Linear mixed models (LMMs), which incorporate fixed and random effects, are key tools for analyzing heterogeneous data, such as in personalized medicine or adaptive marketing. Nowadays, this type of data is increasingly wide, sometimes containing thousands of candidate predictors, necessitating sparsity for prediction and interpretation. However, existing sparse learning methods for LMMs do not scale well beyond tens or hundreds of predictors, leaving a large gap compared with sparse methods for linear models, which ignore random effects. This paper closes the gap with a new $\ell_0$ regularized method for LMM subset selection that can run on datasets containing thousands of predictors in seconds to minutes. On the computational front, we develop a coordinate descent algorithm as our main workhorse and provide a guarantee of its convergence. We also develop a local search algorithm to help traverse the nonconvex optimization surface. Both algorithms readily extend to subset selection in generalized LMMs via a penalized quasi-likelihood approximation. On the statistical front, we provide a finite-sample bound on the Kullback-Leibler divergence of the new method. We then demonstrate its excellent performance in synthetic experiments and illustrate its utility on two datasets from biology and journalism.
Music performances, characterized by dense and continuous audio as well as seamless audio-visual integration, present unique challenges for multimodal scene understanding and reasoning. Recent Music Performance Audio-Visual Question Answering (Music AVQA) datasets have been proposed to reflect these challenges, highlighting the continued need for more effective integration of audio-visual representations in complex question answering. However, existing Music AVQA methods often rely on dense and unoptimized representations, leading to inefficiencies in the isolation of key information, the reduction of redundancy, and the prioritization of critical samples. To address these challenges, we introduce Sparsify, a sparse learning framework specifically designed for Music AVQA. It integrates three sparsification strategies into an end-to-end pipeline and achieves state-of-the-art performance on the Music AVQA datasets. In addition, it reduces training time by 28.32% compared to its fully trained dense counterpart while maintaining accuracy, demonstrating clear efficiency gains. To further improve data efficiency, we propose a key-subset selection algorithm that selects and uses approximately 25% of MUSIC-AVQA v2.0 training data and retains 70-80% of full-data performance across models.
Many model selection algorithms rely on sparse dictionary learning to provide interpretable and physics-based governing equations. The optimization algorithms typically use a hard thresholding process to enforce sparse activations in the model coefficients by removing library elements from consideration. By introducing an annealing scheme that reactivates a fraction of the removed terms with a cooling schedule, we are able to improve the performance of these sparse learning algorithms. We concentrate on two approaches to the optimization, SINDy, and an alternative using hard thresholding pursuit. We see in both cases that annealing can improve model accuracy. The effectiveness of annealing is demonstrated through comparisons on several nonlinear systems pulled from convective flows, excitable systems, and population dynamics. Finally we apply these algorithms to experimental data for projectile motion.
Thermal infrared (TIR) target tracking methods often adopt the correlation filter (CF) framework due to its computational efficiency. However, the low resolution of TIR images, along with tracking interference, significantly limits the perfor-mance of TIR trackers. To address these challenges, we introduce STARS, a novel sparse learning-based CF tracker that incorporates spatio-temporal regulari-zation and super-resolution reconstruction. First, we apply adaptive sparse filter-ing and temporal domain filtering to extract key features of the target while reduc-ing interference from background clutter and noise. Next, we introduce an edge-preserving sparse regularization method to stabilize target features and prevent excessive blurring. This regularization integrates multiple terms and employs the alternating direction method of multipliers to optimize the solution. Finally, we propose a gradient-enhanced super-resolution method to extract fine-grained TIR target features and improve the resolution of TIR images, addressing performance degradation in tracking caused by low-resolution sequences. To the best of our knowledge, STARS is the first to integrate super-resolution methods within a sparse learning-based CF framework. Extensive experiments on the LSOTB-TIR, PTB-TIR, VOT-TIR2015, and VOT-TIR2017 benchmarks demonstrate that STARS outperforms state-of-the-art trackers in terms of robustness.
Sparsified Learning is ubiquitous in many machine learning tasks. It aims to regularize the objective function by adding a penalization term that considers the constraints made on the learned parameters. This paper considers the problem of learning heavy-tailed LSP. We develop a flexible and robust sparse learning framework capable of handling heavy-tailed data with locally stationary behavior and propose concentration inequalities. We further provide non-asymptotic oracle inequalities for different types of sparsity, including $\ell_1$-norm and total variation penalization for the least square loss.
Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from high computational complexity and the inability to directly specify the rank. This work introduces a novel framework for low-rank matrix regression that addresses both unstructured and Hankel matrices. By decomposing the low-rank matrix into rank-1 bases, the problem is reformulated as an infinite-dimensional sparse learning problem. The least-angle regression (LAR) algorithm is then employed to solve this problem efficiently. For unstructured matrices, a closed-form LAR solution is derived with equivalence to a normalized nuclear norm regularization problem. For Hankel matrices, a real-valued polynomial basis reformulation enables effective LAR implementation. Two numerical examples in network modeling and system realization demonstrate that the proposed approach significantly outperforms the nuclear norm method in terms of estimation accuracy and computational efficiency.
