Machine learning algorithms, like logistic regression and support vector machines, are designed for two-class (binary) classification problems. As such, these algorithms must either be modified for multi-class (more than two) classification problems or not used at all. The Error-Correcting Output Codes method is a technique that allows a multi-class classification problem to be reframed as multiple binary classification problems, allowing the use of native binary classification models to be used directly. Unlike one-vs-rest and one-vs-one methods that offer a similar solution by dividing a multi-class classification problem into a fixed number of binary classification problems, the error-correcting output codes technique allows each class to be encoded as an arbitrary number of binary classification problems. When an overdetermined representation is used, it allows the extra models to act as "error-correction" predictions that can result in better predictive performance.

Error-Correcting Output Codes (ECOCs) offer a principled approach for combining simple binary classifiers into multiclass classifiers. In this paper, we investigate the problem of designing optimal ECOCs to achieve both nominal and adversarial accuracy using Support Vector Machines (SVMs) and binary deep learning models. In contrast to previous literature, we present an Integer Programming (IP) formulation to design minimal codebooks with desirable error correcting properties. Our work leverages the advances in IP solvers to generate codebooks with optimality guarantees. To achieve tractability, we exploit the underlying graph-theoretic structure of the constraint set in our IP formulation. This enables us to use edge clique covers to substantially reduce the constraint set. Our codebooks achieve a high nominal accuracy relative to standard codebooks (e.g., one-vs-all, one-vs-one, and dense/sparse codes). We also estimate the adversarial accuracy of our ECOC-based classifiers in a white-box setting. Our IP-generated codebooks provide non-trivial robustness to adversarial perturbations even without any adversarial training.

Diagnosis results are highly dependent on the volume of test set. To derive the most efficient test set, we propose several machine learning based methods to predict the minimum amount of test data that produces relatively accurate diagnosis. By collecting outputs from failing circuits, the feature matrix and label vector are generated, which involves the inference information of the test termination point. Thus we develop a prediction model to fit the data and determine when to terminate testing. The considered methods include LASSO and Support Vector Machine(SVM) where the relationship between goals(label) and predictors(feature matrix) are considered to be linear in LASSO and nonlinear in SVM. Numerical results show that SVM reaches a diagnosis accuracy of 90.4% while deducting the volume of test set by 35.24%.

Self Taught Machine Learning Engineer and Data Scientist.Love Data driven problem and AI,ML and DS. Recognizing handwritten text is a problem that can be traced back to the first automatic machines that needed to recognize individual characters in handwritten documents. Think about, for example, the ZIP codes on letters at the post office and the automation needed to recognize these five digits. Perfect recognition of these codes is necessary in order to sort mail automatically and efficiently. To address this issue in Python, the scikit-learn library provides a good example to better understand this technique, the issues involved, and the possibility of making predictions.

Continuous observation of climate indicators, such as trends in lake freezing, is important to understand the dynamics of the local and global climate system. Consequently, lake ice has been included among the Essential Climate Variables (ECVs) of the Global Climate Observing System (GCOS), and there is a need to set up operational monitoring capabilities. Multi-temporal satellite images and publicly available webcam streams are among the viable data sources to monitor lake ice. In this work we investigate machine learning-based image analysis as a tool to determine the spatio-temporal extent of ice on Swiss Alpine lakes as well as the ice-on and ice-off dates, from both multispectral optical satellite images (VIIRS and MODIS) and RGB webcam images. We model lake ice monitoring as a pixel-wise semantic segmentation problem, i.e., each pixel on the lake surface is classified to obtain a spatially explicit map of ice cover. We show experimentally that the proposed system produces consistently good results when tested on data from multiple winters and lakes. Our satellite-based method obtains mean Intersection-over-Union (mIoU) scores >93%, for both sensors. It also generalises well across lakes and winters with mIoU scores >78% and >80% respectively. On average, our webcam approach achieves mIoU values of 87% (approx.) and generalisation scores of 71% (approx.) and 69% (approx.) across different cameras and winters respectively. Additionally, we put forward a new benchmark dataset of webcam images (Photi-LakeIce) which includes data from two winters and three cameras.

