This paper investigates Support Vector Regression (SVR) in the context of the fundamental risk quadrangle theory, which links optimization, risk management, and statistical estimation. It is shown that both formulations of SVR, $\varepsilon$-SVR and $\nu$-SVR, correspond to the minimization of equivalent error measures (Vapnik error and CVaR norm, respectively) with a regularization penalty. These error measures, in turn, define the corresponding risk quadrangles. By constructing the fundamental risk quadrangle, which corresponds to SVR, we show that SVR is the asymptotically unbiased estimator of the average of two symmetric conditional quantiles. Further, we prove the equivalence of the $\varepsilon$-SVR and $\nu$-SVR in a general stochastic setting. Additionally, SVR is formulated as a regular deviation minimization problem with a regularization penalty. Finally, the dual formulation of SVR in the risk quadrangle framework is derived.

While investigating methods to predict small molecule potencies, we found random forests or support vector machines paired with extended-connectivity fingerprints (ECFP) consistently outperformed recently developed methods. A detailed investigation into regression algorithms and molecular fingerprints revealed gradient-boosted decision trees, particularly CatBoost, in conjunction with a combination of ECFP, Avalon, and ErG fingerprints, as well as 200 molecular properties, to be most effective. Incorporating a graph neural network fingerprint further enhanced performance. We successfully validated our model across 22 Therapeutics Data Commons ADMET benchmarks. Our findings underscore the significance of richer molecular representations for accurate property prediction.

Hyperbolic spaces have been quite popular in the recent past for representing hierarchically organized data. Further, several classification algorithms for data in these spaces have been proposed in the literature. These algorithms mainly use either hyperplanes or geodesics for decision boundaries in a large margin classifiers setting leading to a non-convex optimization problem. In this paper, we propose a novel large margin classifier based on horospherical decision boundaries that leads to a geodesically convex optimization problem that can be optimized using any Riemannian gradient descent technique guaranteeing a globally optimal solution.

Class imbalance is a major problem in many real world classification tasks. Due to the imbalance in the number of samples, the support vector machine (SVM) classifier gets biased toward the majority class. Furthermore, these samples are often observed with a certain degree of noise. Therefore, to remove these problems we propose a novel fuzzy based approach to deal with class imbalanced as well noisy datasets. We propose two approaches to address these problems. The first approach is based on the intuitionistic fuzzy membership, termed as robust energy-based intuitionistic fuzzy least squares twin support vector machine (IF-RELSTSVM). Furthermore, we introduce the concept of hyperplane-based fuzzy membership in our second approach, where the final classifier is termed as robust energy-based fuzzy least square twin support vector machine (F-RELSTSVM). By using this technique, the membership values are based on a projection based approach, where the data points are projected on the hyperplanes. The performance of the proposed algorithms is evaluated on several benchmark and synthetic datasets. The experimental results show that the proposed IF-RELSTSVM and F-RELSTSVM models outperform the baseline algorithms. Statistical tests are performed to check the significance of the proposed algorithms. The results show the applicability of the proposed algorithms on noisy as well as imbalanced datasets.

The COVID-19 pandemic has left a lasting impact on individuals, with many experiencing persistent symptoms, including inflammation, in the post-acute phase of the disease. Detecting and monitoring these inflammatory biomarkers is critical for timely intervention and improved patient outcomes. This study employs machine learning techniques to automate the identification of persistent inflammatory biomarkers in 290 post-COVID-19 patients, based on medical data collected from hospitals in Iraq. The data encompassed a wide array of clinical parameters, such as C-reactive protein and interleukin-6 levels, patient demographics, comorbidities, and treatment histories. Rigorous data preprocessing and feature selection processes were implemented to optimize the dataset for machine learning analysis. Various machine learning algorithms, including logistic regression, random forests, support vector machines, and gradient boosting, were deployed to construct predictive models. These models exhibited promising results, showcasing high accuracy and precision in the identification of patients with persistent inflammation. The findings of this study underscore the potential of machine learning in automating the detection of persistent inflammatory biomarkers in post-COVID-19 patients. These models can serve as valuable tools for healthcare providers, facilitating early diagnosis and personalized treatment strategies for individuals at risk of persistent inflammation, ultimately contributing to improved post-acute COVID-19 care and patient well-being. Keywords: COVID-19, post-COVID-19, inflammation, biomarkers, machine learning, early detection.

