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#assignment #sdsc5003 题目链接 SDSC5003 - Question of Assignment 2 SDSC5003 - Assignment 2 Part 1: Relational Algebra (35 points) a. List the names and ages of employees who work in both the Hardware department and the Software department. (7 points) πename,age(Emp⋈eid(πeid(Works⋈didσdname=’Hardware’(Dept))∩πeid(Works⋈didσdname=’Software’(Dept))))\pi_{\text{ename}, \text{age}} \left( \text{Emp} \bowtie_{\text{eid}} \left( \pi_{\text{eid}} \left( \text{Works} \bowtie_{\text{did}} \sigma_{\text{dna...

#assignment #sdsc5003 原文 NOTE: The university policy on academic dishonesty and plagiarism (cheating) will be taken very seriously in this course. Everything submitted should be your own writing or coding. You must not let other students copy your work. Discussions of the assignment are okay, e.g. understanding the concepts involved. This assignment is an individual one. Upload your work as a single archive file with name A2-XXXX-YYYY.zip where XXXX is your name and YYYY is your student ID. ...

#sdsc6015 English / 中文 Mirror Descent 点击展开 Mirror Descent 复习内容 动机 考虑单纯形约束优化问题： min⁡x∈△df(x)\min_{x \in \triangle_d} f(x) x∈△d​min​f(x) 其中单纯形 △d:={x∈Rd:∑i=1dxi=1,xi≥0,∀i}\triangle_d := \{x \in \mathbb{R}^d : \sum_{i=1}^d x_i = 1, x_i \geq 0, \forall i\}△d​:={x∈Rd:∑i=1d​xi​=1,xi​≥0,∀i}。假设梯度无穷范数有界：∥∇f(x)∥∞=max⁡i=1,…,d∣[∇f(x)]i∣≤1\|\nabla f(x)\|_\infty = \max_{i=1,\ldots,d} |[\nabla f(x)]_i| \leq 1∥∇f(x)∥∞​=maxi=1,…,d​∣[∇f(x)]i​∣≤1。 符号说明：xxx 是优化变量，ddd 是维度，△d\triangle_d△d​ 是概率单纯形。 几何意义：单纯形是概率...

#sdsc6015 English / 中文 投影梯度下降 (Projected Gradient Descent) 投影梯度下降是处理约束优化问题的算法，通过梯度步后投影回可行集来确保约束满足。 约束优化问题定义 约束优化问题形式化定义为： min⁡f(x)subject tox∈X\begin{aligned} &\min f(x) \\ &\text{subject to}\quad x \in X \end{aligned} ​minf(x)subject tox∈X​ 其中： f:Rd→Rf: \mathbb{R}^d \rightarrow \mathbb{R}f:Rd→R 是目标函数 X⊆RdX \subseteq \mathbb{R}^dX⊆Rd 是一个闭凸集（closed convex set） x∈Rdx \in \mathbb{R}^dx∈Rd 是优化变量 几何意义：在满足约束 x∈Xx \in Xx∈X 的前提下，寻找使 f(x)f(x)f(x) 最小的点。 算法描述 投影梯度下降迭代步骤： For t=0,1,2,… ...

#assignment #sdsc6012

#assignment #sdsc6012

SDSC6012 - Assignment 1 #assignment #sdsc6012 Question 1 Trend Component Extraction (Moving Average Method) The trend component is extracted using the centered moving average method: Trendt=1k∑i=t−mt+mxi\text{Trend}_t = \frac{1}{k} \sum_{i=t-m}^{t+m} x_i Trendt​=k1​i=t−m∑t+m​xi​ Where: kkk is the window size (here set to 12, corresponding to the annual cycle) m=⌊k/2⌋m = \lfloor k/2 \rfloorm=⌊k/2⌋ (half-window width for centered moving average) Boundary handling: when t<mt < mt&...

SDSC6007 - Assignment 2 #assignment #sdsc6007 题目链接SDSC6007 - Question of Assignment 2

#assignment #sdsc6007

#sdsc5001 English / 中文 Simple Linear Regression Basic Setup Given data (x1,y1),…,(xn,yn)\left(x_{1}, y_{1}\right),\ldots,\left(x_{n}, y_{n}\right)(x1​,y1​),…,(xn​,yn​), where: xi∈Rx_{i} \in \mathbb{R}xi​∈R is the predictor variable (independent variable, input, feature) yi∈Ry_{i} \in \mathbb{R}yi​∈R is the response variable (dependent variable, output, outcome) The regression function is expressed as: y=f(x)+εy = f(x) + \varepsilon y=f(x)+ε The linear regression model assumes: f(x)=β0+β...