Wasserstein \textbf{D}istributionally \textbf{R}obust \textbf{O}ptimization (DRO) is concerned with finding decisions that perform well on data that are drawn from the worst-case probability distribution within a Wasserstein ball centered at a certain nominal distribution. In recent years, it has been shown that various DRO formulations of learning models admit tractable convex reformulations. However, most existing works propose to solve these convex reformulations by general-purpose solvers, which are not well-suited for tackling large-scale problems. In this paper, we focus on a family of Wasserstein distributionally robust support vector machine (DRSVM) problems and propose two novel epigraphical projection-based incremental algorithms to solve them. The updates in each iteration of these algorithms can be computed in a highly efficient manner. Moreover, we show that the DRSVM problems considered in this paper satisfy a H\"olderian growth condition with explicitly determined growth exponents. Consequently, we are able to establish the convergence rates of the proposed incremental algorithms. Our numerical results indicate that the proposed methods are orders of magnitude faster than the state-of-the-art, and the performance gap grows considerably as the problem size increases.

In recent years, feature selection has become a challenging problem in several machine learning fields, such as classification problems. Support Vector Machine (SVM) is a well-known technique applied in classification tasks. Various methodologies have been proposed in the literature to select the most relevant features in SVM. Unfortunately, all of them either deal with the feature selection problem in the linear classification setting or propose ad-hoc approaches that are difficult to implement in practice. In contrast, we propose an embedded feature selection method based on a min-max optimization problem, where a trade-off between model complexity and classification accuracy is sought. By leveraging duality theory, we equivalently reformulate the min-max problem and solve it without further ado using off-the-shelf software for nonlinear optimization. The efficiency and usefulness of our approach are tested on several benchmark data sets in terms of accuracy, number of selected features and interpretability.

We study a natural extension of classical empirical risk minimization, where the hypothesis space is a random subspace of a given space. In particular, we consider possibly data dependent subspaces spanned by a random subset of the data, recovering as a special case Nystr\"om approaches for kernel methods. Considering random subspaces naturally leads to computational savings, but the question is whether the corresponding learning accuracy is degraded. These statistical-computational tradeoffs have been recently explored for the least squares loss and self-concordant loss functions, such as the logistic loss. Here, we work to extend these results to convex Lipschitz loss functions, that might not be smooth, such as the hinge loss used in support vector machines. This extension requires developing new proofs, that use different technical tools. Our main results show the existence of different settings, depending on how hard the learning problem is, for which computational efficiency can be improved with no loss in performance. Theoretical results are illustrated with simple numerical experiments.

For composite nonsmooth optimization problems, Forward-Backward algorithm achieves model identification (e.g. support identification for the Lasso) after a finite number of iterations, provided the objective function is regular enough. Results concerning coordinate descent are scarcer and model identification has only been shown for specific estimators, the support-vector machine for instance. In this work, we show that cyclic coordinate descent achieves model identification in finite time for a wide class of functions. In addition, we prove explicit local linear convergence rates for coordinate descent. Extensive experiments on various estimators and on real datasets demonstrate that these rates match well empirical results.

Bayesian optimization (BO) is a prominent approach to optimizing expensive-to-evaluate black-box functions. The massive computational capability of edge devices such as mobile phones, coupled with privacy concerns, has led to a surging interest in federated learning (FL) which focuses on collaborative training of deep neural networks (DNNs) via first-order optimization techniques. However, some common machine learning tasks such as hyperparameter tuning of DNNs lack access to gradients and thus require zeroth-order/black-box optimization. This hints at the possibility of extending BO to the FL setting (FBO) for agents to collaborate in these black-box optimization tasks. This paper presents federated Thompson sampling (FTS) which overcomes a number of key challenges of FBO and FL in a principled way: We (a) use random Fourier features to approximate the Gaussian process surrogate model used in BO, which naturally produces the parameters to be exchanged between agents, (b) design FTS based on Thompson sampling, which significantly reduces the number of parameters to be exchanged, and (c) provide a theoretical convergence guarantee that is robust against heterogeneous agents, which is a major challenge in FL and FBO. We empirically demonstrate the effectiveness of FTS in terms of communication efficiency, computational efficiency, and practical performance.