## 数学代写|线性代数代写linear algebra代考|MAST10007

2022年7月13日

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• (Generalized) Linear Models 广义线性模型
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## 数学代写|线性代数代写linear algebra代考|Big Data Considerations and the Texas Sharpshooter Fallacy

One final thought before we close this chapter. As we have discussed, randomness plays such a role in validating our findings and we always have to account for its possibility. Unfortunately with big data, machine learning, and other data-mining tools, the scientific method has suddenly become a practice done backward. This can be precarious; allow me to demonstrate why, adapting an example from Gary Smith’s book Standard Deviations (Overlook Press).

Let’s pretend I draw four playing cards from a fair deck. There’s no game or objective here other than to draw four cards and observe them. I get two $10 \mathrm{~s}$, a 3 , and a 2 . “This is interesting,” I say. “I got two 10s, a 3, and a 2. Is this meaningful? Are the next four cards I draw also going to be two consecutive numbers and a pair? What’s the underlying model here?”

See what I did there? I took something that was completely random and I not only looked for patterns, but I tried to make a predictive model out of them. What has subtly happened here is I never made it my objective to get these four cards with these particular patterns. I observed them after they occurred.

This is exactly what data mining falls victim to every day: finding coincidental patterns in random events. With huge amounts of data and fast algorithms looking for patterns, it’s easy to find things that look meaningful but actually are just random coincidences.

This is also analogous to me firing a gun at a wall. I then draw a target around the hole and bring my friends over to show off my amazing marksmanship. Silly, right? Well, many people in data science figuratively do this every day and it is known as the Texas Sharpshooter Fallacy. They set out to act without an objective, stumble on something rare, and then point out that what they found somehow creates predictive value.

## 数学代写|线性代数代写linear algebra代考|Matrix Vector Multiplication

This brings us to our next big idea in linear algebra. This concept of tracking where $\hat{i}$ and $\hat{j}$ land after a transformation is important because it allows us not just to create vectors but also to transform existing vectors. If you want true linear algebra enlightenment, think why creating vectors and transforming vectors are actually the same thing. It’s all a matter of relativity given your basis vectors being a starting point before and after a transformation.

The formula to transform a vector $\vec{v}$ given basis vectors $\hat{i}$ and $\hat{j}$ packaged as a matrix is: \begin{aligned} &{\left[\begin{array}{l} x_{n e w} \ y_{n e w} \end{array}\right]=\left[\begin{array}{ll} a & b \ c & d \end{array}\right]\left[\begin{array}{l} x \ y \end{array}\right]} \ &{\left[\begin{array}{l} x_{n e w} \ y_{\text {new }} \end{array}\right]=\left[\begin{array}{l} a x+b y \ c x+d y \end{array}\right]} \end{aligned}
$\hat{i}$ is the first column $[a, c]$ and $\hat{j}$ is the column $[b, d]$. We package both of these basis vectors as a matrix, which again is a collection of vectors expressed as a grid of numbers in two or more dimensions. This transformation of a vector by applying basis vectors is known as matrix vector multiplication. This may seem contrived at first, but this formula is a shortcut for scaling and adding $\hat{i}$ and $\hat{j}$ just like we did earlier adding two vectors, and applying the transformation to any vector $\vec{v}$.
So in effect, a matrix really is a transformation expressed as basis vectors.
To execute this transformation in Python using NumPy, we will need to declare our basis vectors as a matrix and then apply it to vector $\vec{v}$ using the dot() operator (Example 4-7). The dot () operator will perform this scaling and addition between our matrix and vector as we just described. This is known as the dot product, and we will explore it throughout this chapter.

# 线性代数代考

## 数学代写|线性代数代写linear algebra代考| Matrix Vector Multiplication

$\left[x_{n e w} y_{\text {new }}\right]=\left[\begin{array}{lll}a & b c & d\end{array}\right][x y] \quad\left[x_{\text {new }} y_{\text {new }}\right]=[a x+b y c x+d y]$
$\hat{i}$ 是第一列 $[a, c]$ 和 $\hat{j}$ 是列 $[b, d]$.㧴们将这两个基向量打包为一个矩阵，该矩阵又是一个向

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。