In this paper, we introduce an end-to-end generative adversarial network (GAN) based on sparse learning for single image blind motion deblurring, which we called SL-CycleGAN. For the first time in blind motion deblurring, we propose a sparse ResNet-block as a combination of sparse convolution layers and a trainable spatial pooler k-winner based on HTM (Hierarchical Temporal Memory) to replace non-linearity such as ReLU in the ResNet-block of SL-CycleGAN generators. Furthermore, unlike many state-of-the-art GAN-based motion deblurring methods that treat motion deblurring as a linear end-to-end process, we take our inspiration from the domain-to-domain translation ability of CycleGAN, and we show that image deblurring can be cycle-consistent while achieving the best qualitative results. Finally, we perform extensive experiments on popular image benchmarks both qualitatively and quantitatively and achieve the record-breaking PSNR of 38.087 dB on GoPro dataset, which is 5.377 dB better than the most recent deblurring method.
Finding neural network weights that generalize well from small datasets is difficult. A promising approach is to learn a weight initialization such that a small number of weight changes results in low generalization error. We show that this form of meta-learning can be improved by letting the learning algorithm decide which weights to change, i.e., by learning where to learn. We find that patterned sparsity emerges from this process, with the pattern of sparsity varying on a problem-by-problem basis. This selective sparsity results in better generalization and less interference in a range of few-shot and continual learning problems. Moreover, we find that sparse learning also emerges in a more expressive model where learning rates are meta-learned. Our results shed light on an ongoing debate on whether meta-learning can discover adaptable features and suggest that learning by sparse gradient descent is a powerful inductive bias for meta-learning systems.
We introduce a new library named abess that implements a unified framework of best-subset selection for solving diverse machine learning problems, e.g., linear regression, classification, and principal component analysis. Particularly, the abess certifiably gets the optimal solution within polynomial times with high probability under the linear model. Our efficient implementation allows abess to attain the solution of best-subset selection problems as fast as or even 20x faster than existing competing variable (model) selection toolboxes. Furthermore, it supports common variants like best group subset selection and $\ell_2$ regularized best-subset selection. The core of the library is programmed in C++. For ease of use, a Python library is designed for conveniently integrating with scikit-learn, and it can be installed from the Python library Index. In addition, a user-friendly R library is available at the Comprehensive R Archive Network. The source code is available at: https://github.com/abess-team/abess.
Various feature selection methods have been recently proposed on different applications to reduce the computational burden of machine learning algorithms as well as the complexity of learned models. Preserving sample similarities and selecting discriminative features are two major factors should be satisfied, especially by unsupervised feature selection methods. This paper aims to propose a novel unsupervised feature selection approach which employs an ℓ 2,1 -norm regularization model to preserve global and local similarities by minimizing an objective function. Cluster analysis is also incorporated in this framework to take the inherent structure of the data into account. The experimental results show the strength of the proposed approach as compared with the earlier well-known methods on a variety of standard datasets.
Accurate automatic liver and tumor segmentation plays a vital role in treatment planning and disease monitoring. Recently, deep convolutional neural network (DCNNs) has obtained tremendous success in 2D and 3D medical image segmentation. However, 2D DCNNs cannot fully leverage the inter-slice information, while 3D DCNNs are computationally expensive and memory intensive. To address these issues, we first propose a novel dense-sparse training flow from a data perspective, in which, densely adjacent slices and sparsely adjacent slices are extracted as inputs for regularizing DCNNs, thereby improving the model performance. Moreover, we design a 2.5D light-weight nnU-Net from a network perspective, in which, depthwise separable convolutions are adopted to improve the efficiency. Extensive experiments on the LiTS dataset have demonstrated the superiority of the proposed method.
