機器學習算法如何應用于控制

A step-by-step tutorial in R

R中的分步教程

1引言 (1 Introduction)

This blog makes up the Machine Learning section of another blog. You can find the main blog here:

該博客構成另一個博客的“機器學習”部分。 您可以在這里找到主要博客：

https://medium.com/@deeganrobbie/nba-most-valuable-player-mvp-award-15c6cfe727ee

https://medium.com/@deeganrobbie/nba-most-valuable-player-mvp-award-15c6cfe727ee

This is a tutorial-based blog that is primarily targeted at the entry-level to intermediate-level machine learning students out there.

這是一個基于教程的博客， 主要針對入門級到中級機器學習的學生。

Table of Contents目錄

The two main focus points of this tutorial are model selection and improving model performance. For each model, there is a “basic version” and an “upgraded version” of the model. The value this brings to the tutorial comes from the justification for the model improvements.

本教程的兩個主要重點是模型選擇和提高模型性能 。 對于每個模型，都有該模型的“ 基本版本”和“ 升級版本” 。 為本教程帶來的價值來自模型改進的理由。

The code of the basic version of each algorithm will be shown, followed by the code of the upgraded version. The basic version will use different R packages, while all the upgraded versions will be using the Caret package.

將顯示每種算法的基本版本的代碼，然后是升級版本的代碼。 基本版本將使用不同的R軟件包，而所有升級版本將使用Caret軟件包 。

The Caret package allows for modifications such as cross-validation, data preprocessing and tuning parameters. (As well as many other useful features) It allows for a streamlined workflow.

Caret軟件包允許進行修改，例如交叉驗證，數據預處理和調整參數。 (以及許多其他有用的功能)，它可以簡化工作流程。

The reason why all the algorithms aren’t implemented through the Caret package is that the Caret package comes with predefined features that automatically improves model output. Such as performing resampling to estimate a realistic R-squared and parameter tuning.

之所以不能通過Caret軟件包實現所有算法，是因為Caret軟件包具有預定義的功能，可以自動改善模型輸出。 例如執行重采樣以估算實際的R平方和參數調整。

1.1假設 (1.1 Hypothesis)

There is no singular statistic that will determine who will win the MVP. There will be some combination of statistics that will decide who will win the MVP. Machine Learning will help solve this problem.

沒有任何統計數據可以確定誰將贏得MVP。 統計數據將決定誰將贏得MVP。 機器學習將幫助解決此問題。

In my opinion, there are two statistics, that when combined, will determine who wins the MVP. The combination of the highest PER and being on a team with a 1 seed. That being said I can think of a few instances off the top of my head where that isn’t the case.

我認為，有兩個統計數據結合起來將確定誰贏得了MVP。 最高PER并以1種子入隊。 話雖這么說，但我可以想到的并非如此。

2數據準備 (2 Data Preparation)

2.1 Web爬網 (2.1 Web Scrapping)

Rvest package was used to perform web scrapping on https://www.basketball-reference.com/

Rvest軟件包用于在https://www.basketball-reference.com/上執行Web抓取

As the code is quite long I thought I would provide it in a link. In this link, you can find the code along with the CSVs created from web-scrapping. Using the csv “big_5.csv” and “Test2020.csv” will give you all the needed data for this tutorial.

由于代碼很長，我想我會在鏈接中提供它。 在此鏈接中，您可以找到代碼以及通過網絡剪貼創建的CSV。 使用csv“ big_5.csv”和“ Test2020.csv”將為您提供本教程所需的所有數據。

However, if you want just the code for web scraping and data preparation: WebScraping_DataPrep.R

但是，如果只需要用于Web抓取和數據準備的代碼： WebScraping_DataPrep.R

• This R code creates the csvs — all.csv, big_5.csv, bigger_5.csv and king.csv

  此R代碼創建了csv-all.csv，big_5.csv，big_5.csv和king.csv

• Two additional csvs — names.csv (needed for joining data) and test.csv which is what we will use to predict who will win this year

  另外兩個csvs： names.csv (需要連接數據)和test.csv ，我們將用它們來預測誰將在今年獲勝

This tutorial will only use the “Updated_Final.R” code

本教程將僅使用“ Updated_Final.R”代碼

Check out my “Sources” document in the same Github repo. This word d includes high-quality links to every topic covered in the tutorial.

