Sparsity-Constraint Optimization via Splicing Iteration

Sparsity-constraint optimization has wide applicability in signal processing, statistics, and machine learning. Existing fast algorithms must burdensomely tune parameters, such as the step size or the implementation of precise stop criteria, which may be challenging to determine in practice. To address this issue, we develop an algorithm named Sparsity-Constraint Optimization via sPlicing itEration (SCOPE) to optimize nonlinear differential objective functions with strong convexity and smoothness in low dimensional subspaces. Algorithmically, the SCOPE algorithm converges effectively without tuning parameters. Theoretically, SCOPE has a linear convergence rate and converges to a solution that recovers the true support set when it correctly specifies the sparsity. We also develop parallel theoretical results without restricted-isometry-property-type conditions. We apply SCOPE's versatility and power to solve sparse quadratic optimization, learn sparse classifiers, and recover sparse Markov networks for binary variables. The numerical results on these specific tasks reveal that SCOPE perfectly identifies the true support set with a 10--1000 speedup over the standard exact solver, confirming SCOPE's algorithmic and theoretical merits. Our open-source Python package skscope based on C++ implementation is publicly available on GitHub, reaching a ten-fold speedup on the competing convex relaxation methods implemented by the cvxpy library.

skscope: Fast Sparsity-Constrained Optimization in Python

Applying iterative solvers on sparsity-constrained optimization (SCO) requires tedious mathematical deduction and careful programming/debugging that hinders these solvers' broad impact. In the paper, the library skscope is introduced to overcome such an obstacle. With skscope, users can solve the SCO by just programming the objective function. The convenience of skscope is demonstrated through two examples in the paper, where sparse linear regression and trend filtering are addressed with just four lines of code. More importantly, skscope's efficient implementation allows state-of-the-art solvers to quickly attain the sparse solution regardless of the high dimensionality of parameter space. Numerical experiments reveal the available solvers in skscope can achieve up to 80x speedup on the competing relaxation solutions obtained via the benchmarked convex solver. skscope is published on the Python Package Index (PyPI) and Conda, and its source code is available at: https://github.com/abess-team/skscope.

Robust Offline Policy Evaluation and Optimization with Heavy-Tailed Rewards

This paper endeavors to augment the robustness of offline reinforcement learning (RL) in scenarios laden with heavy-tailed rewards, a prevalent circumstance in real-world applications. We propose two algorithmic frameworks, ROAM and ROOM, for robust off-policy evaluation (OPE) and offline policy optimization (OPO), respectively. Central to our frameworks is the strategic incorporation of the median-of-means method with offline RL, enabling straightforward uncertainty estimation for the value function estimator. This not only adheres to the principle of pessimism in OPO but also adeptly manages heavy-tailed rewards. Theoretical results and extensive experiments demonstrate that our two frameworks outperform existing methods on the logged dataset exhibits heavy-tailed reward distributions.

A Consistent and Scalable Algorithm for Best Subset Selection in Single Index Models

Analysis of high-dimensional data has led to increased interest in both single index models (SIMs) and best subset selection. SIMs provide an interpretable and flexible modeling framework for high-dimensional data, while best subset selection aims to find a sparse model from a large set of predictors. However, best subset selection in high-dimensional models is known to be computationally intractable. Existing methods tend to relax the selection, but do not yield the best subset solution. In this paper, we directly tackle the intractability by proposing the first provably scalable algorithm for best subset selection in high-dimensional SIMs. Our algorithmic solution enjoys the subset selection consistency and has the oracle property with a high probability. The algorithm comprises a generalized information criterion to determine the support size of the regression coefficients, eliminating the model selection tuning. Moreover, our method does not assume an error distribution or a specific link function and hence is flexible to apply. Extensive simulation results demonstrate that our method is not only computationally efficient but also able to exactly recover the best subset in various settings (e.g., linear regression, Poisson regression, heteroscedastic models).

Best-Subset Selection in Generalized Linear Models: A Fast and Consistent Algorithm via Splicing Technique

In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type, achieving either computational efficiency or statistical guarantees is challenging. In this article, we intend to surmount this obstacle by utilizing a fast algorithm to select the best subset with high certainty. We proposed and illustrated an algorithm for best subset recovery in regularity conditions. Under mild conditions, the computational complexity of our algorithm scales polynomially with sample size and dimension. In addition to demonstrating the statistical properties of our method, extensive numerical experiments reveal that it outperforms existing methods for variable selection and coefficient estimation. The runtime analysis shows that our implementation achieves approximately a fourfold speedup compared to popular variable selection toolkits like glmnet and ncvreg.