Deep spiking neural networks (SNNs) have emerged as a potential alternative to traditional deep learning frameworks, due to their promise to provide increased compute efficiency on event-driven neuromorphic hardware. However, to perform well on complex vision applications, most SNN training frameworks yield large inference latency which translates to increased spike activity and reduced energy efficiency. Hence,minimizing average spike activity while preserving accuracy indeep SNNs remains a significant challenge and opportunity.This paper presents a non-iterative SNN training technique thatachieves ultra-high compression with reduced spiking activitywhile maintaining high inference accuracy. In particular, our framework first uses the attention-maps of an un compressed meta-model to yield compressed ANNs. This step can be tuned to support both irregular and structured channel pruning to leverage computational benefits over a broad range of platforms. The framework then performs sparse-learning-based supervised SNN training using direct inputs. During the training, it jointly optimizes the SNN weight, threshold, and leak parameters to drastically minimize the number of time steps required while retaining compression. To evaluate the merits of our approach, we performed experiments with variants of VGG and ResNet, on both CIFAR-10 and CIFAR-100, and VGG16 on Tiny-ImageNet.The SNN models generated through the proposed technique yield SOTA compression ratios of up to 33.4x with no significant drops in accuracy compared to baseline unpruned counterparts. Compared to existing SNN pruning methods, we achieve up to 8.3x higher compression with improved accuracy.
As one of the most fundamental problems in machine learning, statistics and differential privacy, Differentially Private Stochastic Convex Optimization (DP-SCO) has been extensively studied in recent years. However, most of the previous work can only handle either regular data distribution or irregular data in the low dimensional space case. To better understand the challenges arising from irregular data distribution, in this paper we provide the first study on the problem of DP-SCO with heavy-tailed data in the high dimensional space. In the first part we focus on the problem over some polytope constraint (such as the $\ell_1$-norm ball). We show that if the loss function is smooth and its gradient has bounded second order moment, it is possible to get a (high probability) error bound (excess population risk) of $\tilde{O}(\frac{\log d}{(n\epsilon)^\frac{1}{3}})$ in the $\epsilon$-DP model, where $n$ is the sample size and $d$ is the dimensionality of the underlying space. Next, for LASSO, if the data distribution that has bounded fourth-order moments, we improve the bound to $\tilde{O}(\frac{\log d}{(n\epsilon)^\frac{2}{5}})$ in the $(\epsilon, \delta)$-DP model. In the second part of the paper, we study sparse learning with heavy-tailed data. We first revisit the sparse linear model and propose a truncated DP-IHT method whose output could achieve an error of $\tilde{O}(\frac{s^{*2}\log d}{n\epsilon})$, where $s^*$ is the sparsity of the underlying parameter. Then we study a more general problem over the sparsity ({\em i.e.,} $\ell_0$-norm) constraint, and show that it is possible to achieve an error of $\tilde{O}(\frac{s^{*\frac{3}{2}}\log d}{n\epsilon})$, which is also near optimal up to a factor of $\tilde{O}{(\sqrt{s^*})}$, if the loss function is smooth and strongly convex.
Most sequential recommendation models capture the features of consecutive items in a user-item interaction history. Though effective, their representation expressiveness is still hindered by the sparse learning signals. As a result, the sequential recommender is prone to make inconsistent predictions. In this paper, we propose a model, SSI, to improve sequential recommendation consistency with Self-Supervised Imitation. Precisely, we extract the consistency knowledge by utilizing three self-supervised pre-training tasks, where temporal consistency and persona consistency capture user-interaction dynamics in terms of the chronological order and persona sensitivities, respectively. Furthermore, to provide the model with a global perspective, global session consistency is introduced by maximizing the mutual information among global and local interaction sequences. Finally, to comprehensively take advantage of all three independent aspects of consistency-enhanced knowledge, we establish an integrated imitation learning framework. The consistency knowledge is effectively internalized and transferred to the student model by imitating the conventional prediction logit as well as the consistency-enhanced item representations. In addition, the flexible self-supervised imitation framework can also benefit other student recommenders. Experiments on four real-world datasets show that SSI effectively outperforms the state-of-the-art sequential recommendation methods.
