We develop a machine learning framework that can be applied to data sets derived from the trajectories of Hamilton's equations. The goal is to learn the phase space structures that play the governing role for phase space transport relevant to particular applications. Our focus is on learning reactive islands in two degrees-of-freedom Hamiltonian systems. Reactive islands are constructed from the stable and unstable manifolds of unstable periodic orbits and play the role of quantifying transition dynamics. We show that support vector machines (SVM) is an appropriate machine learning framework for this purpose as it provides an approach for finding the boundaries between qualitatively distinct dynamical behaviors, which is in the spirit of the phase space transport framework. We show how our method allows us to find reactive islands directly in the sense that we do not have to first compute unstable periodic orbits and their stable and unstable manifolds. We apply our approach to the H\'enon-Heiles Hamiltonian system, which is a benchmark system in the dynamical systems community. We discuss different sampling and learning approaches and their advantages and disadvantages.

Support Vector Regression(SVR) SVR is a powerful algorithm that allows us to choose how tolerant we are of errors, both through an acceptable error margin(ϵ) and through tuning our tolerance of falling outside that acceptable error rate. Instead of a simple line, it takes a tube of width epsilon(ϵ) which is an intensive tube. Here, the first part of the formula is used to minimize the coefficients whereas the second part of the formula is responsible for tuning the epsilon(ϵ). The graph on the left represents the regression fit line on linear regression models and the graph on the right represents the regression fit line on SVR. The points outside the Intensive Tube(ϵ) are knowns as support vectors which dictate the position of the Intensive Tube(ϵ).

In this hands-on project, we will train several classification algorithms such as Logistic Regression, Support Vector Machine, K-Nearest Neighbors, and Random Forest Classifier to predict the churn rate of Telecommunication Customers. Machine learning help companies analyze customer churn rate based on several factors such as services subscribed by customers, tenure rate, and payment method. Predicting churn rate is crucial for these companies because the cost of retaining an existing customer is far less than acquiring a new one. Note: This course works best for learners who are based in the North America region.

Inflammatory bowel disease (IBD), which includes ulcerative colitis (UC) and Crohn’s disease (CD), is an idiopathic condition related to a dysregulated immune response to commensal intestinal microflora in a genetically susceptible host. As a global disease, the morbidity of IBD reached a rate of 84.3 per 100,000 persons and reflected a continued gradual upward trajectory. The medical cost of IBD is also notably extremely high. For example, in Europe, it has €3,500 in CD and €2,000 in UC per patient per year, respectively. In addition, taking into account the work productivity loss and the reduced quality of life, the indirect costs are incalculable. In modern times, the diagnosis of IBD is still a subjective judgment based on laboratory tests and medical images. Its early diagnosis and intervention is therefore a challenging goal and also the key to control its progression. Artificial intelligence (AI)-assisted diagnosis and prognosis prediction has proven effective in many fields including gastroenterology. In this study, support vector machines were utilized to distinguish the significant features in IBD. As a result, the reliability of IBD diagnosis due to its impressive performance in classifying and addressing region problems was improved. Convolutional neural networks are advanced image processing algorithms that are currently in existence. Digestive endoscopic images can therefore be better understood by automatically detecting and classifying lesions. This study a...

Coastal water quality management is a public health concern, as poor coastal water quality can harbor pathogens that are dangerous to human health. Tourism-oriented countries need to actively monitor the condition of coastal water at tourist popular sites during the summer season. In this study, routine monitoring data of $Escherichia\ Coli$ and enterococci across 15 public beaches in the city of Rijeka, Croatia, were used to build machine learning models for predicting their levels based on environmental parameters as well as to investigate their relationships with environmental stressors. Gradient Boosting (Catboost, Xgboost), Random Forests, Support Vector Regression and Artificial Neural Networks were trained with measurements from all sampling sites and used to predict $E.\ Coli$ and enterococci values based on environmental features. The evaluation of stability and generalizability with 10-fold cross validation analysis of the machine learning models, showed that the Catboost algorithm performed best with R$^2$ values of 0.71 and 0.68 for predicting $E.\ Coli$ and enterococci, respectively, compared to other evaluated ML algorithms including Xgboost, Random Forests, Support Vector Regression and Artificial Neural Networks. We also use the SHapley Additive exPlanations technique to identify and interpret which features have the most predictive power. The results show that site salinity measured is the most important feature for forecasting both $E.\ Coli$ and enterococci levels. Finally, the spatial and temporal accuracy of both ML models were examined at sites with the lowest coastal water quality. The spatial $E. Coli$ and enterococci models achieved strong R$^2$ values of 0.85 and 0.83, while the temporal models achieved R$^2$ values of 0.74 and 0.67. The temporal model also achieved moderate R$^2$ values of 0.44 and 0.46 at a site with high coastal water quality.

