Introduction

This document contains the questions for Part 5 of your assessed coursework for the unit Algorithms and Machine Learning (MATH20017). The marks for this coursework will count 10% towards your final grade.

Please contact henry.reeve@bristol.ac.uk with any questions regarding this document. Whilst I am unable to provide solutions in advance of all work being handed in, I can provide clarification.

Introduction

This document contains the questions for Part 3 of your assessed coursework for the unit Algorithms and Machine Learning (MATH20017). The marks for this coursework will count 10% towards your final grade.

Please contact henry.reeve@bristol.ac.uk with any questions regarding this document. Whilst I am unable to provide solutions in advance of all work being handed in, I can provide clarification.

In this test, we're aiming to assess the following:

1. Solving a simple scientific problem, 20%
2. Creating Python modules and packages, 30%
3. Version control, 30 %
4. Public dissemination of code, 20%

We're going to do this by creating a package that simulates the flight of a projectile. You'll need to create a working Python package, demonstrate that you have kept track of your changes using git, and publish your code to an online repository.

Introduction

This document contains the questions for Part 3 of your assessed coursework for the unit Algorithms and Machine Learning (MATH20017). The marks for this coursework will count 10% towards your final grade.

Please contact henry.reeve@bristol.ac.uk with any questions regarding this document. Whilst I am unable to provide solutions in advance of all work being handed in, I can provide clarification.

Introduction

This document contains the questions for Part 1 of your assessed coursework for the unit Algorithms and Machine Learning (MATH20017). The marks for this coursework will count 10% towards your final grade.

Please contact henry.reeve@bristol.ac.uk with any questions regarding this document. Whilst I am unable to provide solutions in advance of all work being handed in, I can provide clarification.

Data Science (2)

A data file, icecream.csv, has been provided which contains information on daily ice cream sales for a beach ice cream stall. The dataset contains the following information:

• average temperature of the day in $^{\circ}$C
• number of ice creams sold
• whether or not it rained on the day (1=True, 0=False)
• number of hours of sunshine on the day

Question

What to hand in: answers to Q1–Q4.

Please write the day and time of your tutorial class on your homework.

1. For each of the following regular statistical models (so, e.g., the Fisher Infor-mation Regularity Conditions hold), derive the score function $\ell'(\theta; x)$ and the Fisher Information, $I (\theta)$ , where in both cases you may need to replace $\theta$ with the parameter of interest (e.g. p in the case where $X$ is Geometric or Binomial).

What to hand in: answers to Q1–Q4.

Please write the day and time of your tutorial class on your homework.

1. This question is about ML estimates of transformations of the parameter.

   (a) Suppose that $X \stackrel{\text{iid}}{\sim} \text{Exponential}(\lambda)$ where $\Theta = \mathbb{R}_{++}$ (i.e. the strictly positive real numbers). Consider a transformed parameter $\tau = \frac{1}{1 + \lambda}$ . Write the likelihood function in terms of $\tau$ , then maximize it to find the ML estimate $\hat{\tau}$ . Confirm that $\hat{\tau} = \frac{1}{1 + \hat{\lambda}}$ , where $\hat{\lambda}$ is the ML estimate of $\lambda$ .

   (b) If $X \sim \text{Poisson}(\lambda)$ where $\Theta = \mathbb{R}_{++}$ , then $P\{X = 0; \lambda\} = \exp(-\lambda)$ . Explain why the ML estimate of this probability is $\exp(-\hat{\lambda})$ , where $\hat{\lambda}$ is the ML estimate of $\lambda$ .

2. Suppose that $X_1, X_2, ...$ are i.i.d. Uniform[0,1] random variables, each with density $f(x) = \mathbb{I}(0 \leq x \leq 1)$ .

   (a) Calculate the mean and variance of $\log X_1$ .

   (b) By taking logs, find a random variable $X$ such that as $n \rightarrow \infty$

   $$(X_1 \cdot\cdot\cdot X_n)^{\frac{1}{\sqrt{n}}} e^{\sqrt{n}} \xrightarrow{}_D X.$$

Introduction

This document contains the questions for Part 1 of your assessed coursework for the unit Algorithms and Machine Learning (MATH20017). The marks for this coursework will count 10% towards your final grade.

Please contact henry.reeve@bristol.ac.uk with any questions regarding this document. Whilst I am unable to provide solutions in advance of all work being handed in, I can provide clarification.

1. while 与 for

使用循环得到 0～10 的偶数，存储到 even_lst 列表中。

要求分别使用 while、for 实现。

2. if

What to hand in: answers to Q1–Q2.

Please write the day and time of your tutorial class on your homework.

You should also work through the R exercise in Q3. It is very important that you make progress with R now: do not leave it until just before the first Computer Practical. If you are struggling with Q3 you should attend the Computing Office Hours.

In this short notebook we will implement implement a matrix class and implement some fundamental matrix operations. You may wish to consult the following guide to object oriented programming in Python:
https://realpython.com/python3-object-oriented-programming/.

Welcome to unit MATH20017: Algorithms and Machine Learning.

This unit is aimed at students in their 2nd year of the Data Science BSc.

We will study the following topics:

Introduction to algorithms and computational complexity

Check your learning: topics so far (quiz)

Access Python (Noteable)

• https://www.youtube.com/watch?v=6cA1qMO8fzw

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