Understanding feature representation for deep neural networks (DNNs) remains an open question within the general field of explainable AI. We use principal component analysis (PCA) to study the performance of a k-nearest neighbors classifier (k-NN), nearest class-centers classifier (NCC), and support vector machines on the learned layer-wise representations of a ResNet-18 trained on CIFAR-10. We show that in certain layers, as little as 20% of the intermediate feature-space variance is necessary for high-accuracy classification and that across all layers, the first ~100 PCs completely determine the performance of the k-NN and NCC classifiers. We relate our findings to neural collapse and provide partial evidence for the related phenomenon of intermediate neural collapse. Our preliminary work provides three distinct yet interpretable surrogate models for feature representation with an affine linear model the best performing. We also show that leveraging several surrogate models affords us a clever method to estimate where neural collapse may initially occur within the DNN.

The possibility of automatically classifying high frequency sub-bottom acoustic reflections collected from an Autonomous Underwater Robot is investigated in this paper. In field surveys of Cobalt-rich Manganese Crusts (Mn-crusts), existing methods relies on visual confirmation of seafloor from images and thickness measurements using the sub-bottom probe. Using these visual classification results as ground truth, an autoencoder is trained to extract latent features from bundled acoustic reflections. A Support Vector Machine classifier is then trained to classify the latent space to idetify seafloor classes. Results from data collected from seafloor at 1500m deep regions of Mn-crust showed an accuracy of about 70%.

Controller Area Network bus systems within vehicular networks are not equipped with the tools necessary to ward off and protect themselves from modern cyber-security threats. Work has been done on using machine learning methods to detect and report these attacks, but common methods are not robust towards unknown attacks. These methods usually rely on there being a sufficient representation of attack data, which may not be available due to there either not being enough data present to adequately represent its distribution or the distribution itself is too diverse in nature for there to be a sufficient representation of it. With the use of one-class classification methods, this issue can be mitigated as only normal data is required to train a model for the detection of anomalous instances. Research has been done on the efficacy of these methods, most notably One-Class Support Vector Machine and Support Vector Data Description, but many new extensions of these works have been proposed and have yet to be tested for injection attacks in vehicular networks. In this paper, we investigate the performance of various state-of-the-art one-class classification methods for detecting injection attacks on Controller Area Network bus traffic. We investigate the effectiveness of these techniques on attacks launched on Controller Area Network buses from two different vehicles during normal operation and while being attacked. We observe that the Subspace Support Vector Data Description method outperformed all other tested methods with a Gmean of about 85%.

There is an ongoing effort to find quantum speedups for learning problems. Recently, [Y. Liu et al., Nat. Phys. $\textbf{17}$, 1013--1017 (2021)] have proven an exponential speedup for quantum support vector machines by leveraging the speedup of Shor's algorithm. We expand upon this result and identify a speedup utilizing Grover's algorithm in the kernel of a support vector machine. To show the practicality of the kernel structure we apply it to a problem related to pattern matching, providing a practical yet provable advantage. Moreover, we show that combining quantum computation in a preprocessing step with classical methods for classification further improves classifier performance.

In this paper, we present an adaptation of Newton's method for the optimization of Subspace Support Vector Data Description (S-SVDD). The objective of S-SVDD is to map the original data to a subspace optimized for one-class classification, and the iterative optimization process of data mapping and description in S-SVDD relies on gradient descent. However, gradient descent only utilizes first-order information, which may lead to suboptimal results. To address this limitation, we leverage Newton's method to enhance data mapping and data description for an improved optimization of subspace learning-based one-class classification. By incorporating this auxiliary information, Newton's method offers a more efficient strategy for subspace learning in one-class classification as compared to gradient-based optimization. The paper discusses the limitations of gradient descent and the advantages of using Newton's method in subspace learning for one-class classification tasks. We provide both linear and nonlinear formulations of Newton's method-based optimization for S-SVDD. In our experiments, we explored both the minimization and maximization strategies of the objective. The results demonstrate that the proposed optimization strategy outperforms the gradient-based S-SVDD in most cases.