在同一Github存儲庫中查看我的“ Sources ”文檔。 單詞d包含指向本教程涵蓋的每個主題的高質量鏈接。

2.2數據預處理 (2.2 Data Preprocessing)

There are two ways we used data preprocessing during this project

我們在此項目中使用兩種方法進行數據預處理

Cleaning the data

清理數據

Using caret package to preprocess the cleaned dataset so that certain Machine Learning algorithms can be properly implemented.

使用插入符號包預處理已清理的數據集，以便可以正確實現某些機器學習算法。

After we collected the data from web scraping. We used a few techniques to clean the data. This includes text preprocessing and joining different tables. Please find the code here: WebScraping_DataPrep.R

從網絡抓取中收集數據之后。 我們使用了一些技術來清理數據。 這包括文本預處理和連接不同的表。 請在此處找到代碼： WebScraping_DataPrep.R

Below is an upgraded model that uses processing.

以下是使用處理的升級模型。

Example of Caret package preprocessing in action插入符號包裝預處理示例

As you can see from the highlighted code, incorporating preprocessing is very easy. PreProcess() can be used for many operations on predictors, for this example, we used centering and scaling.

從突出顯示的代碼中可以看到，合并預處理非常容易。 P reProcess()可用于預測變量的許多操作，在本例中，我們使用了居中和縮放。

• “center“: subtract mean from values.

  “ center ”：從值中減去平均值。

• “scale“: divide values by standard deviation.

  “ 刻度 ”：將值除以標準偏差。

2.3特征工程 (2.3 Feature Engineering)

From a subjective point of view, there are typically 5 main MVP candidates. Within this group of 5 candidates (again subjective # choice), we usually compare players by saying “I believe player X is the 1 MVP choice because they lead the other candidates in PPG and play on the team with the most overall wins.”

從主觀角度來看，通常有5個主要的MVP候選人。 在這5名候選人的組中(同樣是主觀＃選擇)，我們通常會說“我相信球員X是1個MVP的選擇，因為他們在PPG中領先其他候選人，并在整體獲勝最多的隊伍中比賽。”

This is just one way we NBA fans justify why a certain player should win MVP over the other candidates. The below code mimics that thought process. It does this by first filtering our data set to only include the top 5 candidates. Then it ranks each statistic within a year. The final data set is named “big_5” and it includes all the normal statistics plus a set of ranked columns. We will first go through the code, then we will look at the first 3 years (15 rows) of the big_5 dataset.

這只是我們NBA球迷為某位球員贏得其他候選人最有價值球員的理由。 下面的代碼模仿了這種思考過程。 為此，它首先過濾我們的數據集，使其僅包括前5個候選對象 。 然后，它將對一年內的每個統計數據進行排名。 最終數據集名為“ big_5 ”，它包括所有常規統計信息以及一組排名列。 我們將首先檢查代碼，然后查看big_5數據集的前三年(15行)。

# Create a df that ranks where the MVPS ended up each year. The Rankings range from 1 - 5 because it's ranking the top 5 MVP canidates of each yearbig_5 <- all %>%
group_by(Year) %>%
filter(Rank < 6) %>%
mutate(Points_Rank = order(order(PTS, decreasing = T))) %>%
mutate(Rebounds_Rank = order(order(TRB, decreasing = T))) %>%
mutate(Assists_Rank = order(order(AST, decreasing = T))) %>%
mutate(Steals_Rank = order(order(STL, decreasing = T))) %>%
mutate(Blocks_Rank = order(order(BLK, decreasing = T))) %>%
mutate(Per_Rank = order(order(PER, decreasing = T))) %>%
mutate(TS_Rank = order(order(TS., decreasing = T)))%>%
mutate(WS_Rank = order(order(WS, decreasing = T)))%>%
mutate(Wins_Rank = order(order(W, decreasing = T)))# Turn into df
big_5 <- as.data.frame(big_5)# If a column is a interger mutate it into a numeric
big_5 <- mutate_if(big_5, is.integer, as.numeric)
big_5$Sum <- rowSums(big_5[,27:34], na.rm=TRUE)# Display first 15 rows of big_5 data set - created in previous step
head(big_five, 15)

The below image is the first 15 rows of the new “big_five” data set. I used paint to visualize that there is 3 years worth of data here. In order to make this graphic more clear I did an example of 3 statistics — Points_rank, Rebounds_Rank and Assists_Rank.

