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# 数学代写|ST310 Machine Learning

## 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）

(foundations: combinatorics)
Let $C(N, K)=1$ for $K=0$ or $K=N$, and $C(N, K)=C(N-1, K)+C(N-1, K-1)$ for $N \geq 1$. Prove that $C(N, K)=\frac{N !}{K !(N-K) !}$ for $N \geq 1$ and $0 \leq K \leq N$.

(foundations: counting)
What is the probability of getting exactly 4 heads when flipping 10 fair coins?
What is the probability of getting a full house (XXXYY) when randomly drawing 5 cards out of a deck of 52 cards?

(foundations: conditional probability)
If your friend flipped a fair coin three times, and tell you that one of the tosses resulted in head, what is the probability that all three tosses resulted in heads?

(foundations: Bayes theorem)
A program selects a random integer $X$ like this: a random bit is first generated uniformly. If the bit is $0, X$ is drawn uniformly from ${0,1, \ldots, 7}$; otherwise, $X$ is drawn uniformly from ${0,-1,-2,-3}$. If we get an $X$ from the program with $|X|=1$, what is the probability that $X$ is negative?

(foundations: union/intersection)
If $P(A)=0.3$ and $P(B)=0.4$,
what is the maximum possible value of $P(A \cap B)$ ? what is the minimum possible value of $P(A \cap B)$ ? what is the maximum possible value of $P(A \cup B)$ ? what is the minimum possible value of $P(A \cup B)$ ?

(techniques: mean/variance)
Let mean $\bar{X}=\frac{1}{N} \sum_{n=1}^N X_n$ and variance $\sigma_X^2=\frac{1}{N-1} \sum_{n=1}^N\left(X_n-\bar{X}\right)^2$. Prove that
$$\sigma_X^2=\frac{N}{N-1}\left(\frac{1}{N} \sum_{n=1}^N X_n^2-\bar{X}^2\right)$$

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