Accelerated Convergence for Counterfactual Learning to Rank

The multinomial logistic regression (MLR) model is widely used in statistics and machine learning. On the one hand, stochastic gradient descent (SGD) is the most common approach for determining the parameters of a such model in big data scenarios, due to its simplicity and low computational complexity property. Furthermore, SGD has proven convergence under reasonable conditions. However, SGD has slow sub-linear rates of convergence and it often reduces convergence speed due to the plateau phenomenon. On the other hand, stochastic natural gradient descent (SNGD), proposed by Amari, is a manifold optimization method shown to be Fisher efficient when it converges, but its convergence properties remain unproven and it is often computationally prohibitive for models with a large number of parameters. Here, we propose dual stochastic natural gradient descent (DSNGD), a stochastic optimization method for MLR based on manifold optimization concepts. In the discrete scenario, DSNGD (i) has linear per-iteration computational complexity in the number of parameters, and (ii) is proven to converge. To achieve (i) we leverage the dual flatness of the family of joint distributions for MLR to simplify computations. To ensure (ii) DSNGD builds on the foundational ideas of convergent stochastic natural gradient descent (CSNGD), a variant of SNGD with guaranteed convergence, using an independent sequence to construct a bounded approximation of the natural gradient. By generalizing a result from Sunehag et al., we prove that DSNGD converges in the discrete case and maintains linear computational complexity per iteration. Beyond its convergence property and linear computational complexity, DSNGD empirically demonstrates fast convergence comparable to SNGD, improves upon SGD performance, and exhibits stability where SNGD does not.

Disturbance rejection is a fundamental problem in control engineering, and there are many methods to achieve a good disturbance rejection. One of the standard methods for the disturbance rejection is to employ an integral compensator. This compensator integrates the error between the reference signal and the output, and use the integrated value with a specific coefficient as a compensating signal. In this work, we discuss the relationship between the machine learning theory and the integral compensation. We focus on single-input-single-output discrete-time time-invariant systems, and show that the integral compensation can be understood in the context of the machine learning in this case. In particular, the integral compensation is identical to the online optimization with the standard stochastic gradient descent [1]. The above idea gives two suggestions. First, the integral compensation may become faster by employing other types of stochastic gradient descent. Many algorithms of stochastic gradient descent have been proposed in the machine learning literature, and such algorithms may improve the classical integral compensation. Second, it may become possible to reject the time-invariant state-dependent disturbance. The modeling error is a typical example of such disturbance. By learning such a disturbance, the control performance for repetitive motions will be improved compared to the integral compensation. This presentation discusses the pros and cons of regarding the integral compensation as the stochastic gradient descent optimization.

Clickbait has been considered a problem in the modern age of technology, especially in Indonesia. Various attempts have been made to research clickbait detection, however, researches which use Indonesian data are relatively scarce compared to other languages such as English because the availability of Indonesian datasets are lacking. Backpropagation Neural Network was used in clickbait detection on article's title and has achieved quite good accuracy result, however there is still a chance to improve the accuracy. This paper shows the results of using a modified backpropagation neural network algorithm to detect clickbait using article titles when compared to the standard algorithm. The research compares the results of standard stochastic gradient descent algorithm, mini-batch gradient descent algorithm, and a version of stochastic gradient descent with Adam optimizer and three hidden layers. The results show that using Adam optimizer and three hidden layers in stochastic gradient descent algorithm significantly improves the results compared to the standard architecture. The modified algorithm shows a precision score of 78% and a recall and F1 score of 76%, where the standard algorithm has a precision score of 67% and a recall and F1 score of 66%. The resulting algorithm is then implemented to a desktop application, which is considered easy to use.