下圖是新的“ big_five”數據集的前15行。 我用油漆來可視化這里有3年的數據。 為了使該圖形更清晰，我舉了3個統計數據的示例-Points_rank，Rebounds_Rank和Assists_Rank。

Explanation of Feature Engineering for this data set此數據集的功能工程說明

• Brown = Top 5 candidates in 2000

  布朗= 2000年的前5名候選人

• Blue = Top 5 candidates in 2001

  藍色= 2001年的前5名候選人

• Pink = Top 5 Candidates in 2002.

  粉紅= 2002年的前5名候選人。

Let’s look at the very last column, named “Sum”. This column is the sum total of the “_Rank” columns. The lower the number in sum the better. As you can see from the red text, this is the only column we use during the modelling process. (However, feel free to use any of the other ones if you try this out)

讓我們看看最后一列，名為“ Sum”。 此列是“ _Rank”列的總和。 總數越低越好。 從紅色文本可以看出，這是我們在建模過程中使用的唯一一列。 ( 但是，如果嘗試此方法，請隨意使用其他任何方法 )

2.4訓練數據和測試數據 (2.4 Training data and Testing data)

Our basic models will use a simple training/testing split. While our upgraded models will incorporate 10-fold cross-validation.

我們的基本模型將使用簡單的訓練/測試拆分。 雖然我們的升級模型將包含10倍交叉驗證。

Basic Approach:

基本方法 ：

Imagine Source想象來源

The image above illustrates the training/testing set split for our basic models. Our training set will use 75% of our data while our test set will include 25% of our data.

上圖顯示了針對我們基本模型的訓練/測試集劃分。 我們的訓練集將使用75％的數據，而測試集將包含25％的數據。

Upgraded Approach: We will split our data into two distinct sets. The training data set and the Hold-out sample set. Then perform 10-fold cross-validation on the training data set. Finally, we will make a prediction of the unseen testing data set.

升級方法 ：我們將數據分成兩個不同的集合。 訓練數據集和保留樣本集 。 然后對訓練數據集執行10倍交叉驗證 。 最后，我們將對看不見的測試數據集進行預測。

Image Source圖片來源 ' This code is how we implement 10-fold cross-validation on the training data set IN CARET !! '# fit controlfitControl <- trainControl(method = "repeatedcv", number = 10, repeats = 10)

The caret package allows us to create a function that performs cross-validation. trainControl() is quite flexible, you can modify the parameters to suit your needs.

插入符號包使我們可以創建執行交叉驗證的函數。 trainControl()非常靈活，您可以修改參數以適合您的需求。

3選型 (3 Model Selection)

Our benchmark models will be logistic regression, multiclass logistic regression and multi-linear regression as they are commonly used and relatively basic models. Each model will be modelled twice. First with a “basic” version applied to an algorithm then followed by an “upgraded” version of the algorithm. The point of the “upgraded” algorithm is to show how models can be improved. Each “upgraded” model will come with a justification/explanation on how it was improved.

我們的基準模型將是邏輯回歸，多類邏輯回歸和多線性回歸，因為它們是常用的相對基礎的模型。 每個模型將建模兩次。 首先，對算法應用“基本”版本，然后對算法進行“升級”版本。 “升級”算法的重點是顯示如何改進模型。 每個“升級的”模型都將附帶說明/說明如何進行改進。

We want to start off with models that produce outputs which are easy to understand. From there we move on to models whose output might be less easy to understand, but because of the added complexity are expected to perform better.

我們想從產生易于理解的輸出的模型開始。 從那里開始，我們轉到其輸出可能較難理解的模型，但由于增加了復雜性，因此預期其性能會更好。

邏輯回歸 (Logistic Regression)

A few reasons why logistic regression is commonly used is because it’s highly interpretable*, doesn’t require too much computational power and doesn’t need its input features to be scaled. Another advantage is that logistic regression is a classification model which outputs probabilities. This is an advantage because you can compare the outputs of two instances and determine which one is predicted to be closer to your target class.

