Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we propose a tensor train (TT)-based kernel technique for the first time, and apply it to the conventional support vector machine (SVM) for image classification. Specifically, we propose a kernelized support tensor train machine that accepts tensorial input and preserves the intrinsic kernel property. The main contributions are threefold. First, we propose a TT-based feature mapping procedure that maintains the TT structure in the feature space. Second, we demonstrate two ways to construct the TT-based kernel function while considering consistency with the TT inner product and preservation of information. Third, we show that it is possible to apply different kernel functions on different data modes. In principle, our method tensorizes the standard SVM on its input structure and kernel mapping scheme. Extensive experiments are performed on real-world tensor data, which demonstrates the superiority of the proposed scheme under few-sample high-dimensional inputs.

In the post-industrial world, data science and analytics have gained paramount importance regarding digital data privacy. Improper methods of establishing privacy for accessible datasets can compromise large amounts of user data even if the adversary has a small amount of preliminary knowledge of a user. Many researchers have been developing high-level privacy-preserving mechanisms that also retain the statistical integrity of the data to apply to machine learning. Recent developments of differential privacy, such as the Laplace and Privelet mechanisms, drastically decrease the probability that an adversary can distinguish the elements in a data set and thus extract user information. In this paper, we develop three privacy-preserving mechanisms with the discrete M-band wavelet transform that embed noise into data. The first two methods (LS and LS+) add noise through a Laplace-Sigmoid distribution that multiplies Laplace-distributed values with the sigmoid function, and the third method utilizes pseudo-quantum steganography to embed noise into the data. We then show that our mechanisms successfully retain both differential privacy and learnability through statistical analysis in various machine learning environments.

Highly non-linear machine learning algorithms have the capacity to handle large, complex datasets. However, the predictive performance of a model usually critically depends on the choice of multiple hyperparameters. Optimizing these (often) constitutes an expensive black-box problem. Model-based optimization is one state-of-the-art method to address this problem. Furthermore, resulting models often lack interpretability, as models usually contain many active features with non-linear effects and higher-order interactions. One model-agnostic way to enhance interpretability is to enforce sparse solutions through feature selection. It is in many applications desirable to forego a small drop in performance for a substantial gain in sparseness, leading to a natural treatment of feature selection as a multi-objective optimization task. Despite the practical relevance of both hyperparameter optimization and feature selection, they are often carried out separately from each other, which is neither efficient, nor does it take possible interactions between hyperparameters and selected features into account. We present, discuss and compare two algorithmically different approaches for joint and multi-objective hyperparameter optimization and feature selection: The first uses multi-objective model-based optimization to tune a feature filter ensemble. The second is an evolutionary NSGA-II-based wrapper-approach to feature selection which incorporates specialized sampling, mutation and recombination operators for the joint decision space of included features and hyperparameter settings. We compare and discuss the approaches on a variety of benchmark tasks. While model-based optimization needs fewer objective evaluations to achieve good performance, it incurs significant overhead compared to the NSGA-II-based approach. The preferred choice depends on the cost of training the ML model on the given data.

Active learning methods, like uncertainty sampling, combined with probabilistic prediction techniques have achieved success in various problems like image classification and text classification. For more complex multivariate prediction tasks, the relationships between labels play an important role in designing structured classifiers with better performance. However, computational time complexity limits prevalent probabilistic methods from effectively supporting active learning. Specifically, while non-probabilistic methods based on structured support vector machines can be tractably applied to predicting bipartite matchings, conditional random fields are intractable for these structures. We propose an adversarial approach for active learning with structured prediction domains that is tractable for matching. We evaluate this approach algorithmically in an important structured prediction problems: object tracking in videos. We demonstrate better accuracy and computational efficiency for our proposed method.

We consider the problem of publicly releasing a dataset for support vector machine classification while not infringing on the privacy of data subjects (i.e., individuals whose private information is stored in the dataset). The dataset is systematically obfuscated using an additive noise for privacy protection. Motivated by the Cramer-Rao bound, inverse of the trace of the Fisher information matrix is used as a measure of the privacy. Conditions are established for ensuring that the classifier extracted from the original dataset and the obfuscated one are close to each other (capturing the utility). The optimal noise distribution is determined by maximizing a weighted sum of the measures of privacy and utility. The optimal privacy-preserving noise is proved to achieve local differential privacy. The results are generalized to a broader class of optimization-based supervised machine learning algorithms. Applicability of the methodology is demonstrated on multiple datasets.

