Uniform Recovery Guarantees for Quantized Corrupted Sensing Using Structured or Generative Priors

This paper studies quantized corrupted sensing where the measurements are contaminated by unknown corruption and then quantized by a dithered uniform quantizer. We establish uniform guarantees for Lasso that ensure the accurate recovery of all signals and corruptions using a single draw of the sub-Gaussian sensing matrix and uniform dither. For signal and corruption with structured priors (e.g., sparsity, low-rankness), our uniform error rate for constrained Lasso typically coincides with the non-uniform one [Sun, Cui and Liu, 2022] up to logarithmic factors. By contrast, our uniform error rate for unconstrained Lasso exhibits worse dependence on the structured parameters due to regularization parameters larger than the ones for non-uniform recovery. For signal and corruption living in the ranges of some Lipschitz continuous generative models (referred to as generative priors), we achieve uniform recovery via constrained Lasso with a measurement number proportional to the latent dimensions of the generative models. Our treatments to the two kinds of priors are (nearly) unified and share the common key ingredients of (global) quantized product embedding (QPE) property, which states that the dithered uniform quantization (universally) preserves inner product. As a by-product, our QPE result refines the one in [Xu and Jacques, 2020] under sub-Gaussian random matrix, and in this specific instance we are able to sharpen the uniform error decaying rate (for the projected-back projection estimator with signals in some convex symmetric set) presented therein from $O(m^{-1/16})$ to $O(m^{-1/8})$.

Improved Analysis of Sparse Linear Regression in Local Differential Privacy Model

In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case where the underlying parameter is $1$-sparse, and extending such bounds to the more general $k$-sparse case has proven to be challenging. Moreover, it is unclear whether efficient non-interactive LDP (NLDP) algorithms exist. To address these issues, we first consider the problem in the $\epsilon$ non-interactive LDP model and provide a lower bound of $\Omega(\frac{\sqrt{dk\log d}}{\sqrt{n}\epsilon})$ on the $\ell_2$-norm estimation error for sub-Gaussian data, where $n$ is the sample size and $d$ is the dimension of the space. We propose an innovative NLDP algorithm, the very first of its kind for the problem. As a remarkable outcome, this algorithm also yields a novel and highly efficient estimator as a valuable by-product. Our algorithm achieves an upper bound of $\tilde{O}({\frac{d\sqrt{k}}{\sqrt{n}\epsilon}})$ for the estimation error when the data is sub-Gaussian, which can be further improved by a factor of $O(\sqrt{d})$ if the server has additional public but unlabeled data. For the sequentially interactive LDP model, we show a similar lower bound of $\Omega({\frac{\sqrt{dk}}{\sqrt{n}\epsilon}})$. As for the upper bound, we rectify a previous method and show that it is possible to achieve a bound of $\tilde{O}(\frac{k\sqrt{d}}{\sqrt{n}\epsilon})$. Our findings reveal fundamental differences between the non-private case, central DP model, and local DP model in the sparse linear regression problem.

On Stability and Generalization of Bilevel Optimization Problem

(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on this problem only focused on analyzing the convergence or improving the convergence rate, while little effort has been devoted to understanding its generalization behaviors. In this paper, we conduct a thorough analysis on the generalization of first-order (gradient-based) methods for the bilevel optimization problem. We first establish a fundamental connection between algorithmic stability and generalization error in different forms and give a high probability generalization bound which improves the previous best one from $\bigO(\sqrt{n})$ to $\bigO(\log n)$, where $n$ is the sample size. We then provide the first stability bounds for the general case where both inner and outer level parameters are subject to continuous update, while existing work allows only the outer level parameter to be updated. Our analysis can be applied in various standard settings such as strongly-convex-strongly-convex (SC-SC), convex-convex (C-C), and nonconvex-nonconvex (NC-NC). Our analysis for the NC-NC setting can also be extended to a particular nonconvex-strongly-convex (NC-SC) setting that is commonly encountered in practice. Finally, we corroborate our theoretical analysis and demonstrate how iterations can affect the generalization error by experiments on meta-learning and hyper-parameter optimization.

Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing

The block-term tensor decomposition model with multilinear rank-$(L_r,L_r,1)$ terms (or, the "LL1 tensor decomposition" in short) offers a valuable alternative for hyperspectral unmixing (HU) under the linear mixture model. Particularly, the LL1 decomposition ensures the endmember/abundance identifiability in scenarios where such guarantees are not supported by the classic matrix factorization (MF) approaches. However, existing LL1-based HU algorithms use a three-factor parameterization of the tensor (i.e., the hyperspectral image cube), which leads to a number of challenges including high per-iteration complexity, slow convergence, and difficulties in incorporating structural prior information. This work puts forth an LL1 tensor decomposition-based HU algorithm that uses a constrained two-factor re-parameterization of the tensor data. As a consequence, a two-block alternating gradient projection (GP)-based LL1 algorithm is proposed for HU. With carefully designed projection solvers, the GP algorithm enjoys a relatively low per-iteration complexity. Like in MF-based HU, the factors under our parameterization correspond to the endmembers and abundances. Thus, the proposed framework is natural to incorporate physics-motivated priors that arise in HU. The proposed algorithm often attains orders-of-magnitude speedup and substantial HU performance gains compared to the existing three-factor parameterization-based HU algorithms.

