offshore from the capital Manama and also home to an oil refinery. In a statement, a Bahraini government spokesperson said the missile successfully intercepted an Iranian drone mid-air, saving lives. In a time of both misinformation and too much information, quality journalism is more crucial than ever.

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower bound on the critical sample complexity required for reliable model selection. More specifically, we show that distinguishing a $k$-component mixture from a simpler model necessitates a sample size scaling of $Ω(Δ^{-(4k-4)})$. We then propose a thresholding-based estimation algorithm that evaluates the spectral gap of an empirical covariance matrix constructed from random Fourier measurement vectors. This parameter-free estimator operates with an efficient time complexity of $\mathcal{O}(k^2 n)$, scaling linearly with the sample size. We demonstrate that the sample complexity of our method matches the established lower bound, confirming its minimax optimality with respect to the component separation distance $Δ$. Conditioned on the estimated model order, we subsequently introduce a gradient-based minimization method for parameter estimation. To effectively navigate the non-convex objective landscape, we employ a data-driven, score-based initialization strategy that guarantees rapid convergence. We prove that this method achieves the optimal parametric convergence rate of $\mathcal{O}_p(n^{-1/2})$ for estimating the component means. To enhance the algorithm's efficiency in high-dimensional regimes where the ambient dimension exceeds the number of mixture components (i.e., \(d > k\)), we integrate principal component analysis (PCA) for dimension reduction. Numerical experiments demonstrate that our Fourier-based algorithmic framework outperforms conventional Expectation-Maximization (EM) methods in both estimation accuracy and computational time.