We prove that, under low noise assumptions, the support vector machine with $N\ll m$ random features (RFSVM) can achieve the learning rate faster than $O(1/\sqrt{m})$ on a training set with $m$ samples when an optimized feature map is used. Our work extends the previous fast rate analysis of random features method from least square loss to 0-1 loss. We also show that the reweighted feature selection method, which approximates the optimized feature map, helps improve the performance of RFSVM in experiments on a synthetic data set. Papers published at the Neural Information Processing Systems Conference.

In many classification problems, the input is represented as a set of features, e.g., the bag-of-words (BoW) representation of documents. Support vector machines (SVMs) are widely used tools for such classification problems. The performance of the SVMs is generally determined by whether kernel values between data points can be defined properly. However, SVMs for BoW representations have a major weakness in that the co-occurrence of different but semantically similar words cannot be reflected in the kernel calculation. To overcome the weakness, we propose a kernel-based discriminative classifier for BoW data, which we call the latent support measure machine (latent SMM).

A new Bayesian formulation is developed for nonlinear support vector machines (SVMs), based on a Gaussian process and with the SVM hinge loss expressed as a scaled mixture of normals. We then integrate the Bayesian SVM into a factor model, in which feature learning and nonlinear classifier design are performed jointly; almost all previous work on such discriminative feature learning has assumed a linear classifier. Inference is performed with expectation conditional maximization (ECM) and Markov Chain Monte Carlo (MCMC). Papers published at the Neural Information Processing Systems Conference.

We propose a structured prediction algorithm for object localization based on Support Vector Machines (SVMs) using privileged information. Privileged information provides useful high-level knowledge for image understanding and facilitates learning a reliable model even with a small number of training examples. In our setting, we assume that such information is available only at training time since it may be difficult to obtain from visual data accurately without human supervision. Our goal is to improve performance by incorporating privileged information into ordinary learning framework and adjusting model parameters for better generalization. We tackle object localization problem based on a novel structural SVM using privileged information, where an alternating loss-augmented inference procedure is employed to handle the term in the objective function corresponding to privileged information.

High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we investiage a broad class of sparse learning approaches formulated as linear programs parametrized by a {\em regularization factor}, and solve them by the parametric simplex method (PSM). PSM offers significant advantages over other competing methods: (1) PSM naturally obtains the complete solution path for all values of the regularization parameter; (2) PSM provides a high precision dual certificate stopping criterion; (3) PSM yields sparse solutions through very few iterations, and the solution sparsity significantly reduces the computational cost per iteration. Particularly, we demonstrate the superiority of PSM over various sparse learning approaches, including Dantzig selector for sparse linear regression, sparse support vector machine for sparse linear classification, and sparse differential network estimation. We then provide sufficient conditions under which PSM always outputs sparse solutions such that its computational performance can be significantly boosted.

Decision tree learning is a popular classification technique most commonly used in machine learning applications. Recent work has shown that decision trees can be used to represent provably-correct controllers concisely. Compared to representations using lookup tables or binary decision diagrams, decision trees are smaller and more explainable. We present dtControl, an easily extensible tool for representing memoryless controllers as decision trees. We give a comprehensive evaluation of various decision tree learning algorithms applied to 10 case studies arising out of correct-by-construction controller synthesis. These algorithms include two new techniques, one for using arbitrary linear binary classifiers in the decision tree learning, and one novel approach for determinizing controllers during the decision tree construction. In particular the latter turns out to be extremely efficient, yielding decision trees with a single-digit number of decision nodes on 5 of the case studies.

Deploying the multi-relational tensor structure of a high dimensional feature space, more efficiently improves the performance of machine learning algorithms. One encounters the \emph{curse of dimensionality}, and working with vectorized data fails to preserve the data structure. To mitigate the nonlinear relationship of tensor data more economically, we propose the \emph{Tensor Train Multi-way Multi-level Kernel (TT-MMK)}. This technique combines kernel filtering of the initial input data (\emph{Kernelized Tensor Train (KTT)}), stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine (\emph{SVM}) Kernel for revealing nonlinear relationships. We demonstrate numerically that the TT-MMK method is more reliable computationally, is less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification compared to similar tensorised SVM methods.

