Recent research shows that the dynamics of an infinitely wide neural network (NN) trained by gradient descent can be characterized by Neural Tangent Kernel (NTK) \citep{jacot2018neural}. Under the squared loss, the infinite-width NN trained by gradient descent with an infinitely small learning rate is equivalent to kernel regression with NTK \citep{arora2019exact}. However, the equivalence is only known for ridge regression currently \citep{arora2019harnessing}, while the equivalence between NN and other kernel machines (KMs), e.g. support vector machine (SVM), remains unknown. Therefore, in this work, we propose to establish the equivalence between NN and SVM, and specifically, the infinitely wide NN trained by soft margin loss and the standard soft margin SVM with NTK trained by subgradient descent. Our main theoretical results include establishing the equivalence between NN and a broad family of $\ell_2$ regularized KMs with finite-width bounds, which cannot be handled by prior work, and showing that every finite-width NN trained by such regularized loss functions is approximately a KM. Furthermore, we demonstrate our theory can enable three practical applications, including (i) \textit{non-vacuous} generalization bound of NN via the corresponding KM; (ii) \textit{non-trivial} robustness certificate for the infinite-width NN (while existing robustness verification methods would provide vacuous bounds); (iii) intrinsically more robust infinite-width NNs than those from previous kernel regression. Our code for the experiments are available at \url{https://github.com/leslie-CH/equiv-nn-svm}.

The hidden layer takes the input in which the pattern might not be linearly separable and transform it into a new space that is more linearly separable. The hidden layer has higher dimensionality than the input layer because the pattern that is not linearly separable often needs to be transformed into higher-dimensional space to be more linearly separable. This is based on Cover's theorem on the separability of patterns, which states that a pattern that is transformed into a higher-dimensional space with nonlinear transformation is more likely to be linearly separable, therefore the number of neurons in the hidden layer should be greater than the number of the input neuron. With that said, the number of neurons in the hidden layer should be less than or equal to the number of samples in the training set. When the number of neurons in the hidden layer is equal to the number of samples in the training set, the model can be thought roughly equivalent to kernel learners such as kernel regression and kernel support vector machines.

SVM is an exciting algorithm and the concepts are relatively simple. You're looking for a complete Support Vector Machines course that teaches you everything you need to create a Support Vector Machines model in Python, right? You've found the right Support Vector Machines techniques course! How this course will help you? Why should you choose this course?

Myocardial infarction (MI) is the leading cause of mortality in the world that occurs due to a blockage of the coronary arteries feeding the myocardium. An early diagnosis of MI and its localization can mitigate the extent of myocardial damage by facilitating early therapeutic interventions. Following the blockage of a coronary artery, the regional wall motion abnormality (RWMA) of the ischemic myocardial segments is the earliest change to set in. Echocardiography is the fundamental tool to assess any RWMA. Assessing the motion of the left ventricle (LV) wall only from a single echocardiography view may lead to missing the diagnosis of MI as the RWMA may not be visible on that specific view. Therefore, in this study, we propose to fuse apical 4-chamber (A4C) and apical 2-chamber (A2C) views in which a total of 11 myocardial segments can be analyzed for MI detection. The proposed method first estimates the motion of the LV wall by Active Polynomials (APs), which extract and track the endocardial boundary to compute myocardial segment displacements. The features are extracted from the A4C and A2C view displacements, which are fused and fed into the classifiers to detect MI. The main contributions of this study are 1) creation of a new benchmark dataset by including both A4C and A2C views in a total of 260 echocardiography recordings, which is publicly shared with the research community, 2) improving the performance of the prior work of threshold-based APs by a Machine Learning based approach, and 3) a pioneer MI detection approach via multi-view echocardiography by fusing the information of A4C and A2C views. Experimental results show that the proposed method achieves 90.91% sensitivity and 86.36% precision for MI detection over multi-view echocardiography.

Motivated by neuroscientific and clinical applications, we empirically examine whether observational measures of information flow can suggest interventions. We do so by performing experiments on artificial neural networks in the context of fairness in machine learning, where the goal is to induce fairness in the system through interventions. Using our recently developed $M$-information flow framework, we measure the flow of information about the true label (responsible for accuracy, and hence desirable), and separately, the flow of information about a protected attribute (responsible for bias, and hence undesirable) on the edges of a trained neural network. We then compare the flow magnitudes against the effect of intervening on those edges by pruning. We show that pruning edges that carry larger information flows about the protected attribute reduces bias at the output to a greater extent. This demonstrates that $M$-information flow can meaningfully suggest targets for interventions, answering the title's question in the affirmative. We also evaluate bias-accuracy tradeoffs for different intervention strategies, to analyze how one might use estimates of desirable and undesirable information flows (here, accuracy and bias flows) to inform interventions that preserve the former while reducing the latter.

