Lecture Notes on Support Vector Machine Feng Li fli@sdu.edu.cn Shandong University, China 1 Hyperplane and Margin In a n-dimensional space, a hyper plane is defined by ωT x + b = 0 (1) where ω ∈ Rn the margin is defined as γ = min i γ(i) (6) 1 ? ? ! ? ! Figure 1: Margin and hyperplane. 2 Support Vector Machine 2.1 Formulation The hyperplane actually serves as a decision boundary to differentiating samples are so-called support vector, i.e., the vectors “supporting” the margin boundaries. We can redefine ω by w = � s∈S αsy(s)x(s) where S denotes the set of the indices of the support vectors 4 Kernel

Lecture 6: Support Vector Machine Feng Li Shandong University fli@sdu.edu.cn December 28, 2021 Feng Li (SDU) SVM December 28, 2021 1 / 82 Outline 1 SVM: A Primal Form 2 Convex Optimization Review parallely along ω (b < 0 means in opposite direction) Feng Li (SDU) SVM December 28, 2021 3 / 82 Support Vector Machine A hyperplane based linear classifier defined by ω and b Prediction rule: y = sign(ωTx Scaling ! and " such that min& ' & !() & + " = 1 Feng Li (SDU) SVM December 28, 2021 14 / 82 Support Vector Machine (Primal Form) Maximizing 1/∥ω∥ is equivalent to minimizing ∥ω∥2 = ωTω min ω,b ωTω

network layers, deep learning optimizers, data loading utilities, and multi-gpu, and multi-node support. Functions are executed immediately instead of enqueued in a static graph, improving ease of use begin Before you can run an NGC deep learning framework container, your Docker ® environment must support NVIDIA GPUs. To run a container, issue the appropriate command as explained in Running A Container Container and specify the registry, repository, and tags. About this task On a system with GPU support for NGC containers, when you run a container, the following occurs: ‣ The Docker engine loads the image

more than two features? In those cases, we could use classical machine learning algorithms like the Support Vector Machine4 (SVM) to learn classifiers that would do this for us. We could rely on deep learning Lookup: Look up the embeddings for the inputs in the embedding table. 4 Support Vector Machine - https://en.wikipedia.org/wiki/Support-vector_machine 3. Train the model: Train the model for the task at hand5 Transformer, which is now showing great promise in computer vision applications as well! Learn Long-Term Dependencies Using Attention Imagine yourself in your favorite buffet restaurant. A variety of

Challenge Problems for Artificial Intelligence Imperfect Information Huge State and Action Space Long-Term Planning Temporal and Spatial Reasoning Adversarial Real-time Strategy Multiagent Cooperation

Linux (aarch64) CPU 支持 支持 支持 Mac (CPU) 支持 支持 支持 当前最新稳定版本是 Pytorch 1.9.0、长期支持版本是 Pytorch 1.8.2（LTS），此外Python语言支持版本3.6表示支持3.6.x版本， 其中 x 表示 3.6 版本下的各个小版本，依此类推 3.7、3.8 同样 如此。本书代码演示以 Python3.6.5 版本作为

1998)中的手写数字。当时，Yann LeCun发表了第一篇通过反向传播成功训练卷积神经网络的 研究，这项工作代表了十多年来神经网络研究开发的成果。 当时，LeNet取得了与支持向量机（support vector machines）性能相媲美的成果，成为监督学习的主流方 法。LeNet被广泛用于自动取款机（ATM）机中，帮助识别处理支票的数字。时至今日，一些自动取款机仍 在运行Yann 效果，但是在更大、更真实的数据集上训练卷积神经 网络的性能和可行性还有待研究。事实上，在上世纪90年代初到2012年之间的大部分时间里，神经网络往往 被其他机器学习方法超越，如支持向量机（support vector machines）。 在计算机视觉中，直接将神经网络与其他机器学习方法进行比较也许不公平。这是因为，卷积神经网络的输 入是由原始像素值或是经过简单预处理（例如居中、缩放）的像 Schmidhuber, J., & others (2001). Gradient flow in recurrent nets: the difficulty of learning long-term dependencies. [Hochreiter & Schmidhuber, 1997] Hochreiter, S., & Schmidhuber, J. (1997). Long short‐term

Experimental support Experimental support Experimental support Supported planned post 2.0 Supported Custom training loop Experimental support Experimental support Support planned post post 2.0 Support planned post 2.0 No support yet Supported Estimator API Limited Support Not supported Limited Support Limited Support Limited Support Limited Support SavedModel：生产级 TensorFlow 模型格式

支持向量机概述 01 支持向量机概述 02 线性可分支持向量机 03 线性支持向量机 04 线性不可分支持向量机 4 1.支持向量机概述 支 持 向 量 机 （ Support Vector Machine, SVM ） 是 一 类 按 监 督 学 习 （ supervised learning）方式对数据进行二元分类的广义线性 分类器（generalized linear 误的情 况。软间隔，就是允许一定量的样本分类错误。 软间隔 硬间隔 线性可分 线性不可分 6 支持向量 1.支持向量机概述 算法思想 找到集合边缘上的若干数据（称为 支持向量（Support Vector）） ，用这些点找出一个平面（称为决 策面），使得支持向量到该平面的 距离最大。 距离 7 1.支持向量机概述 背景知识 任意超平面可以用下面这个线性方程来描述： 大于50000，则使用支 持向量机会非常慢，解决方案是创造、增加更多的特征，然后使用逻辑回归 或不带核函数的支持向量机。 28 参考文献 [1] CORTES C, VAPNIK V. Support-vector networks[J]. Machine learning, 1995, 20(3): 273–297. [2] Andrew Ng. Machine Learning[EB/OL]

state that in this book, we have chosen to work with Tensorflow 2.0 (TF) because it has exhaustive support for building and deploying efficient models on devices ranging from TPUs to edge devices at the time would lead to a 32 / 8 = 4x reduction in space. This fits in well since there is near-universal support for unsigned and signed 8-bit integer data types. 4. The quantized weights are persisted with the addition and subtraction, these gains need to be evaluated in practical settings because they require support from the underlying hardware. Moreover, multiplications and divisions are cheaper at lower precisions