A residual dense vision transformer for medical image super-resolution with segmentation-based perceptual loss fine-tuning

Super-resolution plays an essential role in medical imaging because it provides an alternative way to achieve high spatial resolutions and image quality with no extra acquisition costs. In the past few decades, the rapid development of deep neural networks has promoted super-resolution performance with novel network architectures, loss functions and evaluation metrics. Specifically, vision transformers dominate a broad range of computer vision tasks, but challenges still exist when applying them to low-level medical image processing tasks. This paper proposes an efficient vision transformer with residual dense connections and local feature fusion to achieve efficient single-image super-resolution (SISR) of medical modalities. Moreover, we implement a general-purpose perceptual loss with manual control for image quality improvements of desired aspects by incorporating prior knowledge of medical image segmentation. Compared with state-of-the-art methods on four public medical image datasets, the proposed method achieves the best PSNR scores of 6 modalities among seven modalities. It leads to an average improvement of $+0.09$ dB PSNR with only 38\% parameters of SwinIR. On the other hand, the segmentation-based perceptual loss increases $+0.14$ dB PSNR on average for SOTA methods, including CNNs and vision transformers. Additionally, we conduct comprehensive ablation studies to discuss potential factors for the superior performance of vision transformers over CNNs and the impacts of network and loss function components. The code will be released on GitHub with the paper published.

An Instrumental Variable Approach to Confounded Off-Policy Evaluation

Off-policy evaluation (OPE) is a method for estimating the return of a target policy using some pre-collected observational data generated by a potentially different behavior policy. In some cases, there may be unmeasured variables that can confound the action-reward or action-next-state relationships, rendering many existing OPE approaches ineffective. This paper develops an instrumental variable (IV)-based method for consistent OPE in confounded Markov decision processes (MDPs). Similar to single-stage decision making, we show that IV enables us to correctly identify the target policy's value in infinite horizon settings as well. Furthermore, we propose an efficient and robust value estimator and illustrate its effectiveness through extensive simulations and analysis of real data from a world-leading short-video platform.

Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process

This paper is concerned with constructing a confidence interval for a target policy's value offline based on a pre-collected observational data in infinite horizon settings. Most of the existing works assume no unmeasured variables exist that confound the observed actions. This assumption, however, is likely to be violated in real applications such as healthcare and technological industries. In this paper, we show that with some auxiliary variables that mediate the effect of actions on the system dynamics, the target policy's value is identifiable in a confounded Markov decision process. Based on this result, we develop an efficient off-policy value estimator that is robust to potential model misspecification and provide rigorous uncertainty quantification. Our method is justified by theoretical results, simulated and real datasets obtained from ridesharing companies.

abess: A Fast Best Subset Selection Library in Python and R

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 under the linear model. Our efficient implementation allows abess to attain the solution of best-subset selection problems as fast as or even 100x 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.

MIASSR: An Approach for Medical Image Arbitrary Scale Super-Resolution

Single image super-resolution (SISR) aims to obtain a high-resolution output from one low-resolution image. Currently, deep learning-based SISR approaches have been widely discussed in medical image processing, because of their potential to achieve high-quality, high spatial resolution images without the cost of additional scans. However, most existing methods are designed for scale-specific SR tasks and are unable to generalise over magnification scales. In this paper, we propose an approach for medical image arbitrary-scale super-resolution (MIASSR), in which we couple meta-learning with generative adversarial networks (GANs) to super-resolve medical images at any scale of magnification in (1, 4]. Compared to state-of-the-art SISR algorithms on single-modal magnetic resonance (MR) brain images (OASIS-brains) and multi-modal MR brain images (BraTS), MIASSR achieves comparable fidelity performance and the best perceptual quality with the smallest model size. We also employ transfer learning to enable MIASSR to tackle SR tasks of new medical modalities, such as cardiac MR images (ACDC) and chest computed tomography images (COVID-CT). The source code of our work is also public. Thus, MIASSR has the potential to become a new foundational pre-/post-processing step in clinical image analysis tasks such as reconstruction, image quality enhancement, and segmentation.