University campuses are essentially a microcosm of a city. They comprise diverse facilities such as residences, sport centres, lecture theatres, parking spaces, and public transport stops. Universities are under constant pressure to improve efficiencies while offering a better experience to various stakeholders including students, staff, and visitors. Nonetheless, anecdotal evidence indicates that campus assets are not being utilised efficiently, often due to the lack of data collection and analysis, thereby limiting the ability to make informed decisions on the allocation and management of resources. Advances in the Internet of Things (IoT) technologies that can sense and communicate data from the physical world, coupled with data analytics and Artificial intelligence (AI) that can predict usage patterns, have opened up new opportunities for organisations to lower cost and improve user experience. This thesis explores this opportunity via theory and experimentation using UNSW Sydney as a living laboratory.

An ensemble of decision trees is known as Random Forest. As suggested by Breiman, the strength of unstable learners and the diversity among them are the ensemble models' core strength. In this paper, we propose two approaches known as oblique and rotation double random forests. In the first approach, we propose a rotation based double random forest. In rotation based double random forests, transformation or rotation of the feature space is generated at each node. At each node different random feature subspace is chosen for evaluation, hence the transformation at each node is different. Different transformations result in better diversity among the base learners and hence, better generalization performance. With the double random forest as base learner, the data at each node is transformed via two different transformations namely, principal component analysis and linear discriminant analysis. In the second approach, we propose oblique double random forest. Decision trees in random forest and double random forest are univariate, and this results in the generation of axis parallel split which fails to capture the geometric structure of the data. Also, the standard random forest may not grow sufficiently large decision trees resulting in suboptimal performance. To capture the geometric properties and to grow the decision trees of sufficient depth, we propose oblique double random forest. The oblique double random forest models are multivariate decision trees. At each non-leaf node, multisurface proximal support vector machine generates the optimal plane for better generalization performance. Also, different regularization techniques (Tikhonov regularisation and axis-parallel split regularisation) are employed for tackling the small sample size problems in the decision trees of oblique double random forest.

Machine learning is a field of artificial intelligence in which a system is designed to learn automatically given a set of input data. After the system has learnt (we say that the system has been trained), we can use it to make predictions for new data, unseen before. This approach makes it possible to solve complex problems which are difficult or impossible to solve with traditional sequential programming. Recognizing handwritten text is a problem that traces 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.

We establish a broad methodological foundation for mixed-integer optimization with learned constraints. We propose an end-to-end pipeline for data-driven decision making in which constraints and objectives are directly learned from data using machine learning, and the trained models are embedded in an optimization formulation. We exploit the mixed-integer optimization-representability of many machine learning methods, including linear models, decision trees, ensembles, and multi-layer perceptrons. The consideration of multiple methods allows us to capture various underlying relationships between decisions, contextual variables, and outcomes. We also characterize a decision trust region using the convex hull of the observations, to ensure credible recommendations and avoid extrapolation. We efficiently incorporate this representation using column generation and clustering. In combination with domain-driven constraints and objective terms, the embedded models and trust region define a mixed-integer optimization problem for prescription generation. We implement this framework as a Python package (OptiCL) for practitioners. We demonstrate the method in both chemotherapy optimization and World Food Programme planning. The case studies illustrate the benefit of the framework in generating high-quality prescriptions, the value added by the trust region, the incorporation of multiple machine learning methods, and the inclusion of multiple learned constraints.

Solving Constraint Optimization Problems (COPs) can be dramatically simplified by boundary estimation, that is, providing tight boundaries of cost functions. By feeding a supervised Machine Learning (ML) model with data composed of known boundaries and extracted features of COPs, it is possible to train the model to estimate boundaries of a new COP instance. In this paper, we first give an overview of the existing body of knowledge on ML for Constraint Programming (CP) which learns from problem instances. Second, we introduce a boundary estimation framework that is applied as a tool to support a CP solver. Within this framework, different ML models are discussed and evaluated regarding their suitability for boundary estimation, and countermeasures to avoid unfeasible estimations that avoid the solver to find an optimal solution are shown. Third, we present an experimental study with distinct CP solvers on seven COPs. Our results show that near-optimal boundaries can be learned for these COPs with only little overhead. These estimated boundaries reduce the objective domain size by 60-88% and can help the solver to find near-optimal solutions early during search.