Sparse regularization techniques are well-established in machine learning, yet their application in neural networks remains challenging due to the non-differentiability of penalties like the $L_1$ norm, which is incompatible with stochastic gradient descent. A promising alternative is shallow weight factorization, where weights are decomposed into two factors, allowing for smooth optimization of $L_1$-penalized neural networks by adding differentiable $L_2$ regularization to the factors. In this work, we introduce deep weight factorization, extending previous shallow approaches to more than two factors. We theoretically establish equivalence of our deep factorization with non-convex sparse regularization and analyze its impact on training dynamics and optimization. Due to the limitations posed by standard training practices, we propose a tailored initialization scheme and identify important learning rate requirements necessary for training factorized networks. We demonstrate the effectiveness of our deep weight factorization through experiments on various architectures and datasets, consistently outperforming its shallow counterpart and widely used pruning methods.
The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under system dynamics. In this paper, we study the Koopman operator via its action on the reproducing kernel Hilbert space (RKHS), and explore the mis-specified scenario where the dynamics may escape the chosen function space. We relate the Koopman operator to the conditional mean embeddings (CME) operator and then present an operator stochastic approximation algorithm to learn the Koopman operator iteratively with control over the complexity of the representation. We provide both asymptotic and finite-time last-iterate guarantees of the online sparse learning algorithm with trajectory-based sampling with an analysis that is substantially more involved than that for finite-dimensional stochastic approximation. Numerical examples confirm the effectiveness of the proposed algorithm.
Evolutionary sparse learning (ESL) uses a supervised machine learning approach, Least Absolute Shrinkage and Selection Operator (LASSO), to build models explaining the relationship between a hypothesis and the variation across genomic features (e.g., sites) in sequence alignments. ESL employs sparsity between and within the groups of genomic features (e.g., genomic loci) by using sparse-group LASSO. Although some software packages are available for performing sparse group LASSO, we found them less well-suited for processing and analyzing genome-scale data containing millions of features, such as bases. MyESL software fills the need for open-source software for conducting ESL analyses with facilities to pre-process the input hypotheses and large alignments, make LASSO flexible and computationally efficient, and post-process the output model to produce different metrics useful in functional or evolutionary genomics. MyESL can take phylogenetic trees and sequence alignments as input and transform them into numeric responses and features, respecetively. The model outputs are processed into user-friendly text and graphical files. The computational core of MyESL is written in C++, which offers model building with or without group sparsity, while the pre- and post-processing of inputs and model outputs is performed using customized functions written in Python. One of its applications in phylogenomics showcases the utility of MyESL. Our analysis of empirical genome-scale datasets shows that MyESL can build evolutionary models quickly and efficiently on a personal desktop, while other computational packages were unable due to their prohibitive requirements of computational resources and time. MyESL is available for Python environments on Linux and distributed as a standalone application for Windows and macOS. It is available from https://github.com/kumarlabgit/MyESL.
Pruning of deep neural networks has been an effective technique for reducing model size while preserving most of the performance of dense networks, crucial for deploying models on memory and power-constrained devices. While recent sparse learning methods have shown promising performance up to moderate sparsity levels such as 95% and 98%, accuracy quickly deteriorates when pushing sparsities to extreme levels. Obtaining sparse networks at such extreme sparsity levels presents unique challenges, such as fragile gradient flow and heightened risk of layer collapse. In this work, we explore network performance beyond the commonly studied sparsities, and propose a collection of techniques that enable the continuous learning of networks without accuracy collapse even at extreme sparsities, including 99.90%, 99.95% and 99.99% on ResNet architectures. Our approach combines 1) Dynamic ReLU phasing, where DyReLU initially allows for richer parameter exploration before being gradually replaced by standard ReLU, 2) weight sharing which reuses parameters within a residual layer while maintaining the same number of learnable parameters, and 3) cyclic sparsity, where both sparsity levels and sparsity patterns evolve dynamically throughout training to better encourage parameter exploration. We evaluate our method, which we term Extreme Adaptive Sparse Training (EAST) at extreme sparsities using ResNet-34 and ResNet-50 on CIFAR-10, CIFAR-100, and ImageNet, achieving significant performance improvements over state-of-the-art methods we compared with.