Works on lottery ticket hypothesis (LTH) and single-shot network pruning (SNIP) have raised a lot of attention currently on post-training pruning (iterative magnitude pruning), and before-training pruning (pruning at initialization). The former method suffers from an extremely large computation cost and the latter usually struggles with insufficient performance. In comparison, during-training pruning, a class of pruning methods that simultaneously enjoys the training/inference efficiency and the comparable performance, temporarily, has been less explored. To better understand during-training pruning, we quantitatively study the effect of pruning throughout training from the perspective of pruning plasticity (the ability of the pruned networks to recover the original performance). Pruning plasticity can help explain several other empirical observations about neural network pruning in literature. We further find that pruning plasticity can be substantially improved by injecting a brain-inspired mechanism called neuroregeneration, i.e., to regenerate the same number of connections as pruned. We design a novel gradual magnitude pruning (GMP) method, named gradual pruning with zero-cost neuroregeneration (\textbf{GraNet}), that advances state of the art. Perhaps most impressively, its sparse-to-sparse version for the first time boosts the sparse-to-sparse training performance over various dense-to-sparse methods with ResNet-50 on ImageNet without extending the training time. We release all codes in https://github.com/Shiweiliuiiiiiii/GraNet.
Performing reliability analysis on complex systems is often computationally expensive. In particular, when dealing with systems having high input dimensionality, reliability estimation becomes a daunting task. A popular approach to overcome the problem associated with time-consuming and expensive evaluations is building a surrogate model. However, these computationally efficient models often suffer from the curse of dimensionality. Hence, training a surrogate model for high-dimensional problems is not straightforward. Henceforth, this paper presents a framework for solving high-dimensional reliability analysis problems. The basic premise is to train the surrogate model on a low-dimensional manifold, discovered using the active subspace algorithm. However, learning the low-dimensional manifold using active subspace is non-trivial as it requires information on the gradient of the response variable. To address this issue, we propose using sparse learning algorithms in conjunction with the active subspace algorithm; the resulting algorithm is referred to as the sparse active subspace (SAS) algorithm. We project the high-dimensional inputs onto the identified low-dimensional manifold identified using SAS. A high-fidelity surrogate model is used to map the inputs on the low-dimensional manifolds to the output response. We illustrate the efficacy of the proposed framework by using three benchmark reliability analysis problems from the literature. The results obtained indicate the accuracy and efficiency of the proposed approach compared to already established reliability analysis methods in the literature.
We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on optimal solutions for the $\ell_0$-regularized formulation, a problem that is relatively unexplored due to computational challenges. Our methodology covers both high-dimensional linear regression and nonparametric sparse additive modeling with smooth components. Our algorithmic framework consists of approximate and exact algorithms. The approximate algorithms are based on coordinate descent and local search, with runtimes comparable to popular sparse learning algorithms. Our exact algorithm is based on a standalone branch-and-bound (BnB) framework, which can solve the associated mixed integer programming (MIP) problem to certified optimality. By exploiting the problem structure, our custom BnB algorithm can solve to optimality problem instances with $5 \times 10^6$ features and $10^3$ observations in minutes to hours -- over $1000$ times larger than what is currently possible using state-of-the-art commercial MIP solvers. We also explore statistical properties of the $\ell_0$-based estimators. We demonstrate, theoretically and empirically, that our proposed estimators have an edge over popular group-sparse estimators in terms of statistical performance in various regimes. We provide an open-source implementation of our proposed framework.
In this paper, we introduce a new perspective on training deep neural networks capable of state-of-the-art performance without the need for the expensive over-parameterization by proposing the concept of In-Time Over-Parameterization (ITOP) in sparse training. By starting from a random sparse network and continuously exploring sparse connectivities during training, we can perform an Over-Parameterization in the space-time manifold, closing the gap in the expressibility between sparse training and dense training. We further use ITOP to understand the underlying mechanism of Dynamic Sparse Training (DST) and indicate that the benefits of DST come from its ability to consider across time all possible parameters when searching for the optimal sparse connectivity. As long as there are sufficient parameters that have been reliably explored during training, DST can outperform the dense neural network by a large margin. We present a series of experiments to support our conjecture and achieve the state-of-the-art sparse training performance with ResNet-50 on ImageNet. More impressively, our method achieves dominant performance over the overparameterization-based sparse methods at extreme sparsity levels. When trained on CIFAR-100, our method can match the performance of the dense model even at an extreme sparsity (98%). Code can be found https://github.com/Shiweiliuiiiiiii/In-Time-Over-Parameterization.
