Classification with imbalanced data is a common challenge in data analysis, where certain classes (minority classes) account for a small fraction of the training data compared with other classes (majority classes). Classical statistical theory based on large-sample asymptotics and finite-sample corrections is often ineffective for high-dimensional data, leaving many overfitting phenomena in empirical machine learning unexplained. In this paper, we develop a statistical theory for high-dimensional imbalanced classification by investigating support vector machines and logistic regression. We find that dimensionality induces truncation or skewing effects on the logit distribution, which we characterize via a variational problem under high-dimensional asymptotics. In particular, for linearly separable data generated from a two-component Gaussian mixture model, the logits from each class follow a normal distribution $\mathsf{N}(0,1)$ on the testing set, but asymptotically follow a rectified normal distribution $\max\{\kappa, \mathsf{N}(0,1)\}$ on the training set -- which is a pervasive phenomenon we verified on tabular data, image data, and text data. This phenomenon explains why the minority class is more severely affected by overfitting. Further, we show that margin rebalancing, which incorporates class sizes into the loss function, is crucial for mitigating the accuracy drop for the minority class. Our theory also provides insights into the effects of overfitting on calibration and other uncertain quantification measures.

Restricted kernel machines (RKMs) have considerably improved generalization in machine learning. Recent advancements explored various techniques within the RKM framework, integrating kernel functions with least squares support vector machines (LSSVM) to mirror the energy function of restricted Boltzmann machines (RBM), leading to enhanced performance. However, RKMs may face challenges in generalization when dealing with unevenly distributed or complexly clustered data. Additionally, as the dataset size increases, the computational burden of managing high-dimensional feature spaces can become substantial, potentially hindering performance in large-scale datasets. To address these challenges, we propose twin restricted kernel machine (TRKM). TRKM combines the benefits of twin models with the robustness of the RKM framework to enhance classification and regression tasks. By leveraging the Fenchel-Young inequality, we introduce a novel conjugate feature duality, allowing the formulation of classification and regression problems in terms of dual variables. This duality provides an upper bound to the objective function of the TRKM problem, resulting in a new methodology under the RKM framework. The model uses an energy function similar to that of RBM, incorporating both visible and hidden variables corresponding to both classes. Additionally, the kernel trick is employed to map data into a high-dimensional feature space, where the model identifies an optimal separating hyperplane using a regularized least squares approach. Experiments on UCI and KEEL datasets confirm TRKM's superiority over baselines, showcasing its robustness and efficiency in handling complex data. Furthermore, We implemented the TRKM model on the brain age dataset, demonstrating its efficacy in predicting brain age.

Privacy-preserving network anomaly detection has become an essential area of research due to growing concerns over the protection of sensitive data. Traditional anomaly de- tection models often prioritize accuracy while neglecting the critical aspect of privacy. In this work, we propose a hybrid ensemble model that incorporates privacy-preserving techniques to address both detection accuracy and data protection. Our model combines the strengths of several machine learning algo- rithms, including K-Nearest Neighbors (KNN), Support Vector Machines (SVM), XGBoost, and Artificial Neural Networks (ANN), to create a robust system capable of identifying network anomalies while ensuring privacy. The proposed approach in- tegrates advanced preprocessing techniques that enhance data quality and address the challenges of small sample sizes and imbalanced datasets. By embedding privacy measures into the model design, our solution offers a significant advancement over existing methods, ensuring both enhanced detection performance and strong privacy safeguards.

Probabilities of causation play a crucial role in modern decision-making. This paper addresses the challenge of predicting probabilities of causation for subpopulations with insufficient data using machine learning models. Tian and Pearl first defined and derived tight bounds for three fundamental probabilities of causation: the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN). However, estimating these probabilities requires both experimental and observational distributions specific to each subpopulation, which are often unavailable or impractical to obtain with limited population-level data. We assume that the probabilities of causation for each subpopulation are determined by its characteristics. To estimate these probabilities for subpopulations with insufficient data, we propose using machine learning models that draw insights from subpopulations with sufficient data. Our evaluation of multiple machine learning models indicates that, given sufficient population-level data and an appropriate choice of machine learning model and activation function, PNS can be effectively predicted. Through simulation studies, we show that our multilayer perceptron (MLP) model with the Mish activation function achieves a mean absolute error (MAE) of approximately 0.02 in predicting PNS for 32,768 subpopulations using data from around 2,000 subpopulations.