Machine Learning (ML) algorithms have been used for assessing soil quality parameters along with non-destructive methodologies. Among spectroscopic analytical methodologies, energy dispersive X-ray fluorescence (EDXRF) is one of the more quick, environmentally friendly and less expensive when compared to conventional methods. However, some challenges in EDXRF spectral data analysis still demand more efficient methods capable of providing accurate outcomes. Using Multi-target Regression (MTR) methods, multiple parameters can be predicted, and also taking advantage of inter-correlated parameters the overall predictive performance can be improved. In this study, we proposed the Multi-target Stacked Generalisation (MTSG), a novel MTR method relying on learning from different regressors arranged in stacking structure for a boosted outcome. We compared MTSG and 5 MTR methods for predicting 10 parameters of soil fertility. Random Forest and Support Vector Machine (with linear and radial kernels) were used as learning algorithms embedded into each MTR method. Results showed the superiority of MTR methods over the Single-target Regression (the traditional ML method), reducing the predictive error for 5 parameters. Particularly, MTSG obtained the lowest error for phosphorus, total organic carbon and cation exchange capacity. When observing the relative performance of Support Vector Machine with a radial kernel, the prediction of base saturation percentage was improved in 19%. Finally, the proposed method was able to reduce the average error from 0.67 (single-target) to 0.64 analysing all targets, representing a global improvement of 4.48%.

Systems developed in wearable devices with sensors onboard are widely used to collect data of humans and animals activities with the perspective of an on-board automatic classification of data. An interesting application of these systems is to support animals' behaviour monitoring gathered by sensors' data analysis. This is a challenging area and in particular with fixed memories capabilities because the devices should be able to operate autonomously for long periods before being retrieved by human operators, and being able to classify activities onboard can significantly improve their autonomy. In this paper, we focus on the identification of prey handling activity in seals (when the animal start attaching and biting the prey), which is one of the main movement that identifies a successful foraging activity. Data taken into consideration are streams of 3D accelerometers and depth sensors values collected by devices attached directly on seals. To analyse these data, we propose an automatic model based on Machine Learning (ML) algorithms. In particular, we compare the performance (in terms of accuracy and F1score) of three ML algorithms: Input Delay Neural Networks, Support Vector Machines, and Echo State Networks. We attend to the final aim of developing an automatic classifier on-board. For this purpose, in this paper, the comparison is performed concerning the performance obtained by each ML approach developed and its memory footprint. In the end, we highlight the advantage of using an ML algorithm, in terms of feasibility in wild animals' monitoring.

The 01 loss is robust to outliers and tolerant to noisy data compared to convex loss functions. We conjecture that the 01 loss may also be more robust to adversarial attacks. To study this empirically we have developed a stochastic coordinate descent algorithm for a linear 01 loss classifier and a single hidden layer 01 loss neural network. Due to the absence of the gradient we iteratively update coordinates on random subsets of the data for fixed epochs. We show our algorithms to be fast and comparable in accuracy to the linear support vector machine and logistic loss single hidden layer network for binary classification on several image benchmarks, thus establishing that our method is on-par in test accuracy with convex losses. We then subject them to accurately trained substitute model black box attacks on the same image benchmarks and find them to be more robust than convex counterparts. On CIFAR10 binary classification task between classes 0 and 1 with adversarial perturbation of 0.0625 we see that the MLP01 network loses 27\% in accuracy whereas the MLP-logistic counterpart loses 83\%. Similarly on STL10 and ImageNet binary classification between classes 0 and 1 the MLP01 network loses 21\% and 20\% while MLP-logistic loses 67\% and 45\% respectively. On MNIST that is a well-separable dataset we find MLP01 comparable to MLP-logistic and show under simulation how and why our 01 loss solver is less robust there. We then propose adversarial training for our linear 01 loss solver that significantly improves its robustness on MNIST and all other datasets and retains clean test accuracy. Finally we show practical applications of our method to deter traffic sign and facial recognition adversarial attacks. We discuss attacks with 01 loss, substitute model accuracy, and several future avenues like multiclass, 01 loss convolutions, and further adversarial training.