Optimization algorithms constitute essential components within artificial intelligence systems designed to enhance the diagnosis of cardiovascular diseases. In their absence, even structurally sound neural networks may fail to learn effectively from noisy or heterogeneous clinical datasets. This review focuses on two main categories of non-linear stochastic optimization methods: gradient-based algorithms—such as Stochastic Gradient Descent, Adaptive Gradient Algorithm, Root Mean Square Propagation, and Adaptive Moment Estimation—and gradient-free approaches, including Simulated Annealing, Metropolis-Hastings, and Swarm Intelligence algorithms. Among these, Adaptive Moment Estimation demonstrates robust and efficient convergence during neural network training, while Simulated Annealing proves effective in exploring a broad range of hyperparameter configurations, especially in scenarios involving uncertainty and physiological signal processing. Based on these complementary strengths, a hybrid optimization strategy is proposed, integrating both methods to address local refinement and global exploration in model development. Although no experimental results are included, the proposed framework is expected to outperform conventional techniques—such as logistic regression and standard gradient descent—by improving sensitivity, specificity, and model calibration, while also reducing overfitting and enhancing generalization. The resulting system is envisioned as a secure, web-based application incorporating interpretability and auditability features to support clinical decision-making.

In this work, we explore the limiting dynamics of deep neural networks trained with stochastic gradient descent (SGD). As observed previously, long after performance has converged, networks continue to move through parameter space by a process of anomalous diffusion in which distance traveled grows as a power law in the number of gradient updates with a nontrivial exponent. We reveal an intricate interaction among the hyperparameters of optimization, the structure in the gradient noise, and the Hessian matrix at the end of training that explains this anomalous diffusion. To build this understanding, we first derive a continuous-time model for SGD with finite learning rates and batch sizes as an underdamped Langevin equation. We study this equationin the setting of linear regression, where we can derive exact, analytic expressions for the phase-space dynamics of the parameters and their instantaneous velocities from initialization to stationarity. Using the Fokker-Planck equation, we show that the key ingredient driving these dynamics is not the original training loss but rather the combination of a modified loss, which implicitly regularizes the velocity, and probability currents that cause oscillations in phase space. We identify qualitative and quantitative predictions of this theory in the dynamics of a ResNet-18 model trained on ImageNet. Through the lens of statistical physics, we uncover a mechanistic origin for the anomalous limiting dynamics of deep neural networks trained with SGD. Understanding the limiting dynamics of SGD, and its dependence on various important hyperparameters like batch size, learning rate, and momentum, can serve as a basis for future work that can turn these insights into algorithmic gains.

FAST ONLINE TRAINING OF L1 SUPPORT VECTOR MACHINES By Gabriella Melki A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science at Virginia Commonwealth University. Virginia Commonwealth University, 2016. Directors: Vojislav Kecman, Alberto Cano Department of Computer Science This thesis proposes a novel experimental environment (non-linear stochastic gradient descent, NL-SGD), as well as a novel online learning algorithm (OL SVM), for solving a classic nonlinear Soft Margin L1 Support Vector Machine (SVM) problem using a Stochastic Gradient Descent (SGD) algorithm. The NL-SGD implementation has a unique method of random sampling and alpha calculations. The developed code produces a competitive accuracy and speed in comparison with the solutions of the Direct L2 SVM obtained by software for Minimal Norm SVM (MN-SVM) and Non-Negative Iterative Single Data Algorithm (NN-ISDA). The latter two algorithms have shown excellent performances on large datasets; which is why we chose to compare NL-SGD and OL SVM to them. All experiments have been done under strict double (nested) cross-validation, and the results are reported in terms of accuracy and CPU times. OL SVM has been implemented within MATLAB and is compared to the classic Sequential Minimal Optimization (SMO) algorithm implemented within MATLAB’s solver, fitcsvm. The experiments with OL SVM have been done using k-fold cross-validation and the results reported in % error and % speedup of CPU Time. viii

Efficiency of large-scale learning is a hot topic in both academic and industry. The stochastic gradient descent (SGD) algorithm, and its extension mini-batch SGD, allow the model to be updated without scanning the whole data set. However, the use of approximate gradient leads to the uncertainty issue, slowing down the decreasing of objective function. Furthermore, such uncertainty may result in a high frequency of meaningless update on the model, causing a communication issue in parallel learning environment. In this work, we develop a batch-adaptive stochastic gradient descent (BA-SGD) algorithm, which can dynamically choose a proper batch size as learning proceeds. Particularly on the basis of Taylor extension and central limit theorem, it models the decrease of objective value as a Gaussian random walk game with rebound. In this game, a heuristic strategy of determining batch size is adopted to maximize the utility of each incremental sampling. By evaluation on multiple real data sets, we demonstrate that by smartly choosing the batch size, the BA-SGD not only conserves the fast convergence of SGD algorithm but also avoids too frequent model updates.

