## Lecture 2: Linear Regression Feng Li Shandong University fli@sdu.edu.cn September 13, 2023 ## Lecture 2: Linear Regression  1 Supervised Learning: Regression and Classification  Linear Regression  6 A Probabilistic Interpretation to Linear Regression ## Supervised Learning • Regression: Predict a continuous value • Classification: Predict a discrete value,

# Lecture Notes on Linear Regression Feng Li fli@sdu.edu.cn Shandong University, China ## 1 Linear Regression Problem In regression problem, we aim at predicting a continuous target value given an feature vector is denoted by $ x \in R^{n} $ , while $ y \in R $ is the output variable. In linear regression models, the hypothesis function is defined by $$ h_{\theta}(x)=\theta_{n}x_{n}+\theta_{n- $$ J(\theta)=\frac{1}{2}\sum_{i=1}^{m}\left(h_{\theta}(x^{(i)})-y^{(i)}\right)^{2} $$ Our linear regression problem can be formulated as $$ \min_{\theta}J(\theta)=\frac{1}{2}\sum_{i=1}^{m}\left(\th

# Experiment 1: Linear Regression August 27, 2018 ## 1 Description This first exercise will give you practice with linear regression. These exercises have been extensively tested with Matlab, but they option in the installer, and available for Linux from Octave-Forge). ## 2 Linear Regression Recall that the linear regression model is $$ h_{\theta}(x)=\theta^{T}x=\sum_{j=0}^{n}\theta_{j}x_{j}, $$ “learning rate” based on which we can tune the convergence of the gradient descent. ## 3 2D Linear Regression We start a very simple case where n = 1. Download data1.zip, and extract the files (ex1x.dat

## Lecture 3: Logistic Regression Feng Li Shandong University fli@sdu.edu.cn September 20, 2023 ## Lecture 3: Logistic Regression  Logistic Regression  Newton's tumor)}\\1:\text{“Positive Class”(e.g., malignant tumor)}\end{cases} $$ ## Warm-Up What if applying linear regress to classification? ![Image](/uploads/documents/d/1/d/0/d1d0c1c4777b3147223dd9bee38b41a5/p4_1

## Linear Algebra with The Eigen C++ Library ## +24 ## DANIEL HANSON ## Outline • A short history – linear algebra and C++ (1998 – Present) • The Eigen C++ Template Library for Linear Algebra • Linear with Eigen ## Disclaimers/Caveats • This presentation is on solving problems using • The Eigen linear algebra library • stdBLAS in C++26 • Not affiliated with Eigen but have used it in financial programming 1998: • C++ growing in popularity • Wide adoption in financial programming • But, no support for linear algebra (pining for Fortran...) • Your options essentially were: • Write your own Matrix class

jpg)  ## How about Linear Equations $$ \cdot y=w*x+b $$ $$ ■1.567=w^{*}1+b $$ $$ ■3.043=w^{*}2+b $$ $$ \cdot W=1 jpg) ## Linear Regression Linear Regression - Logistic Regression Classification  ## 下一课时 实战Linear Regression ## Thank

## +23 ## std::Finalog: Linear Algebra Coming to Standard C++ ## MARK HOEMMEN ## 20 23 October 01 - 06 ## std::linalg: Linear Algebra Coming to Standard C++ Mark Hoemmen, NVIDIA | CppCon 2023 ![Im a969ea0c8/p3_1.jpg) ## Agenda Motivating example: Matrix multiply Where std::linalg fits in linear algebra's layers std::linalg builds on the C++ Standard Library std::linalg builds on the scaled(alpha, A), transposed(B), scaled(beta, C), C); ## Does a “linear algebra library” do linear algebra? Aspirational linearity |We use math words|We mean a computer representation|

## +23 ## Continuous Regression Testing for Safer and Faster Refactoring PEJMAN GHORBANZADE ## Continuous Regression Testing for Safer and Faster Refactoring  "Write tests. Not too many. Mostly integration." - Guillermo Rauch ## Continuous regression testing ## Continuously verifying that the software works as well as before, during the development

# 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 [Image](/uploads/documents/8/8/2/c/882c391243e0c52fc5514fe0c1a55576/p2_1.jpg) ## 4 Logistic Regression Recall that in logistic regression, the hypothesis function is $$ h_{\theta}(x)=g(\theta^{T}x)=\frac{1}{1+e^{ $ \epsilon $ , i.e. $$ |L^{+}(\theta)-L(\theta)|\leq\epsilon $$ Try to resolve the logistic regression problem using gradient descent method with the initialization $ \theta = 0 $ , and answer the

## PyTorch ## Logistic Regression 主讲人：龙良曲 ## Recap for continuous: $ y = xw + b $ • for probability output: $ y = \sigma(xw + b) $ σ: sigmoid or logistic ## Binary Classification interpret network output ∈ [0, 1] which is exactly what logistic function comes in! #### Goal v.s. Approach ## For regression: Goal: pred = y ■ Approach: minimize dist(pred, y) ## For classification: Goal: maximize benchmark since the number of correct is not continuous ### Q2. why call logistic regression use sigmoid - Controversial! MSE => regression - Cross Entropy => classification 0.7 0.7 0.3 ## Binary Classification