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered equation to noise and the complexities of model selection. In this work, we propose an advanced Bayesian sparse learning algorithm for PDE discovery with variable coefficients, predominantly when the coefficients are spatially or temporally dependent. Specifically, we apply threshold Bayesian group Lasso regression with a spike-and-slab prior (tBGL-SS) and leverage a Gibbs sampler for Bayesian posterior estimation of PDE coefficients. This approach not only enhances the robustness of point estimation with valid uncertainty quantification but also relaxes the computational burden from Bayesian inference through the integration of coefficient thresholds as an approximate MCMC method. Moreover, from the quantified uncertainties, we propose a Bayesian total error bar criteria for model selection, which outperforms classic metrics including the root mean square and the Akaike information criterion. The capability of this method is illustrated by the discovery of several classical benchmark PDEs with spatially or temporally varying coefficients from solution data obtained from the reference simulations. In the experiments, we show that the tBGL-SS method is more robust than the baseline methods under noisy environments and provides better model selection criteria along the regularization path.
Nonconvex sparse learning plays an essential role in many areas, such as signal processing and deep network compression. Iterative hard thresholding (IHT) methods are the state-of-the-art for nonconvex sparse learning due to their capability of recovering true support and scalability with large datasets. Theoretical analysis of IHT is currently based on centralized IID data. In realistic large-scale situations, however, data are distributed, hardly IID, and private to local edge computing devices. It is thus necessary to examine the property of IHT in federated settings, which update in parallel on local devices and communicate with a central server only once in a while without sharing local data. In this paper, we propose two IHT methods: Federated Hard Thresholding (Fed-HT) and Federated Iterative Hard Thresholding (FedIter-HT). We prove that both algorithms enjoy a linear convergence rate and have strong guarantees to recover the optimal sparse estimator, similar to traditional IHT methods, but now with decentralized non-IID data. Empirical results demonstrate that the Fed-HT and FedIter-HT outperform their competitor - a distributed IHT, in terms of decreasing the objective values with lower requirements on communication rounds and bandwidth.
After selection with the Group LASSO (or generalized variants such as the overlapping, sparse, or standardized Group LASSO), inference for the selected parameters is unreliable in the absence of adjustments for selection bias. In the penalized Gaussian regression setup, existing approaches provide adjustments for selection events that can be expressed as linear inequalities in the data variables. Such a representation, however, fails to hold for selection with the Group LASSO and substantially obstructs the scope of subsequent post-selective inference. Key questions of inferential interest -- for example, inference for the effects of selected variables on the outcome -- remain unanswered. In the present paper, we develop a consistent, post-selective, Bayesian method to address the existing gaps by deriving a likelihood adjustment factor and an approximation thereof that eliminates bias from the selection of groups. Experiments on simulated data and data from the Human Connectome Project demonstrate that our method recovers the effects of parameters within the selected groups while paying only a small price for bias adjustment.
