The wide usage of Machine Learning (ML) has lead to research on the attack vectors and vulnerability of these systems. The defenses in this area are however still an open problem, and often lead to an arms race. We define a naive, secure classifier at test time and show that a Gaussian Process (GP) is an instance of this classifier given two assumptions: one concerns the distances in the training data, the other rejection at test time. Using these assumptions, we are able to show that a classifier is either secure, or generalizes and thus learns. Our analysis also points towards another factor influencing robustness, the curvature of the classifier. This connection is not unknown for linear models, but GP offer an ideal framework to study this relationship for nonlinear classifiers. We evaluate on five security and two computer vision datasets applying test and training time attacks and membership inference. We show that we only change which attacks are needed to succeed, instead of alleviating the threat. Only for membership inference, there is a setting in which attacks are unsuccessful (<10% increase in accuracy over random guess). Given these results, we define a classification scheme based on voting, ParGP. This allows us to decide how many points vote and how large the agreement on a class has to be. This ensures a classification output only in cases when there is evidence for a decision, where evidence is parametrized. We evaluate this scheme and obtain promising results.

We propose a new semiparametric approach to binary classification that exploits the modeling flexibility of sparse graphical models. Specifically, we assume that each class can be represented by a forest-structured graphical model. Under this assumption, the optimal classifier is linear in the log of the one- and two-dimensional marginal densities. Our proposed procedure non-parametrically estimates the univariate and bivariate marginal densities, maps each sample to the logarithm of these estimated densities and constructs a linear SVM in the transformed space. We prove convergence of the resulting classifier to an oracle SVM classifier and give finite sample bounds on its excess risk. Experiments with simulated and real data indicate that the resulting classifier is competitive with several popular methods across a range of applications.

Due to the advantage of achieving a better performance under weak regularization, elastic net has attracted wide attention in statistics, machine learning, bioinformatics, and other fields. In particular, a variation of the elastic net, adaptive elastic net (AEN), integrates the adaptive grouping effect. In this paper, we aim to develop a new algorithm: Adaptive Elastic Net with Conditional Mutual Information (AEN-CMI) that further improves AEN by incorporating conditional mutual information into the gene selection process. We apply this new algorithm to screen significant genes for two kinds of cancers: colon cancer and leukemia. Compared with other algorithms including Support Vector Machine, Classic Elastic Net and Adaptive Elastic Net, the proposed algorithm, AEN-CMI, obtains the best classification performance using the least number of genes.

In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a constrained optimization problem wherein the sum of the norm of the weights in each layer of the network is minimized, under the constraint of exactly fitting training data. It draws inspiration from support vector machines (SVMs), which are able to generalize well, despite often having an infinite number of free parameters in their primal form, and from recent theoretical generalization bounds on NNs which suggest that lower norm solutions generalize better. To solve this constrained optimization problem, our method employs Lagrange multipliers that act as integrators of error over training and identify `support vector'-like examples. The method can be implemented as a wrapper around gradient based methods and uses standard back-propagation of gradients from the NN for both regression and classification versions of the algorithm. We provide theoretical justifications for the effectiveness of this algorithm in comparison to early stopping and $L_2$-regularization using simple, analytically tractable settings. In particular, we show faster convergence to the max-margin hyperplane in a shallow network (compared to vanilla gradient descent); faster convergence to the minimum-norm solution in a linear chain (compared to $L_2$-regularization); and initialization-independent generalization performance in a deep linear network. Finally, using the MNIST dataset, we demonstrate that this algorithm can boost test accuracy and identify difficult examples in real-world datasets.

We show that gradient descent on full-width linear convolutional networks of depth $L$ converges to a linear predictor related to the $\ell_{2/L}$ bridge penalty in the frequency domain. This is in contrast to linearly fully connected networks, where gradient descent converges to the hard margin linear support vector machine solution, regardless of depth.

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce hyperbolic SVM, a hyperbolic formulation of support vector machine classifiers, and elucidate through new theoretical work its connection to the Euclidean counterpart. We demonstrate the performance improvement of hyperbolic SVM for multi-class prediction tasks on real-world complex networks as well as simulated datasets. Our work allows analytic pipelines that take the inherent hyperbolic geometry of the data into account in an end-to-end fashion without resorting to ill-fitting tools developed for Euclidean space.

This month we are delighted to have Professor Paul Walsh from CIT speaking at Cork AI. The talk will introduce Support vector machines (SVMs), which are supervised machine learning algorithms that are widely used for a range of real word problems. Key terms and concepts will be described and it will be shown how SVM algorithms can build linear and complex models that can accurately classify unseen data. In order to get the best machine learning performance, the tuning and evaluation of SVMs will also be demonstrated. Live demos and hands on coding opportunities will be provided and a real-world application will be show-cased.

This paper analyzes asymptotic performance of a regularized multi-task learning model where task parameters are optimized jointly. If tasks are closely related, empirical work suggests multi-task learning models to outperform single-task ones in finite sample cases. As data size grows indefinitely, we show the learned multi-classifier to optimize an average misclassification error function which depicts the risk of applying multi-task learning algorithm to making decisions. This technique conclusion demonstrates the regularized multi-task learning model to be able to produce reliable decision rule for each task in the sense that it will asymptotically converge to the corresponding Bayes rule. Also, we find the interaction effect between tasks vanishes as data size growing indefinitely, which is quite different from the behavior in finite sample cases.

Active Learning (AL) requires learners to retrain the classifier with the minimum human supervisions or labeling in the unlabeled data pool when the current training set is not enough. However, general AL sampling strategies with a few label support inevitably suffer from performance decrease. To identify which samples determine the performance of the classification hyperplane, Core Vector Machine (CVM) and Ball Vector Machine (BVM) use the geometry boundary points of each Minimum Enclosing Ball (MEB) to train the classification hypothesis. Their theoretical analysis and experimental results show that the improved classifiers not only converge faster but also obtain higher accuracies compared with Support Vector Machine (SVM). Inspired by this, we formulate the cluster boundary point detection issue as the MEB boundary problem after presenting a convincing proof of this observation. Because the enclosing ball boundary may have a high fitting ratio when it can not enclose the class tightly, we split the global ball problem into two kinds of small Local Minimum Enclosing Ball (LMEB): Boundary ball (B-ball) and Core ball (C-ball) to tackle its over-fitting problem. Through calculating the update of radius and center when extending the local ball space, we adopt the minimum update ball to obtain the geometric update optimization scheme of B-ball and C-ball. After proving their update relationship, we design the LEB (Local Enclosing Ball) algorithm using centers of B-ball of each class to detect the enclosing ball boundary points for AL sampling. Experimental and theoretical studies have shown that the classification accuracy, time, and space performance of our proposed method significantly are superior than the state-of-the-art algorithms.

Human lives are important. The decision to allow self-driving vehicles operate on our roads carries great weight. This has been a hot topic of debate between policy-makers, technologists and public safety institutions. The recent Uber Inc. self-driving car crash, resulting in the death of a pedestrian, has strengthened the argument that autonomous vehicle technology is still not ready for deployment on public roads. In this work, we analyze the Uber car crash and shed light on the question, "Could the Uber Car Crash have been avoided?". We apply state-of-the-art Computer Vision models to this highly practical scenario. More generally, our experimental results are an evaluation of various image enhancement and object recognition techniques for enabling pedestrian safety in low-lighting conditions using the Uber crash as a case study.