In the 70s a novel branch of statistics emerged focusing its effort in selecting a function in the pattern recognition problem, which fulfils a definite relationship between the quality of the approximation and its complexity. These data-driven approaches are mainly devoted to problems of estimating dependencies with limited sample sizes and comprise all the empirical out-of sample generalization approaches, e.g. cross validation (CV) approaches. Although the latter are \emph{not designed for testing competing hypothesis or comparing different models} in neuroimaging, there are a number of theoretical developments within this theory which could be employed to derive a Statistical Agnostic (non-parametric) Mapping (SAM) at voxel or multi-voxel level. Moreover, SAMs could relieve i) the problem of instability in limited sample sizes when estimating the actual risk via the CV approaches, e.g. large error bars, and provide ii) an alternative way of Family-wise-error (FWE) corrected p-value maps in inferential statistics for hypothesis testing. In this sense, we propose a novel framework in neuroimaging based on concentration inequalities, which results in (i) a rigorous development for model validation with a small sample/dimension ratio, and (ii) a less-conservative procedure than FWE p-value correction, to determine the brain significance maps from the inferences made using small upper bounds of the actual risk.

This course is about artificial neural networks. Artificial intelligence and machine learning are getting more and more popular nowadays. In the beginning, other techniques such as Support Vector Machines outperformed neural networks, but in the 21th century neural networks again gain popularity. In spite of the slow training procedure, neural networks can be very powerful. In the first part of the course you will learn about the theoretical background of neural networks, later you will learn how to implement them.

Robust support vector machine (RSVM) has been shown to perform remarkably well to improve the generalization performance of support vector machine under the noisy environment. Unfortunately, in order to handle the non-convexity induced by ramp loss in RSVM, existing RSVM solvers often adopt the DC programming framework which is computationally inefficient for running multiple outer loops. This hinders the application of RSVM to large-scale problems. Safe sample screening that allows for the exclusion of training samples prior to or early in the training process is an effective method to greatly reduce computational time. However, existing safe sample screening algorithms are limited to convex optimization problems while RSVM is a non-convex problem. To address this challenge, in this paper, we propose two safe sample screening rules for RSVM based on the framework of concave-convex procedure (CCCP). Specifically, we provide screening rule for the inner solver of CCCP and another rule for propagating screened samples between two successive solvers of CCCP. To the best of our knowledge, this is the first work of safe sample screening to a non-convex optimization problem. More importantly, we provide the security guarantee to our sample screening rules to RSVM. Experimental results on a variety of benchmark datasets verify that our safe sample screening rules can significantly reduce the computational time.

--Operating envelope is an important concept in industrial operations. Accurate identification for operating envelope can be extremely beneficial to stakeholders as it provides a set of operational parameters that optimizes some key performance indicators (KPI) such as product quality, operational safety, equipment efficiency, environmental impact, etc. Given the importance, data-driven approaches for computing the operating envelope are gaining popularity. These approaches typically use classifiers such as support vector machines, to set the operating envelope by learning the boundary in the operational parameter spaces between the manually assigned'large KPI' and'small KPI' groups. One challenge to these approaches is that the assignment to these groups is often ad-hoc and hence arbitrary. However, a bigger challenge with these approaches is that they don't take into account two key features that are needed to operationalize operating envelopes: (i) interpretability of the envelope by the operator and (ii) implementability of the envelope from a practical standpoint. In this work, we propose a new definition for operating envelope which directly targets the expected magnitude of KPI (i.e., no need to arbitrarily bin the data instances into groups) and accounts for the interpretability and the implementability. We then propose a regularized'GA penalty' algorithm that outputs an envelope where the user can tradeoff between bias and variance. The validity of our proposed algorithm is demonstrated by two sets of simulation studies and an application to a real-world challenge in the mining processes of a flotation plant. In industrial operations, an important concept is that of the operating envelope. Conceptually, the operating envelope is a set of operational parameters, such that some KPI is optimized. In the industrial context, typical KPIs include product quality, operational safety, equipment efficiency, environmental impact, etc [1]-[4]. The operating envelope has wide application since it directly targets the business outcome and yields actionable recommendations in the operations space.

We present secml, an open-source Python library for secure and explainable machine learning. It implements the most popular attacks against machine learning, including not only test-time evasion attacks to generate adversarial examples against deep neural networks, but also training-time poisoning attacks against support vector machines and many other algorithms. These attacks enable evaluating the security of learning algorithms and of the corresponding defenses under both white-box and black-box threat models. To this end, secml provides built-in functions to compute security evaluation curves, showing how quickly classification performance decreases against increasing adversarial perturbations of the input data. secml also includes explainability methods to help understand why adversarial attacks succeed against a given model, by visualizing the most influential features and training prototypes contributing to each decision. It is distributed under the Apache License 2.0, and hosted at https://gitlab.com/secml/secml.