KNN classification is an improvisational learning mode, in which they are carried out only when a test data is predicted that set a suitable K value and search the K nearest neighbors from the whole training sample space, referred them to the lazy part of KNN classification. This lazy part has been the bottleneck problem of applying KNN classification due to the complete search of K nearest neighbors. In this paper, a one-step computation is proposed to replace the lazy part of KNN classification. The one-step computation actually transforms the lazy part to a matrix computation as follows. Given a test data, training samples are first applied to fit the test data with the least squares loss function. And then, a relationship matrix is generated by weighting all training samples according to their influence on the test data. Finally, a group lasso is employed to perform sparse learning of the relationship matrix. In this way, setting K value and searching K nearest neighbors are both integrated to a unified computation. In addition, a new classification rule is proposed for improving the performance of one-step KNN classification. The proposed approach is experimentally evaluated, and demonstrated that the one-step KNN classification is efficient and promising
Sparse learning has been widely studied to capture critical information from enormous data sources in the filed of system identification. Often, it is essential to understand internal working mechanisms of unknown systems (e.g. biological networks) in addition to input-output relationships. For this purpose, various feature selection techniques have been developed. For example, sparse Bayesian learning (SBL) was proposed to learn major features from a dictionary of basis functions, which makes identified models interpretable. Reweighted L1-regularization algorithms are often applied in SBL to solve optimization problems. However, they are expensive in both computation and memory aspects, thus not suitable for large-scale problems. This paper proposes an adaptive support driven Bayesian reweighted (ASDBR) algorithm for sparse signal recovery. A restart strategy based on shrinkage-thresholding is developed to conduct adaptive support estimate, which can effectively reduce computation burden and memory demands. Moreover, ASDBR accurately extracts major features and excludes redundant information from large datasets. Numerical experiments demonstrate the proposed algorithm outperforms state-of-the-art methods.
This paper considers the design of tunable decision schemes capable of rejecting with high probability mismatched signals embedded in Gaussian interference with unknown covariance matrix. To this end, a sparse recovery technique is exploited to enhance the resolution at which the target angle of arrival is estimated with the objective to obtain high-selective detectors. The outcomes of this estimation procedure are used to devise detection architectures relying on either the twostage design paradigm or heuristic design procedures based upon the generalized likelihood ratio test. Remarkably, the new decision rules exhibit a bounded-constant false alarm rate property and allow for a tradeoff between the matched detection performance and the rejection of undesired signals by tuning a design parameter. At the analysis stage, the performance of the newly proposed detectors is assessed also in comparison with existing selective competitors. The results show that the new detectors can outperform the considered counterparts in terms of rejection of unwanted signals, while retaining reasonable detection performance of matched signals.
Sparse learning has been shown to be effective in solving many real-world problems. Finding sparse representations is a fundamentally important topic in many fields of science including signal processing, computer vision, genome study and medical imaging. One important issue in applying sparse representation is to find the basis to represent the data,especially in computer vision and medical imaging where the data is not necessary incoherent. In medical imaging, clinicians often grade the severity or measure the risk score of a disease based on images. This process is referred to as medical image grading. Manual grading of the disease severity or risk score is often used. However, it is tedious, subjective and expensive. Sparse learning has been used for automatic grading of medical images for different diseases. In the grading, we usually begin with one step to find a sparse representation of the testing image using a set of reference images or atoms from the dictionary. Then in the second step, the selected atoms are used as references to compute the grades of the testing images. Since the two steps are conducted sequentially, the objective function in the first step is not necessarily optimized for the second step. In this paper, we propose a novel sparse range-constrained learning(SRCL)algorithm for medical image grading.Different from most of existing sparse learning algorithms, SRCL integrates the objective of finding a sparse representation and that of grading the image into one function. It aims to find a sparse representation of the testing image based on atoms that are most similar in both the data or feature representation and the medical grading scores. We apply the new proposed SRCL to CDR computation and cataract grading. Experimental results show that the proposed method is able to improve the accuracy in cup-to-disc ratio computation and cataract grading.
Nesterov's accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence issues may arise when it is applied to nonconvex penalties, such as SCAD. A recent proposal generalizes Nesterov's AG method to the nonconvex setting. The proposed algorithm requires specification of several hyperparameters for its practical application. Aside from some general conditions, there is no explicit rule for selecting the hyperparameters, and how different selection can affect convergence of the algorithm. In this article, we propose a hyperparameter setting based on the complexity upper bound to accelerate convergence, and consider the application of this nonconvex AG algorithm to high-dimensional linear and logistic sparse learning problems. We further establish the rate of convergence and present a simple and useful bound to characterize our proposed optimal damping sequence. Simulation studies show that convergence can be made, on average, considerably faster than that of the conventional proximal gradient algorithm. Our experiments also show that the proposed method generally outperforms the current state-of-the-art methods in terms of signal recovery.