Cocalc Lecture10 Svm Dual Ipynb

In this lecture, we continue looking at Support Vector Machines (SVMs), and define a new formulation of the max-margin problem. Before we do that, we start with a general concept -- Lagrange duality. At a high level, a supervised machine learning problem has the following structure: We saw that maximizing the margin of a linear model amounts to solving the following optimization problem. min⁡θ,θ012∣∣θ∣∣2 subject to y(i)((x(i))⊤θ+θ0)≥1 for all i\begin{align*} \min_{\theta,\theta_0} \frac{1}{2}||\theta||^2 \; & \\ \text{subject to } \; & y^{(i)}((x^{(i)})^\top\theta+\theta_0)\geq 1 \; \text{for all $i$} \end{align*}θ,θ0​min​21​∣∣θ∣∣2subject to ​y(i)((x(i))⊤θ+θ0​)≥1for all i​ We are going to look at a different way of optimizing this objective.

But first, we start by defining Lagrange duality. There was an error while loading. Please reload this page. Support vector machines (SVMs) are a set of supervised learning methods used for classification, regression and outliers detection. Still effective in cases where number of dimensions is greater than the number of samples. Uses a subset of training points in the decision function (called support vectors), so it is also memory efficient.

Versatile: different Kernel functions can be specified for the decision function. Common kernels are provided, but it is also possible to specify custom kernels. If the number of features is much greater than the number of samples, avoid over-fitting in choosing Kernel functions and regularization term is crucial. There was an error while loading. Please reload this page. There was an error while loading.

Please reload this page. After completing this lab you will be able to: Use scikit-learn to Support Vector Machine to classify In this notebook, you will use SVM (Support Vector Machines) to build and train a model using human cell records, and classify cells to whether the samples are benign or malignant. SVM works by mapping data to a high-dimensional feature space so that data points can be categorized, even when the data are not otherwise linearly separable. A separator between the categories is found, then the data is transformed in such a way that the separator could be drawn as a hyperplane.

Following this, characteristics of new data can be used to predict the group to which a new record should belong. The ID field contains the patient identifiers. The characteristics of the cell samples from each patient are contained in fields Clump to Mit. The values are graded from 1 to 10, with 1 being the closest to benign.

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