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.

A support vector machine (SVM) is a supervised machine learning model that uses classification algorithms for two-group classification problems. After giving an SVM model sets of labeled training data for each category, they're able to categorize new text. You're refining your training data, and maybe you've even tried stuff out using Naive Bayes. But now you're feeling confident in your dataset, and want to take it one step further. Enter Support Vector Machines (SVM): a fast and dependable classification algorithm that performs very well with a limited amount of data to analyze.

Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory performance for the categorical response, especially for the binary-response. To address this issue, we propose a novel estimation method of sufficient dimension reduction subspace (SDR subspace) using optimal transport. The proposed method, named principal optimal transport direction (POTD), estimates the basis of the SDR subspace using the principal directions of the optimal transport coupling between the data respecting different response categories. The proposed method also reveals the relationship among three seemingly irrelevant topics, i.e., sufficient dimension reduction, support vector machine, and optimal transport. We study the asymptotic properties of POTD and show that in the cases when the class labels contain no error, POTD estimates the SDR subspace exclusively. Empirical studies show POTD outperforms most of the state-of-the-art linear dimension reduction methods.