目的 基于计算机的胸腔X线影像疾病检测和分类目前存在误诊率高，准确率低的问题。本文在视觉Transformer（vision Transformer，ViT）预训练模型的基础上，通过迁移学习方法，实现胸腔X线影像辅助诊断，提高诊断准确率和效率。方法 选用带有卷积神经网络（convolutional neural network，CNN）的ViT模型，其在超大规模自然图像数据集中进行了预训练；通过微调模型结构，使用预训练的ViT模型参数初始化主干网络，并迁移至胸腔X线影像数据集中再次训练，实现疾病多标签分类。结果 在IU X-Ray数据集中对ViT迁移学习前、后模型平均AUC（area under ROC curve）得分进行对比分析实验。结果表明，预训练ViT模型平均AUC得分为0.774，与不使用迁移学习相比提升了0.208。并针对模型结构和数据预处理进行了消融实验，对ViT中的注意力机制进行可视化，进一步验证了模型有效性。最后使用Chest X-Ray14和CheXpert数据集训练微调后的ViT模型，平均AUC得分为0.839和0.806，与对比方法相比分别有0.014～0.031的提升。结论 与其他方法相比，ViT模型胸腔X线影像的多标签分类精确度更高，且迁移学习可以在降低训练成本的同时提升ViT模型的分类性能和泛化性。消融实验与模型可视化表明，包含CNN结构的ViT模型能重点关注有意义的区域，高效获取胸腔X线影像的视觉特征。;Objective The chest X-ray-relevant screening and diagnostic method is essential for radiology nowadays. Most of chest X-ray images interpretation is still restricted by clinical experience and challenged for misdiagnose and missed diagnoses. To detect and identify one or more potential diseases in images automatically，it is beneficial for improving diagnostic efficiency and accuracy using computer-based technique. Compared to natural images，multiple lesions are challenged to be detected and distinguished accurately in a single image because abnormal areas have a small proportion and complex representations in chest X-ray images. Current convolutional neural network（CNN）based deep learning models have been widely used in the context of medical imaging. The structure of the CNN convolution kernel has sensitive to local detail information，and it is possible to extract richer image features. However，the convolution kernel cannot be used to get global information，and the features-extracted are restricted of redundant information like its relevance of background， muscles，and bones. The model’s performance in multi-label classification tasks are affected to a certain extent. At present，the vision Transformer（ViT）model has achieved its priorities in computer vision-related tasks. The ViT can be used to capture information simultaneously and effectively for multiple regions of the entire image. However，it is required to use large-scale dataset training to achieve good performance. Due to some factors like patient privacy and manual annotate costs，the size of the chest X-ray image data set has been limited. To reduce the model's dependence on data scale and improve the performance of multi-label classification，we develop the CNN-based ViT pre-training model in terms of the transfer learning method for diagnosis-assisted of chest X-ray image and multi-label classification. Method The CNN-based ViT model is pre-trained on a huge scale ground truth dataset，and it is used to obtain the initial parameters of the model. The model structure is fine-tuned according to the features of chest X-ray dataset. A 1×1 convolution layer is used to convert the chest X-ray images channels between 1 to 3. The number of output nodes of the linear layer in the classifier is balanced from 1 000 to the number of chest X-ray classification labels，and the Sigmoid is used as an activation function. The parameters of the backbone network are initialized in terms of the pre-trained ViT model parameters，and it is trained in the chest X-ray dataset after that to complete multi-label classification. The experiment is configured of Python3. 7 and PyTorch1. 8 to construct the model and RTX3090 GPU for training. Stochastic gradient descent（SGD）optimizer，binary cross-entropy（BCE）loss function，an initial learning rate of 1E-3，the cosine annealing learning rate decay are used. For training，each image is scaled to a size of 512×512 pixels，and a 224×224 pixels area and it is then cropped in random as the model input，and data augmentation is performed randomly by some of the flipping，perspective transformation， shearing，translation，zooming，and changing brightness. For testing，the chest X-ray image is scaled to 256×256 pixels and center crop a 224×224 area to input the trained model. Result The experiment is performed on the IU X-Ray，which is a small-scale chest X-ray dataset. This model is evaluated in quantitative using the average of area under ROC curve （AUC）scores across all classification labels. The results show that the average AUC score of the pre-trained ViT model is 0. 774. The accuracy and training efficiency of the non-pre-trained ViT model is dropped significantly. The average AUC score is reached to 0. 566 only，which is 0. 208 lower. In addition，the attention mechanism heat map is generated based on the ViT model，which can strengthen the interpretability of the model. A series of ablation experiments are carried out for data augmentation，model structure，and batch size design. The fine-tuned ViT model is trained on the Chest-Ray14 and CheXpert dataset as well. The average AUC score is reached to 0. 839 and 0. 806，which is optimized by 0. 014 and 0. 031. Conclusion A pre-trained ViT model is used for the multi-label classification of chest X-ray images via transfer learning. The experimental results illustrate that the ViT has its stronger multi-label classification performance in chest Xray images，and its attention mechanism is beneficial for lesions precision-focused like the interior of the chest cavity and the heart. Transfer learning is potential to improve the classification performance and model generalization of the ViT in small-scale datasets，and the training cost is reduced greatly. Ablation experiments demonstrate that the incorporated model of CNN and Transformer has its priority beyond single-structure model. Data enhancement and the batch size cutting can improve the performance of the model，but smaller scale of batch is still interlinked to longer training span. To improve the model's ability，we predict that future research direction can be focused on the extraction for complex disease and highlevel semantic information，such as their small lesions，disease location，and severity.