Attention guided global enhancement and local refinement network for semantic segmentation

The encoder-decoder architecture is widely used as a lightweight semantic segmentation network. However, it struggles with a limited performance compared to a well-designed Dilated-FCN model for two major problems. First, commonly used upsampling methods in the decoder such as interpolation and deconvolution suffer from a local receptive field, unable to encode global contexts. Second, low-level features may bring noises to the network decoder through skip connections for the inadequacy of semantic concepts in early encoder layers. To tackle these challenges, a Global Enhancement Method is proposed to aggregate global information from high-level feature maps and adaptively distribute them to different decoder layers, alleviating the shortage of global contexts in the upsampling process. Besides, a Local Refinement Module is developed by utilizing the decoder features as the semantic guidance to refine the noisy encoder features before the fusion of these two (the decoder features and the encoder features). Then, the two methods are integrated into a Context Fusion Block, and based on that, a novel Attention guided Global enhancement and Local refinement Network (AGLN) is elaborately designed. Extensive experiments on PASCAL Context, ADE20K, and PASCAL VOC 2012 datasets have demonstrated the effectiveness of the proposed approach. In particular, with a vanilla ResNet-101 backbone, AGLN achieves the state-of-the-art result (56.23% mean IoU) on the PASCAL Context dataset. The code is available at https://github.com/zhasen1996/AGLN.

Category Guided Attention Network for Brain Tumor Segmentation in MRI

Objective: Magnetic resonance imaging (MRI) has been widely used for the analysis and diagnosis of brain diseases. Accurate and automatic brain tumor segmentation is of paramount importance for radiation treatment. However, low tissue contrast in tumor regions makes it a challenging task.Approach: We propose a novel segmentation network named Category Guided Attention U-Net (CGA U-Net). In this model, we design a Supervised Attention Module (SAM) based on the attention mechanism, which can capture more accurate and stable long-range dependency in feature maps without introducing much computational cost. Moreover, we propose an intra-class update approach to reconstruct feature maps by aggregating pixels of the same category. Main results: Experimental results on the BraTS 2019 datasets show that the proposed method outperformers the state-of-the-art algorithms in both segmentation performance and computational complexity. Significance: The CGA U-Net can effectively capture the global semantic information in the MRI image by using the SAM module, while significantly reducing the computational cost. Code is available at https://github.com/delugewalker/CGA-U-Net.

TransBTS: Multimodal Brain Tumor Segmentation Using Transformer

Transformer, which can benefit from global (long-range) information modeling using self-attention mechanisms, has been successful in natural language processing and 2D image classification recently. However, both local and global features are crucial for dense prediction tasks, especially for 3D medical image segmentation. In this paper, we for the first time exploit Transformer in 3D CNN for MRI Brain Tumor Segmentation and propose a novel network named TransBTS based on the encoder-decoder structure. To capture the local 3D context information, the encoder first utilizes 3D CNN to extract the volumetric spatial feature maps. Meanwhile, the feature maps are reformed elaborately for tokens that are fed into Transformer for global feature modeling. The decoder leverages the features embedded by Transformer and performs progressive upsampling to predict the detailed segmentation map. Experimental results on the BraTS 2019 dataset show that TransBTS outperforms state-of-the-art methods for brain tumor segmentation on 3D MRI scans. Code is available at https://github.com/Wenxuan-1119/TransBTS

Differentially-private Federated Neural Architecture Search

Neural architecture search, which aims to automatically search for architectures (e.g., convolution, max pooling) of neural networks that maximize validation performance, has achieved remarkable progress recently. In many application scenarios, several parties would like to collaboratively search for a shared neural architecture by leveraging data from all parties. However, due to privacy concerns, no party wants its data to be seen by other parties. To address this problem, we propose federated neural architecture search (FNAS), where different parties collectively search for a differentiable architecture by exchanging gradients of architecture variables without exposing their data to other parties. To further preserve privacy, we study differentially-private FNAS (DP-FNAS), which adds random noise to the gradients of architecture variables. We provide theoretical guarantees of DP-FNAS in achieving differential privacy. Experiments show that DP-FNAS can search highly-performant neural architectures while protecting the privacy of individual parties. The code is available at https://github.com/UCSD-AI4H/DP-FNAS

Tensor completion via nonconvex tensor ring rank minimization with guaranteed convergence

In recent studies, the tensor ring (TR) rank has shown high effectiveness in tensor completion due to its ability of capturing the intrinsic structure within high-order tensors. A recently proposed TR rank minimization method is based on the convex relaxation by penalizing the weighted sum of nuclear norm of TR unfolding matrices. However, this method treats each singular value equally and neglects their physical meanings, which usually leads to suboptimal solutions in practice. In this paper, we propose to use the logdet-based function as a nonconvex smooth relaxation of the TR rank for tensor completion, which can more accurately approximate the TR rank and better promote the low-rankness of the solution. To solve the proposed nonconvex model efficiently, we develop an alternating direction method of multipliers algorithm and theoretically prove that, under some mild assumptions, our algorithm converges to a stationary point. Extensive experiments on color images, multispectral images, and color videos demonstrate that the proposed method outperforms several state-of-the-art competitors in both visual and quantitative comparison. Key words: nonconvex optimization, tensor ring rank, logdet function, tensor completion, alternating direction method of multipliers.

Tensor train rank minimization with nonlocal self-similarity for tensor completion

The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has not exploited the potential of TT rank for high-order tensors. The TT rank minimization accompany with \emph{ket augmentation}, which transforms a lower-order tensor (e.g., visual data) into a higher-order tensor, suffers from serious block-artifacts. To tackle this issue, we suggest the TT rank minimization with nonlocal self-similarity for tensor completion by simultaneously exploring the spatial, temporal/spectral, and nonlocal redundancy in visual data. More precisely, the TT rank minimization is performed on a formed higher-order tensor called group by stacking similar cubes, which naturally and fully takes advantage of the ability of TT rank for high-order tensors. Moreover, the perturbation analysis for the TT low-rankness of each group is established. We develop the alternating direction method of multipliers tailored for the specific structure to solve the proposed model. Extensive experiments demonstrate that the proposed method is superior to several existing state-of-the-art methods in terms of both qualitative and quantitative measures.