Experiment 2: Logistic Regression and Newton’s Method August 29, 2018 1 Description In this exercise, you will use Newton’s Method to implement logistic regression on a classification problem. 2 Data college and 40 students who were not admitted. Each (x(i), y(i)) training example contains a student’s score on two standardized exams and a label of whether the student was admitted. Your task is to build build a binary classification model that estimates college admission chances based on a student’s scores on two exams. In your training data, the first column of your x array represents all Test 1 scores

此外，在附录中，我们提供了本书所涵盖的大多数数学知识的复习。大多数时候，我们会优先考虑直觉和想 法，而不是数学的严谨性。有许多很棒的书可以引导感兴趣的读者走得更远。Bela Bollobas的《线性分析》 (Bollobás, 1999) 对线性代数和函数分析进行了深入的研究。(Wasserman, 2013) 是一本很好的统计学指南。 如果读者以前没有使用过Python语言，那么可以仔细阅读这个Python教程3。 列的准确性，因为模型在开始生成新序列之前不再 需要记住整个序列。 • 多阶段设计。例如，存储器网络 (Sukhbaatar et al., 2015) 和神经编程器‐解释器 (Reed and De Freitas, 2015)。它们允许统计建模者描述用于推理的迭代方法。这些工具允许重复修改深度神经网络的内部状 态，从而执行推理链中的后续步骤，类似于处理器如何修改用于计算的存储器。 • 另一个关键的发展是生成对抗网络 legend(); 每条实线对应于骰子的6个值中的一个，并给出骰子在每组实验后出现值的估计概率。当我们通过更多的实 验获得更多的数据时，这6条实体曲线向真实概率收敛。 概率论公理 在处理骰子掷出时，我们将集合S = {1, 2, 3, 4, 5, 6} 称为样本空间（sample space）或结果空间（outcome space），其中每个元素都是结果（outcome）。事件（event）是一组给定样本空间的随机结果。例如，“看

point is: why are we talking about them in the same breadth as efficiency? To answer this question, let’s break down the two prominent ways to benchmark the model in the training phase namely sample efficiency achieves accuracy similar to the baseline, but does so in fewer epochs. We could ideally save an epoch’s worth of training time by terminating the training early, if we adopt this hypothetical sample efficient converge to the desired accuracy. We will cover it in detail later on in this chapter. But first, let’s get ourselves familiar with label efficiency. Label Efficiency The number of labeled examples required

macosx_10_10_intel.macosx_10_10_x86_64.whl (14.4MB) |████████████████████████████████| 14.4MB 2.8MB/s Keras 5 pandas pip install pandas We could see the following response: Collecting macosx_10_10_intel.macosx_10_10_x86_64.whl (14.4MB) |████████████████████████████████| 14.4MB 2.8MB/s matplotlib pip install matplotlib We could see the following response: Collecting matplotlib macosx_10_10_intel.macosx_10_10_x86_64.whl (14.4MB) |████████████████████████████████| 14.4MB 2.8MB/s scipy pip install scipy We could see the following response: Collecting scipy Downloading

20, 2023 1 / 29 Lecture 3: Logistic Regression 1 Classification 2 Logistic Regression 3 Newton’s Method 4 Multiclass Classification Feng Li (SDU) Logistic Regression September 20, 2023 2 / 29 Classification (SDU) Logistic Regression September 20, 2023 10 / 29 Logistic Regression: A Closer Look ... What’s the underlying decision rule in logistic regression? At the decision boundary, both classes are equiprobable; then p(y | x; θ) = 1 1 + exp(−yθTx) Assuming the training examples were generated independently, we de- fine the likelihood of the parameters as L(θ) = m � i=1 p(y(i) | x(i); θ) = m � i=1 (hθ(x(i)))y(i)(1

= N � i=1 K � k=1 zi,k∥xi − µk∥2 = ∥X − Zµ∥2 where X is N × D, Z is N × K and µ is K × D Let’s have a closer look X − Zµ = � ���� xT 1 xT 2... xT N � ���� − � ���� zT 1 zT 2... zT N � b)TS−1(a − b) (S is the Covariance ma- trix) Feng Li (SDU) K-Means December 28, 2021 32 / 46 Hierarchical Clustering (Contd.) How to compute the dissimilarity between two clusters R and S? Min-link or chaining (clusters can get very large) d(R, S) = min xR∈R,xS∈S d(xR, xS) Max-link or complete-link: results in small, round shaped clusters d(R, S) = max xR∈R,xS∈S d(xR, xS) Average-link: compromise between

Guidelines PyTorch Symbol Clearspace While our system encourages a flexible use of elements, it’s important to present the symbol in its entirety maintaining legibility and clarity. We use the reference for clear space surrounding the symbol. Please keep at least 1/2 distance of the symbol’s width at all times. 3 Brand Guidelines PyTorch Symbol Sizing When sizing or scaling the symbol Guidelines PyTorch Lockup The PyTorch wordmark is just as important as the symbol itself. It’s important for the wordmark to always be displayed in the typeface Freight Sans Regular, and to maintain

什么是卷积 主讲人：龙良曲 Feature Maps Feature maps Feature maps What’s wrong with Linear ▪ 4 Hidden Layers: [784, 256, 256, 256, 256, 10] ▪ 390K parameters ▪ 1.6MB memory ▪ 80386 http://slazebni.cs.illinois Receptive Field https://medium.freecodecamp.org/an-intuitive-guide-to-convolutional-neural- networks-260c2de0a050 Weight sharing ▪ ~60k parameters ▪ 6 Layers http://yann.lecun.com/exdb/publis/pdf/lecun-89e

Animation https://medium.freecodecamp.org/an-intuitive-guide-to-convolutional-neural- networks-260c2de0a050 Notation Input_channels: Kernel_channels: 2 ch Kernel_size: Stride: Padding: Multi-Kernels

PAPERT, et al. Perceptrons : An Introduction to Computational Geometry[J]. The MIT Press, 1969. [6] DE Rumelhart, Hinton G E, Williams R J. Learning Representations by Back Propagating Errors[J]. Nature