Biased outcomes in machine learning models can arise due to various factors, including limited training data, imbalanced class distribution, suboptimal training methodologies, and overfitting. In training neural networks with Stochastic Gradient Descent (SGD) and backpropagation, the choice of hyperparameters like learning rate and momentum is crucial to influencing the model’s performance. A comprehensive grid search study was conducted using static hyperparameters with standard SGD and dynamic hyperparameters with the Adam optimizer. The investigation focused on a multifaceted analysis across different tasks —- classification, segmentation, and detection — and was applied to four image-based applications: digit classification using the MNIST dataset, tuberculosis detection from chest X-ray images, lung segmentation in chest X-ray images, and the detection of malaria parasites in blood smear images. In the first comparative study on the MNIST dataset, the SGD algorithm consistently outperformed the Adam algorithm as noise levels increased. SGD held a slight advantage in accuracy over Adam in a noise-free environment. This advantage became more apparent as noise was introduced and increased to moderate levels. At high noise levels, both algorithms experienced a significant decline in performance, yet SGD maintained a relatively better accuracy compared to Adam. This trend underscored SGD’s superior ability to generalize across varying noise conditions. For TB detection in the second application, the DenseNet121 architecture was used, and it was found that Adam showed better performance on the larger TBX11K dataset. However, SGD outperformed Adam on a smaller subset of TBX11K. In the third comparative study for lung segmentation using COVID-19 and NLM datasets, SGD slightly outperformed Adam based on the mean and Hausdorff distances. In the case of malaria parasite detection using the YOLOv8 architecture, SGD and Adam optimizers showed varying performances across different conditions. Initially, both achieved high accuracies on the full dataset, with Adam slightly outperforming SGD. However, with decreasing dataset size, SGD maintained more consistent performance, while Adam’s accuracy fluctuated significantly. In noise tests, both showed equal accuracy on clean data, but under noise conditions, SGD maintained higher accuracies, suggesting better generalization capabilities. Further experiments assessed how well SGD and Adam could cope with domain shifts, mainly when using data from different countries. SGD’s generalization performance was superior to Adam’s performance in these experiments. In summary, although Adam is arguably the more popular of the two optimization techniques, SGD held its own in the experiments and showed superior performance when it came to generalization or classifying in noisy conditions.

