MY-ASSIGNMENTEXPERT™可以为您提供lse.ac.uk ST310 Machine Learning机器学习课程的代写代考和辅导服务！
这是伦敦政经学校机器学习课程的代写成功案例。
ST310课程简介
Teacher responsible
Dr Joshua Loftus
Availability
This course is compulsory on the BSc in Data Science. This course is available on the BSc in Actuarial Science, BSc in Mathematics with Economics, BSc in Mathematics, Statistics and Business and BSc in Politics and Data Science. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.
This course cannot be taken with ST309 Elementary Data Analytics.
Prerequisites
The primary focus of this course is on the core machine learning techniques in the context of high-dimensional or large datasets (i.e. big data). The first part of the course covers elementary and important statistical methods including nearest neighbours, linear regression, logistic regression, regularisation, cross-validation, and variable selection. The second part of the course deals with more advanced machine learning methods including regression and classification trees, random forests, bagging, boosting, deep neural networks, k-means clustering and hierarchical clustering. The course will also introduce causal inference motivated by analogy between double machine learning and two-stage least squares. All the topics will be delivered using illustrative real data examples. Students will also gain hands-on experience using R or Python programming languages and software environments for data analysis, computing and visualisation.
ST310 Machine Learning HELP（EXAM HELP， ONLINE TUTOR）
(1) (foundations: rank)
What is the rank of $\left(\begin{array}{ccc}1 & 2 & 1 \ 1 & 0 & 3 \ 1 & 1 & 2\end{array}\right)$ ?
(2) (foundations: inverse)
What is the inverse of $\left(\begin{array}{lll}0 & 2 & 4 \ 2 & 4 & 2 \ 3 & 3 & 1\end{array}\right)$ ?
(3) (foundations: eigenvalues/eigenvectors)
What are the eigenvalues and eigenvectors of $\left(\begin{array}{ccc}3 & 1 & 1 \ 2 & 4 & 2 \ -1 & -1 & 1\end{array}\right)$ ?
(4) (foundations: singular value decomposition)
(a) For a real matrix $M$, let $M=U \Sigma V^T$ be its singular value decomposition. Define $\mathrm{M}^{\dagger}=\mathrm{V}^{\dagger} \mathrm{U}^T$, where $\Sigma^{\dagger}[i][j]=\frac{1}{\Sigma[i][j]}$ when $\Sigma[i][j]$ is nonzero, and 0 otherwise. Prove that $\mathrm{MM}^{\dagger} \mathrm{M}=\mathrm{M}$.
(b) If $\mathrm{M}$ is invertible, prove that $\mathrm{M}^{\dagger}=\mathrm{M}^{-1}$.
(5) (foundations: PD/PSD)
A symmetric real matrix $\mathrm{A}$ is positive definite (PD) iff $\mathbf{x}^T \mathrm{~A} \mathbf{x}>0$ for all $\mathbf{x} \neq \mathbf{0}$, and positive semidefinite (PSD) if “>” is changed to ” $\geq$. Prove:
(a) For any real matrix $\mathrm{Z}, \mathrm{ZZ}^T$ is $\mathrm{PSD}$.
(b) A symmetric A is PD iff all eigenvalues of A are strictly positive.
(6) (foundations: inner product)
Consider $\mathbf{x} \in R^d$ and some $\mathbf{u} \in R^d$ with $|\mathbf{u}|=1$.
What is the maximum value of $\mathbf{u}^T \mathbf{x}$ ? What $\mathbf{u}$ results in the maximum value?
What is the minimum value of $\mathbf{u}^T \mathbf{x}$ ? What $\mathbf{u}$ results in the minimum value?
What is the minimum value of $\left|\mathbf{u}^T \mathbf{x}\right|$ ? What $\mathbf{u}$ results in the minimum value?
MY-ASSIGNMENTEXPERT™可以为您提供LSE.AC.UK ST310 MACHINE LEARNING机器学习课程的代写代考和辅导服务！
