Support Vector Machine(SVM) is a powerful classifier that works with both linear and non-linear data. If you have a n-dimensional space, then the dimension of the hyperplane will be (n-1). The goal of SVM is to find an optimal hyperplane that best separates our data so that distance from the nearest points in space to itself is maximized. To keep it simple, consider a road, which separates the left, right-side cars, buildings, pedestrians and makes the widest lane as possible. And those cars, buildings, really close to the street are the support vectors.

Introduction to Machine Learning:- What is Machine Learning?,

Breathing rate (BR), minute ventilation (VE), and other respiratory parameters are essential for real-time patient monitoring in many acute health conditions, such as asthma. The clinical standard for measuring respiration, namely Spirometry, is hardly suitable for continuous use. Wearables can track many physiological signals, like ECG and motion, yet not respiration. Deriving respiration from other modalities has become an area of active research. In this work, we infer respiratory parameters from wearable ECG and wrist motion signals. We propose a modular and generalizable classification-regression pipeline to utilize available context information, such as physical activity, in learning context-conditioned inference models. Morphological and power domain novel features from the wearable ECG are extracted to use with these models. Exploratory feature selection methods are incorporated in this pipeline to discover application-specific interpretable biomarkers. Using data from 15 subjects, we evaluate two implementations of the proposed pipeline: for inferring BR and VE. Each implementation compares generalized linear model, random forest, support vector machine, Gaussian process regression, and neighborhood component analysis as contextual regression models. Permutation, regularization, and relevance determination methods are used to rank the ECG features to identify robust ECG biomarkers across models and activities. This work demonstrates the potential of wearable sensors not only in continuous monitoring, but also in designing biomarker-driven preventive measures.

Understanding performance and prioritizing resources for the maintenance of the drinking-water pipe network throughout its life-cycle is a key part of water asset management. Renovation of this vital network is generally hindered by the difficulty or impossibility to gain physical access to the pipes. We study a statistical and machine learning framework for the prediction of water pipe failures. We employ classical and modern classifiers for a short-term prediction and survival analysis to provide a broader perspective and long-term forecast, usually needed for the economic analysis of the renovation. To enrich these models, we introduce new predictors based on water distribution domain knowledge and employ a modern oversampling technique to remedy the high imbalance coming from the few failures observed each year. For our case study, we use a dataset containing the failure records of all pipes within the water distribution network in Barcelona, Spain. The results shed light on the effect of important risk factors, such as pipe geometry, age, material, and soil cover, among others, and can help utility managers conduct more informed predictive maintenance tasks.

Are you ready to start your path to becoming a Machine Learning expert! Are you ready to train your machine like a father trains his son! A breakthrough in Machine Learning would be worth ten Microsofts." -Bill Gates There are lots of courses and lectures out there regarding Support Vector Machine. This course is truly a step-by-step. In every new tutorial we build on what had already learned and move one extra step forward and then we assign you a small task that is solved in the beginning of next video.

There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal matrices. In this work, we prove a general analytical formula for the reconstruction performance of convex generalized linear models, and go beyond such matrices by considering all rotationally-invariant data matrices with arbitrary bounded spectrum, proving a decade-old conjecture originally derived using the replica method from statistical physics. This is achieved by leveraging on state-of-the-art advances in message passing algorithms and the statistical properties of their iterates. Our proof is crucially based on the construction of converging sequences of an oracle multi-layer vector approximate message passing algorithm, where the convergence analysis is done by checking the stability of an equivalent dynamical system. Beyond its generality, our result also provides further insight into overparametrized non-linear models, a fundamental building block of modern machine learning. We illustrate our claim with numerical examples on mainstream learning methods such as logistic regression and linear support vector classifiers, showing excellent agreement between moderate size simulation and the asymptotic prediction.