We study the statistical properties of the dynamic trajectory of stochastic gradient descent (SGD). We approximate the mini-batch SGD and the momentum SGD as stochastic differential equations. We exploit the continuous formulation of SDE and the theory of Fokker–Planck equations to develop new results on the escaping phenomenon and the relationship with large batch and sharp minima. In particular, we find that the stochastic process solution tends to converge to flatter minima regardless of the batch size in the asymptotic regime. However, the convergence rate is rigorously proven to depend on the batch size. These results are validated empirically with various datasets and models.

Decentralized learning over a network with Nyström approximation using SGD

In the literature, there exists a number of blind signal recovery algorithms that are implemented as stochastic gradient descent (SGD)-based adaptive schemes. SGD typically has low complexity at the expense of slower convergence. On the other hand, packet-based data transmission in many practical digital communication systems makes it attractive to develop steepest descent (SD) implementation in order to speed-up convergence. This work aims at developing SD implementation of several well-known blind signal recovery algorithms for multi-channel equalisation and source separation. The authors SD formulation is more amenable to additional parametric and signal subspace constraint for faster convergence and superior performance.

In this article, we introduce gradient descent and stochastic gradient descent for solving large‐scale statistical and machine learning problems. We introduce in detail how to derive gradient descent and stochastic gradient descent algorithms, briefly highlight their convergence properties, and show how to apply them to solve statistical and machine learning problems. In the end, we also discuss some open problems when applying stochastic gradient descent to train large‐scale machine learning models.

Automatic classification of fruits is vital in packing and processing factories. In recent years many paradigms have been proposed to classify fruits from images. Gradient descent, being the backbone of most of the optimizers has been optimized frequently for fast convergence of cost function. In this paper, we have compared and analyzed the performance of the four different optimizers namely Gradient Descent, Stochastic Gradient Descent (SGD), RMSProp and Adam for the classification of oranges. The classifier with SGD with momentum=0.95 is 97.5% accurate in classifying the oranges. Different metrics precision, recall, F1 score, ROC-AUC have been evaluated which confirms the brilliance of the classifier. The trained model can now be used for classifying oranges on the production line in the processing industry.

The oxidation of volatile organic compounds (VOCs) affects particulate matter and oxidant levels in the troposphere, making it vital to simulate for climate models and to predict air quality. Full-complexity oxidation mechanisms for VOCs such as isoprene, however, are too large to be simulated in a 3-dimensional atmospheric chemical transport model. Reduced VOC oxidation mechanisms have been developed, but all must make a small number of reactions represent a much larger set, leading to imprecision in stoichiometric coefficients. Some of the sacrifice of accuracy incurred in the reduction process can be recuperated by optimizing the stoichiometric coefficients after reduction. In this work, we present Coefficient Optimization for Automated MOdel REduction (CO-AMORE), a new set of tools for the optimization of reduced mechanism stoichiometric coefficients using graph theory-assisted gradient descent. These methods include the application of gradient descent and two new algorithms for preprocessing coefficients: Anti-Community Clustering (ACC) and Bipartite Graph Sorting (BGS). Our application of gradient descent with data preprocessed using our ACC algorithm improved the accuracy of a reduced isoprene mechanism by up to 40% in a box model simulation. Gradient descent with data preprocessed using BGS was able to achieve similar levels of optimization as ACC across multiple mechanisms. In addition, ACC was over four times faster than standard gradient descent, showing the promise of this novel methodology. Optimized reduced mechanisms allow atmospheric models to be more accurate, enabling a better understanding of particulate matter sources and offering the potential to benefit public health.