The recent rapid advancement of machine learning has been driven by increasingly powerful models with the growing availability of training data and computational resources. However, real-time decision-making tasks with limited time and sparse learning signals remain challenging. One way of improving the learning speed and performance of these agents is to leverage human guidance. In this work, we introduce GUIDE, a framework for real-time human-guided reinforcement learning by enabling continuous human feedback and grounding such feedback into dense rewards to accelerate policy learning. Additionally, our method features a simulated feedback module that learns and replicates human feedback patterns in an online fashion, effectively reducing the need for human input while allowing continual training. We demonstrate the performance of our framework on challenging tasks with sparse rewards and visual observations. Our human study involving 50 subjects offers strong quantitative and qualitative evidence of the effectiveness of our approach. With only 10 minutes of human feedback, our algorithm achieves up to 30% increase in success rate compared to its RL baseline.
We address three key challenges in learning continuous kernel representations: computational efficiency, parameter efficiency, and spectral bias. Continuous kernels have shown significant potential, but their practical adoption is often limited by high computational and memory demands. Additionally, these methods are prone to spectral bias, which impedes their ability to capture high-frequency details. To overcome these limitations, we propose a novel approach that leverages sparse learning in the Fourier domain. Our method enables the efficient scaling of continuous kernels, drastically reduces computational and memory requirements, and mitigates spectral bias by exploiting the Gibbs phenomenon.
Direct speech translation (ST) models often struggle with rare words. Incorrect translation of these words can have severe consequences, impacting translation quality and user trust. While rare word translation is inherently challenging for neural models due to sparse learning signals, real-world scenarios often allow access to translations of past recordings on similar topics. To leverage these valuable resources, we propose a retrieval-and-demonstration approach to enhance rare word translation accuracy in direct ST models. First, we adapt existing ST models to incorporate retrieved examples for rare word translation, which allows the model to benefit from prepended examples, similar to in-context learning. We then develop a cross-modal (speech-to-speech, speech-to-text, text-to-text) retriever to locate suitable examples. We demonstrate that standard ST models can be effectively adapted to leverage examples for rare word translation, improving rare word translation accuracy over the baseline by 17.6% with gold examples and 8.5% with retrieved examples. Moreover, our speech-to-speech retrieval approach outperforms other modalities and exhibits higher robustness to unseen speakers. Our code is publicly available (https://github.com/SiqiLii/Retrieve-and-Demonstration-ST).
The quasi-potential is a key concept in stochastic systems as it accounts for the long-term behavior of the dynamics of such systems. It also allows us to estimate mean exit times from the attractors of the system, and transition rates between states. This is of significance in many applications across various areas such as physics, biology, ecology, and economy. Computation of the quasi-potential is often obtained via a functional minimization problem that can be challenging. This paper combines a sparse learning technique with action minimization methods in order to: (i) Identify the orthogonal decomposition of the deterministic vector field (drift) driving the stochastic dynamics; (ii) Determine the quasi-potential from this decomposition. This decomposition of the drift vector field into its gradient and orthogonal parts is accomplished with the help of a machine learning-based sparse identification technique. Specifically, the so-called sparse identification of non-linear dynamics (SINDy) [1] is applied to the most likely trajectory in a stochastic system (instanton) to learn the orthogonal decomposition of the drift. Consequently, the quasi-potential can be evaluated even at points outside the instanton path, allowing our method to provide the complete quasi-potential landscape from this single trajectory. Additionally, the orthogonal drift component obtained within our framework is important as a correction to the exponential decay of transition rates and exit times. We implemented the proposed approach in 2- and 3-D systems, covering various types of potential landscapes and attractors.
For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called "l0 norm" which counts the number of non-zero components in a vector, is a strong reliable mechanism of enforcing sparsity when incorporated into an optimization problem. However, in big data settings wherein noisy estimates of the gradient must be evaluated out of computational necessity, the literature is scant on methods that reliably converge. In this paper we present an approach towards solving expectation objective optimization problems with cardinality constraints. We prove convergence of the underlying stochastic process, and demonstrate the performance on two Machine Learning problems.
Schizophrenia is a serious psychiatric disorder. Its pathogenesis is not completely clear, making it difficult to treat patients precisely. Because of the complicated non-Euclidean network structure of the human brain, learning critical information from brain networks remains difficult. To effectively capture the topological information of brain neural networks, a novel multimodal graph attention network based on sparse interaction mechanism (Multi-SIGATnet) was proposed for SZ classification was proposed for SZ classification. Firstly, structural and functional information were fused into multimodal data to obtain more comprehensive and abundant features for patients with SZ. Subsequently, a sparse interaction mechanism was proposed to effectively extract salient features and enhance the feature representation capability. By enhancing the strong connections and weakening the weak connections between feature information based on an asymmetric convolutional network, high-order interactive features were captured. Moreover, sparse learning strategies were designed to filter out redundant connections to improve model performance. Finally, local and global features were updated in accordance with the topological features and connection weight constraints of the higher-order brain network, the features being projected to the classification target space for disorder classification. The effectiveness of the model is verified on the Center for Biomedical Research Excellence (COBRE) and University of California Los Angeles (UCLA) datasets, achieving 81.9\% and 75.8\% average accuracy, respectively, 4.6\% and 5.5\% higher than the graph attention network (GAT) method. Experiments showed that the Multi-SIGATnet method exhibited good performance in identifying SZ.