Measuring soil health indicators is an important and challenging task that affects farmers' decisions on timing, placement, and quantity of fertilizers applied in the farms. Most existing methods to measure soil health indicators (SHIs) are in-lab wet chemistry or spectroscopy-based methods, which require significant human input and effort, time-consuming, costly, and are low-throughput in nature. To address this challenge, we develop an artificial intelligence (AI)-driven near real-time unmanned aerial vehicle (UAV)-based multispectral sensing (UMS) solution to estimate total nitrogen (TN) of the soil, an important macro-nutrient or SHI that directly affects the crop health. Accurate prediction of soil TN can significantly increase crop yield through informed decision making on the timing of seed planting, and fertilizer quantity and timing. We train two machine learning models including multi-layer perceptron and support vector machine to predict the soil nitrogen using a suite of data classes including multispectral characteristics of the soil and crops in red, near-infrared, and green spectral bands, computed vegetation indices, and environmental variables including air temperature and relative humidity.

We will train a support vector machine to predict whether a new patient has diabetes based on such measurements. In this one hour long project-based course, you will learn the basics of support vector machines using Python and scikit-learn. The dataset we are going to use comes from the National Institute of Diabetes and Digestive and Kidney Diseases, and contains anonymized diagnostic measurements for a set of female patients. We will train a support vector machine to predict whether a new patient has diabetes based on such measurements. By the end of this course, you will be able to model an existing dataset with the goal of making predictions about new data.

Support Vector Machine (SVM) is a supervised machine learning algorithm capable of performing classification, regression and even outlier detection. The linear SVM classifier works by drawing a straight line between two classes. This type of algorithm classifies output data and makes predictions. The output of this model is a set of visualized scattered plots separated with a straight line. You will learn the fundamental theory and practical illustrations behind Support Vector Machines and learn to fit, examine, and utilize supervised Classification models using SVM to classify data, using Python.

Systemic bias with respect to gender, race and ethnicity, often unconscious, is prevalent in datasets involving choices among individuals. Consequently, society has found it challenging to alleviate bias and achieve diversity in a way that maintains meritocracy in such settings. We propose (a) a novel optimization approach based on optimally flipping outcome labels and training classification models simultaneously to discover changes to be made in the selection process so as to achieve diversity without significantly affecting meritocracy, and (b) a novel implementation tool employing optimal classification trees to provide insights on which attributes of individuals lead to flipping of their labels, and to help make changes in the current selection processes in a manner understandable by human decision makers. We present case studies on three real-world datasets consisting of parole, admissions to the bar and lending decisions, and demonstrate that the price of diversity is low and sometimes negative, that is we can modify our selection processes in a way that enhances diversity without affecting meritocracy significantly, and sometimes improving it.

As a review summarizing what has been done (up to 2017) already exists, it is advisable to start from there. The paper written by Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe and Seth Lloyd, focuses on quantum basic linear algebra subroutines (BLAS) -- as Fourier transforms, finding eigenvectors and eigenvalues, etc -- which are heavily used in machine learning algorithms, highlighting the advantages of using quantum rather than classical hardware. Indeed, the achievements are mainly in computational speed, although discussions on quantum support vector machine and quantum kernel appears. There is a very good introduction to quantum annealing and quantum Boltzman machine. An updated version (2018) is available on arXiv, although you cannot expect an over-comprehensive summary as the field of quantum computing is having a revolution each week. Nevertheless, the authors are among the pioneers thinking about the combination of both fields.