The research paper empirically investigates several machine learning algorithms to forecast stock prices depending on insider trading information. Insider trading offers special insights into market sentiment, pointing to upcoming changes in stock prices. This study examines the effectiveness of algorithms like decision trees, random forests, support vector machines (SVM) with different kernels, and K-Means Clustering using a dataset of Tesla stock transactions. Examining past data from April 2020 to March 2023, this study focuses on how well these algorithms identify trends and forecast stock price fluctuations. The paper uses Recursive Feature Elimination (RFE) and feature importance analysis to optimize the feature set and, hence, increase prediction accuracy. While it requires substantially greater processing time than other models, SVM with the Radial Basis Function (RBF) kernel displays the best accuracy. This paper highlights the trade-offs between accuracy and efficiency in machine learning models and proposes the possibility of pooling multiple data sources to raise prediction performance. The results of this paper aim to help financial analysts and investors in choosing strong algorithms to optimize investment strategies.

Many applications of machine learning involve structured output with large domain, where learning of structured predictor is prohibitive due to repetitive calls to expensive inference oracle. In this work, we show that, by decomposing training of Structural Support Vector Machine (SVM) into a series of multiclass SVM problems connected through messages, one can replace expensive structured oracle with Factorwise Maximization Oracle (FMO) that allows efficient implementation of complexity sublinear to the factor domain. A Greedy Direction Method of Multiplier (GDMM) algorithm is proposed to exploit sparsity of messages which guarantees \epsilon sub-optimality after O(log(1/\epsilon)) passes of FMO calls. We conduct experiments on chain-structured problems and fully-connected problems of large output domains. The proposed approach is orders-of-magnitude faster than the state-of-the-art training algorithms for Structural SVM.

The learning of appropriate distance metrics is a critical problem in image classification and retrieval.

In this paper, we point out that there exist scaling and initialization problems in most existing multiple kernel learning (MKL) approaches, which employ the large margin principle to jointly learn both a kernel and an SVM classifier. The reason is that the margin itself can not well describe how good a kernel is due to the negligence of the scaling. We use the ratio between the margin and the radius of the minimum enclosing ball to measure the goodness of a kernel, and present a new minimization formulation for kernel learning. This formulation is invariant to scalings of learned kernels, and when learning linear combination of basis kernels it is also invariant to scalings of basis kernels and to the types (e.g., L

Restricted kernel machines (RKMs) have demonstrated a significant impact in enhancing generalization ability in the field of machine learning. Recent studies have introduced various methods within the RKM framework, combining kernel functions with the least squares support vector machine (LSSVM) in a manner similar to the energy function of restricted boltzmann machines (RBM), such that a better performance can be achieved. However, RKM's efficacy can be compromised by the presence of outliers and other forms of contamination within the dataset. These anomalies can skew the learning process, leading to less accurate and reliable outcomes. To address this critical issue and to ensure the robustness of the model, we propose the novel one-class RKM (OCRKM). In the framework of OCRKM, we employ an energy function akin to that of the RBM, which integrates both visible and hidden variables in a nonprobabilistic setting. The formulation of the proposed OCRKM facilitates the seamless integration of one-class classification method with the RKM, enhancing its capability to detect outliers and anomalies effectively. The proposed OCRKM model is evaluated over UCI benchmark datasets. Experimental findings and statistical analyses consistently emphasize the superior generalization capabilities of the proposed OCRKM model over baseline models across all scenarios.

Accurate monitoring of eating behavior is crucial for managing obesity and eating disorders such as bulimia nervosa. At the same time, existing methods rely on multiple and/or specialized sensors, greatly harming adherence and ultimately, the quality and continuity of data. This paper introduces a novel approach for estimating the weight of a bite, from a commercial smartwatch. Our publicly-available dataset contains smartwatch inertial data from ten participants, with manually annotated start and end times of each bite along with their corresponding weights from a smart scale, under semi-controlled conditions. The proposed method combines extracted behavioral features such as the time required to load the utensil with food, with statistical features of inertial signals, that serve as input to a Support Vector Regression model to estimate bite weights. Under a leave-one-subject-out cross-validation scheme, our approach achieves a mean absolute error (MAE) of 3.99 grams per bite. To contextualize this performance, we introduce the improvement metric, that measures the relative MAE difference compared to a baseline model. Our method demonstrates a 17.41% improvement, while the adapted state-of-the art method shows a -28.89% performance against that same baseline. The results presented in this work establish the feasibility of extracting meaningful bite weight estimates from commercial smartwatch inertial sensors alone, laying the groundwork for future accessible, non-invasive dietary monitoring systems.