Recently, deep learning has made remarkable strides, especially with generative modeling, such as large language models and probabilistic diffusion models. However, training these models often involves significant computational resources, requiring billions of petaFLOPs. This high resource consumption results in substantial energy usage and a large carbon footprint, raising critical environmental concerns. Back-propagation (BP) is a major source of computational expense during training deep learning models. To advance research on energy-efficient training and allow for sparse learning on any machine and device, we propose a general, energy-efficient convolution module that can be seamlessly integrated into any deep learning architecture. Specifically, we introduce channel-wise sparsity with additional gradient selection schedulers during backward based on the assumption that BP is often dense and inefficient, which can lead to over-fitting and high computational consumption. Our experiments demonstrate that our approach reduces 40\% computations while potentially improving model performance, validated on image classification and generation tasks. This reduction can lead to significant energy savings and a lower carbon footprint during the research and development phases of large-scale AI systems. Additionally, our method mitigates over-fitting in a manner distinct from Dropout, allowing it to be combined with Dropout to further enhance model performance and reduce computational resource usage. Extensive experiments validate that our method generalizes to a variety of datasets and tasks and is compatible with a wide range of deep learning architectures and modules. Code is publicly available at https://github.com/lujiazho/ssProp.
Long-term time series forecasting (LTSF) has been widely applied in finance, traffic prediction, and other domains. Recently, patch-based transformers have emerged as a promising approach, segmenting data into sub-level patches that serve as input tokens. However, existing methods mostly rely on predetermined patch lengths, necessitating expert knowledge and posing challenges in capturing diverse characteristics across various scales. Moreover, time series data exhibit diverse variations and fluctuations across different temporal scales, which traditional approaches struggle to model effectively. In this paper, we propose a dynamic tokenizer with a dynamic sparse learning algorithm to capture diverse receptive fields and sparse patterns of time series data. In order to build hierarchical receptive fields, we develop a multi-scale Transformer model, coupled with multi-scale sequence extraction, capable of capturing multi-resolution features. Additionally, we introduce a group-aware rotary position encoding technique to enhance intra- and inter-group position awareness among representations across different temporal scales. Our proposed model, named DRFormer, is evaluated on various real-world datasets, and experimental results demonstrate its superiority compared to existing methods. Our code is available at: https://github.com/ruixindingECNU/DRFormer.
Learning performance data, such as correct or incorrect responses to questions in Intelligent Tutoring Systems (ITSs) is crucial for tracking and assessing the learners' progress and mastery of knowledge. However, the issue of data sparsity, characterized by unexplored questions and missing attempts, hampers accurate assessment and the provision of tailored, personalized instruction within ITSs. This paper proposes using the Generative Adversarial Imputation Networks (GAIN) framework to impute sparse learning performance data, reconstructed into a three-dimensional (3D) tensor representation across the dimensions of learners, questions and attempts. Our customized GAIN-based method computational process imputes sparse data in a 3D tensor space, significantly enhanced by convolutional neural networks for its input and output layers. This adaptation also includes the use of a least squares loss function for optimization and aligns the shapes of the input and output with the dimensions of the questions-attempts matrices along the learners' dimension. Through extensive experiments on six datasets from various ITSs, including AutoTutor, ASSISTments and MATHia, we demonstrate that the GAIN approach generally outperforms existing methods such as tensor factorization and other generative adversarial network (GAN) based approaches in terms of imputation accuracy. This finding enhances comprehensive learning data modeling and analytics in AI-based education.
Large language models (LLMs) have shown impressive capabilities across various tasks. However, training LLMs from scratch requires significant computational power and extensive memory capacity. Recent studies have explored low-rank structures on weights for efficient fine-tuning in terms of parameters and memory, either through low-rank adaptation or factorization. While effective for fine-tuning, low-rank structures are generally less suitable for pretraining because they restrict parameters to a low-dimensional subspace. In this work, we propose to parameterize the weights as a sum of low-rank and sparse matrices for pretraining, which we call SLTrain. The low-rank component is learned via matrix factorization, while for the sparse component, we employ a simple strategy of uniformly selecting the sparsity support at random and learning only the non-zero entries with the fixed support. While being simple, the random fixed-support sparse learning strategy significantly enhances pretraining when combined with low-rank learning. Our results show that SLTrain adds minimal extra parameters and memory costs compared to pretraining with low-rank parameterization, yet achieves substantially better performance, which is comparable to full-rank training. Remarkably, when combined with quantization and per-layer updates, SLTrain can reduce memory requirements by up to 73% when pretraining the LLaMA 7B model.