Deep Neural Networks are prone to learning spurious correlations embedded in the training data, leading to potentially biased predictions. This poses risks when deploying these models for high-stake decision-making, such as in medical applications. Current methods for post-hoc model correction either require input-level annotations which are only possible for spatially localized biases, or augment the latent feature space, thereby hoping to enforce the right reasons. We present a novel method for model correction on the concept level that explicitly reduces model sensitivity towards biases via gradient penalization. When modeling biases via Concept Activation Vectors, we highlight the importance of choosing robust directions, as traditional regression-based approaches such as Support Vector Machines tend to result in diverging directions. We effectively mitigate biases in controlled and real-world settings on the ISIC, Bone Age, ImageNet and CelebA datasets using VGG, ResNet and EfficientNet architectures. Code is available on https://github.com/frederikpahde/rrclarc.

Gaussian Radial Basis Function (RBF) Kernels are the most-often-employed kernels in artificial intelligence and machine learning routines for providing optimally-best results in contrast to their respective counter-parts. However, a little is known about the application of the Generalized Gaussian Radial Basis Function on various machine learning algorithms namely, kernel regression, support vector machine (SVM) and pattern-recognition via neural networks. The results that are yielded by Generalized Gaussian RBF in the kernel sense outperforms in stark contrast to Gaussian RBF Kernel, Sigmoid Function and ReLU Function. This manuscript demonstrates the application of the Generalized Gaussian RBF in the kernel sense on the aforementioned machine learning routines along with the comparisons against the aforementioned functions as well.

Classification and probability estimation have broad applications in modern machine learning and data science applications, including biology, medicine, engineering, and computer science. The recent development of a class of weighted Support Vector Machines (wSVMs) has shown great values in robustly predicting the class probability and classification for various problems with high accuracy. The current framework is based on the $\ell^2$-norm regularized binary wSVMs optimization problem, which only works with dense features and has poor performance at sparse features with redundant noise in most real applications. The sparse learning process requires a prescreen of the important variables for each binary wSVMs for accurately estimating pairwise conditional probability. In this paper, we proposed novel wSVMs frameworks that incorporate automatic variable selection with accurate probability estimation for sparse learning problems. We developed efficient algorithms for effective variable selection for solving either the $\ell^1$-norm or elastic net regularized binary wSVMs optimization problems. The binary class probability is then estimated either by the $\ell^2$-norm regularized wSVMs framework with selected variables or by elastic net regularized wSVMs directly. The two-step approach of $\ell^1$-norm followed by $\ell^2$-norm wSVMs show a great advantage in both automatic variable selection and reliable probability estimators with the most efficient time. The elastic net regularized wSVMs offer the best performance in terms of variable selection and probability estimation with the additional advantage of variable grouping in the compensation of more computation time for high dimensional problems. The proposed wSVMs-based sparse learning methods have wide applications and can be further extended to $K$-class problems through ensemble learning.

Counterfactual explanations have been widely studied in explainability, with a range of application dependent methods prominent in fairness, recourse and model understanding. The major shortcoming associated with these methods, however, is their inability to provide explanations beyond the local or instance-level. While many works touch upon the notion of a global explanation, typically suggesting to aggregate masses of local explanations in the hope of ascertaining global properties, few provide frameworks that are both reliable and computationally tractable. Meanwhile, practitioners are requesting more efficient and interactive explainability tools. We take this opportunity to propose Global & Efficient Counterfactual Explanations (GLOBE-CE), a flexible framework that tackles the reliability and scalability issues associated with current state-of-the-art, particularly on higher dimensional datasets and in the presence of continuous features. Furthermore, we provide a unique mathematical analysis of categorical feature translations, utilising it in our method. Experimental evaluation with publicly available datasets and user studies demonstrate that GLOBE-CE performs significantly better than the current state-of-the-art across multiple metrics (e.g., speed, reliability).

A smoothing algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an important measure of its cost for very large datasets. The algorithm uses smoothing for the hinge-loss function, and an active set approach for the $\ell^{1}$ penalty. The smoothing parameter $\alpha$ is initially large, but typically halved when the smoothed problem is solved to sufficient accuracy. Convergence theory is presented that shows $\mathcal{O}(1+\log(1+\log_+(1/\alpha)))$ guarded Newton steps for each value of $\alpha$ except for asymptotic bands $\alpha=\Theta(1)$ and $\alpha=\Theta(1/N)$, with only one Newton step provided $\eta\alpha\gg1/N$, where $N$ is the number of data points and the stopping criterion that the predicted reduction is less than $\eta\alpha$. The experimental results show that our algorithm is capable of strong test accuracy without sacrificing training speed.

Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to manually label these instances. Semi-supervised support vector machines (S3VMs) extend the well-known SVM classifiers to the semi-supervised approach, aiming at maximizing the margin between samples in the presence of unlabeled data. By leveraging both labeled and unlabeled data, S3VMs attempt to achieve better accuracy and robustness compared to traditional SVMs. Unfortunately, the resulting optimization problem is non-convex and hence difficult to solve exactly. In this paper, we present a new branch-and-cut approach for S3VMs using semidefinite programming (SDP) relaxations. We apply optimality-based bound tightening to bound the feasible set. Box constraints allow us to include valid inequalities, strengthening the lower bound. The resulting SDP relaxation provides bounds significantly stronger than the ones available in the literature. For the upper bound, instead, we define a local search exploiting the solution of the SDP relaxation. Computational results highlight the efficiency of the algorithm, showing its capability to solve instances with a number of data points 10 times larger than the ones solved in the literature.

Deep anomaly detection methods have become increasingly popular in recent years, with methods like Stacked Autoencoders, Variational Autoencoders, and Generative Adversarial Networks greatly improving the state-of-the-art. Other methods rely on augmenting classical models (such as the One-Class Support Vector Machine), by learning an appropriate kernel function using Neural Networks. Recent developments in representation learning by self-supervision are proving to be very beneficial in the context of anomaly detection. Inspired by the advancements in anomaly detection using self-supervised learning in the field of computer vision, this thesis aims to develop a method for detecting anomalies by exploiting pretext tasks tailored for text corpora. This approach greatly improves the state-of-the-art on two datasets, 20Newsgroups, and AG News, for both semi-supervised and unsupervised anomaly detection, thus proving the potential for self-supervised anomaly detectors in the field of natural language processing.

Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for its classically challenging representational capacity, notable improvements in average precision compared to classical counterparts were observed in previous studies. Conventional calculations of these kernels, however, present a quadratic time complexity concerning data size, posing challenges in practical applications. To mitigate this, we explore two distinct approaches: utilizing randomized measurements to evaluate the quantum kernel and implementing the variable subsampling ensemble method, both targeting linear time complexity. Experimental results demonstrate a substantial reduction in training and inference times by up to 95\% and 25\% respectively, employing these methods. Although unstable, the average precision of randomized measurements discernibly surpasses that of the classical Radial Basis Function kernel, suggesting a promising direction for further research in scalable, efficient quantum computing applications in machine learning.

This paper utilizes finite Fourier series to represent a time-continuous motion and proposes a novel planning method that adjusts the motion harmonics of each manipulator joint. Primarily, we sum the potential energy for collision detection and the kinetic energy up to calculate the Hamiltonian of the manipulator motion harmonics. Though the adaptive interior-point method is designed to modify the harmonics in its finite frequency domain, we still encounter the local minima due to the non-convexity of the collision field. In this way, we learn the collision field through a support vector machine with a Gaussian kernel, which is highly convex. The learning-based collision field is applied for Hamiltonian, and the experiment results show our method's high reliability and efficiency.

Support Vector Machine (SVM) stands out as a prominent machine learning technique widely applied in practical pattern recognition tasks. It achieves binary classification by maximizing the "margin", which represents the minimum distance between instances and the decision boundary. Although many efforts have been dedicated to expanding SVM for multi-class case through strategies such as one versus one and one versus the rest, satisfactory solutions remain to be developed. In this paper, we propose a novel method for multi-class SVM that incorporates pairwise class loss considerations and maximizes the minimum margin. Adhering to this concept, we embrace a new formulation that imparts heightened flexibility to multi-class SVM. Furthermore, the correlations between the proposed method and multiple forms of multi-class SVM are analyzed. The proposed regularizer, akin to the concept of "margin", can serve as a seamless enhancement over the softmax in deep learning, providing guidance for network parameter learning. Empirical evaluations demonstrate the effectiveness and superiority of our proposed method over existing multi-classification methods.Code is available at https://github.com/zz-haooo/M3SVM.