Machine learning systems that rely on training data collected from untrusted sources are vulnerable to poisoning attacks, in which adversaries controlling some of the collected data are able to induce a corrupted model. In this paper, we consider poisoning attacks where there is an adversary who has a particular target classifier in mind and hopes to induce a classifier close to that target by adding as few poisoning points as possible. We propose an efficient poisoning attack based on online convex optimization. Unlike previous model-targeted poisoning attacks, our attack comes with provable convergence to any achievable target classifier. The distance from the induced classifier to the target classifier is inversely proportional to the square root of the number of poisoning points. We also provide a certified lower bound on the minimum number of poisoning points needed to achieve a given target classifier. We report on experiments showing our attack has performance that is similar to or better than the state-of-the-art attacks in terms of attack success rate and distance to the target model, while providing the advantages of provable convergence, and the efficiency benefits associated with being an online attack that can determine near-optimal poisoning points incrementally.

Elastography ultrasound (EUS) provides additional bio-mechanical information about lesion for B-mode ultrasound (BUS) in the diagnosis of breast cancers. However, joint utilization of both BUS and EUS is not popular due to the lack of EUS devices in rural hospitals, which arouses a novel modality imbalance problem in computer-aided diagnosis (CAD) for breast cancers. Current transfer learning (TL) pay little attention to this special issue of clinical modality imbalance, that is, the source domain (EUS modality) has fewer labeled samples than those in the target domain (BUS modality). Moreover, these TL methods cannot fully use the label information to explore the intrinsic relation between two modalities and then guide the promoted knowledge transfer. To this end, we propose a novel doubly supervised TL network (DDSTN) that integrates the Learning Using Privileged Information (LUPI) paradigm and the Maximum Mean Discrepancy (MMD) criterion into a unified deep TL framework. The proposed algorithm can not only make full use of the shared labels to effectively guide knowledge transfer by LUPI paradigm, but also perform additional supervised transfer between unpaired data. We further introduce the MMD criterion to enhance the knowledge transfer. The experimental results on the breast ultrasound dataset indicate that the proposed DDSTN outperforms all the compared state-of-the-art algorithms for the BUSbased CAD. Keywords: Ultrasound imaging, Breast cancer, Deep doubly supervised transfer learning, Support vector machine plus, Maximum mean discrepancy.

The main success stories of deep learning, starting with ImageNet, depend on convolutional networks, which on certain tasks perform significantly better than traditional shallow classifiers, such as support vector machines. Is there something special about deep convolutional networks that other learning machines do not possess? Recent results in approximation theory have shown that there is an exponential advantage of deep convolutional-like networks in approximating functions with hierarchical locality in their compositional structure. These mathematical results, however, do not say which tasks are expected to have input-output functions with hierarchical locality. Among all the possible hierarchically local tasks in vision, text and speech we explore a few of them experimentally by studying how they are affected by disrupting locality in the input images. We also discuss a taxonomy of tasks ranging from local, to hierarchically local, to global and make predictions about the type of networks required to perform efficiently on these different types of tasks.

We investigate how the training curve of isotropic kernel methods depends on the symmetry of the task to be learned, in several settings. (i) We consider a regression task, where the target function is a Gaussian random field that depends only on $d_\parallel$ variables, fewer than the input dimension $d$. We compute the expected test error $\epsilon$ that follows $\epsilon\sim p^{-\beta}$ where $p$ is the size of the training set. We find that $\beta\sim\frac{1}{d}$ independently of $d_\parallel$, supporting previous findings that the presence of invariants does not resolve the curse of dimensionality for kernel regression. (ii) Next we consider support-vector binary classification and introduce the {\it stripe model} where the data label depends on a single coordinate $y(\underline x) = y(x_1)$, corresponding to parallel decision boundaries separating labels of different signs, and consider that there is no margin at these interfaces. We argue and confirm numerically that for large bandwidth, $\beta = \frac{d-1+\xi}{3d-3+\xi}$, where $\xi\in (0,2)$ is the exponent characterizing the singularity of the kernel at the origin. This estimation improves classical bounds obtainable from Rademacher complexity. In this setting there is no curse of dimensionality since $\beta\rightarrow\frac{1}{3}$ as $d\rightarrow\infty$. (iii) We confirm these findings for the {\it spherical model} for which $y(\underline x) = y(|\!|\underline x|\!|)$. (iv) In the stripe model, we show that if the data are compressed along their invariants by some factor $\lambda$ (an operation believed to take place in deep networks), the test error is reduced by a factor $\lambda^{-\frac{2(d-1)}{3d-3+\xi}}$.