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#sdsc6015 English / 中文 Mirror Descent Click to expand Mirror Descent review content Motivation Consider the simplex-constrained optimization problem: min⁡x∈△df(x)\min_{x \in \triangle_d} f(x) x∈△d​min​f(x) where the simplex △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}. Assume the gradient’s infinity norm is bounded: ∥∇f(x)∥∞=max⁡i=1,…,d∣[∇f(x)]i∣≤1\|\nabla f(x)\|_\infty = \max_{i=1,\ldots,d} |[...

#sdsc6015 English / 中文 Projected Gradient Descent Projected Gradient Descent is an algorithm for constrained optimization problems that ensures constraint satisfaction by projecting gradient steps back onto the feasible set. Constrained Optimization Problem Definition The constrained optimization problem is formally defined as: 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​ where: f:Rd→Rf: \mathbb{R}^d \righta...

#assignment #sdsc5001 题目链接SDSC5001 - Question of Assignment 2 Question 1 When the number of features p is large, there tends to be a deterioration in the performance of KNN and other local approaches that perform prediction using only observations that are near the test observation for which a prediction must be made. This phenomenon is known as the curse of dimensionality, and it ties into the fact that non-parametric approaches often perform poorly when p is large. We will now investigate t...

#assignment #sdsc5001 Question 1 When the number of features p is large, there tends to be a deterioration in the performance of KNN and other local approaches that perform prediction using only observations that are near the test observation for which a prediction must be made. This phenomenon is known as the curse of dimensionality, and it ties into the fact that non-parametric approaches often perform poorly when p is large. We will now investigate this curse. (a) Suppose tha...

#assignment #sdsc6015 题目链接SDSC6015 - Question of Assignment 2 Problem 1[10 marks] Prove that if the function f:Rd→Rf: \mathbb{R}^{d}\rightarrow \mathbb{R}f:Rd→R has a subgradient at every point in its domain, then fff is convex. Solution: Let x,y∈Rdx, y \in \mathbb{R}^dx,y∈Rd, λ∈[0,1]\lambda \in [0,1]λ∈[0,1], and define z=λx+(1−λ)yz = \lambda x + (1-\lambda)yz=λx+(1−λ)y. Since a subgradient exists at every point, for any gz∈∂f(z)g_z \in \partial f(z)gz​∈∂f(z), we have: f(x)≥f(z)+⟨gz,x−z⟩,f(y...

SDSC 5002 - Assignment 1 #assignment #sdsc5002

📅 TODO SDSC5001 - Assignment 2 SDSC6015 - Assignment 2 SDSC6007 - Assignment 2 SDSC5003 - Assignment 2 SDSC6012 - Assignment 1 SDSC5001 - Assignment 1 SDSC5002 - Assignment 1 SDSC5003 - Assignment 1 SDSC6007 - Assignment 1 SDSC6015 - Assignment 1 其他文件 总课表 作业清单 SDSC5001 Statistical Machine Learning I SDSC5001 课程信息 SDSC5001 课程 1-概率论与数理统计复习 SDSC5001 课程 2-数据探索 SDSC5001 课程 3-统计机器学习概述 SDSC5001 课程 4-线性回归 SDSC5002 Exploratory Data Analysis and Visualization SDSC5002 课程信息 SDSC5002 课程 2-EDA SDSC5003 S...

#assignment #sdsc6015

#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. ...