邏輯回歸通常被使用的幾個原因是因為它具有高度可解釋性*，不需要太多的計算能力并且不需要縮放其輸入特征。 Logistic回歸的另一個優點是輸出概率的分類模型。 這是一個優點，因為您可以比較兩個實例的輸出并確定哪個實例更接近您的目標類。

To improve on logistic regression models you can use regularization techniques, which can help avoid overfitting. It can be used as a good benchmark model when comparing other, more complex, machine learning algorithms. One thing to look out for when implementing logistic regression is that it cannot solve non-linear problems.

要改善邏輯回歸模型，可以使用正則化技術，這可以幫助避免過度擬合。 在比較其他更復雜的機器學習算法時，它可以用作良好的基準模型。 實施邏輯回歸時要注意的一件事是它不能解決非線性問題。

*When comparing the logistic regression model to the linear regression model — interpretation is more difficult because the interpretation of the weights is multiplicative and not additive

*將邏輯回歸模型與線性回歸模型進行比較時，由于權重的解釋是可乘的而不是累加的，因此解釋更加困難

多項式Lo??gistic回歸 (Multinomial Logistic Regression)

The multinomial logistic regression model is an extension of the binomial logistic regression model. The log odds of the outcomes are modelled as a linear combination of the predictor variables. The advantages and disadvantages that apply to binary logistic regression can also be applied to multinomial logistic regression.

多項式邏輯回歸模型是二項式邏輯回歸模型的擴展。 結果的對數賠率被建模為預測變量的線性組合。 適用于二進制邏輯回歸的優缺點也可以應用于多項邏輯回歸。

***Multinomial is used when the dependent variable has more than two nominal (unordered) categories. As Rank is an ordered variable, the more appropriate machine learning algorithm to implement is Ordinal Logistic Regression.

***當因變量具有兩個以上名義( 無序 )類別時，將使用多項式。 由于Rank是有序變量，因此要實現的更合適的機器學習算法是Ordinal Logistic回歸。

多元線性回歸(MLR) (Multiple linear regression (MLR))

Multiple linear regression is a very popular machine learning algorithm for regression tasks. It is simple to implement and easy to interpret what the output coefficients mean. If there is a linear relationship between variables then this is a preferred choice to more complex models. However, MLR cannot handle non-linear data. MLR allows for the implementation of regularization or cross-validation to overcome over-fitting.

多元線性回歸是一種非常流行的用于回歸任務的機器學習算法。 它易于實現且易于解釋輸出系數的含義。 如果變量之間存在線性關系，那么這是更復雜模型的首選。 但是，MLR無法處理非線性數據。 MLR允許實施正則化或交叉驗證以克服過度擬合。

決策樹 (Decision Tree)

Decision Trees are also a very popular machine learning algorithm. They are able to model both classification and regression tasks. Some advantages of decision tree models include that they’re intuitive and easy to explain, can model non-linear relationships and are fairly robust to outliers. Decision trees require less effort during the data preparation phase as they do not require normalization or scaling of data. With decision trees, feature selection occurs automatically. A disadvantage of decision trees is that the model tends to overfit. Since decision trees are a greedy algorithm the final model may not be the optimal solution.

決策樹也是一種非常流行的機器學習算法。 他們能夠為分類和回歸任務建模。 決策樹模型的一些優點包括它們直觀，易于解釋，可以對非線性關系進行建模并且對異常值相當健壯。 決策樹在數據準備階段所需的精力較少，因為它們不需要數據的規范化或縮放。 使用決策樹時，功能選擇會自動發生。 決策樹的缺點是模型趨于過度擬合。 由于決策樹是一種貪婪算法，因此最終模型可能不是最佳解決方案。

人工神經網絡 (Artificial Neural Networks)

“ANNs are best applied to problems where the input data and output data arewell-understood or at least fairly simple, yet the process that relates the input to output is extremely complex”- Brett Lantz

“人工神經網絡最適用于輸入數據和輸出數據易于理解或至少相當簡單的問題，但是將輸入與輸出相關聯的過程非常復雜”-Brett Lantz

ANNs can model both regression and classification tasks. Can be implemented in supervised, unsupervised and reinforcement learning. Improve over time be iteratively updating weights in their network, which allows ANN’s to automatically learn from examples. ANN’s have the ability to model non-linear and complex relationships.

人工神經網絡可以對回歸和分類任務進行建模。 可以在有監督，無監督和強化學習中實施。 通過不斷地更新其網絡中的權重來逐步改進，這使ANN可以自動從示例中學習。 人工神經網絡具有建模非線性和復雜關系的能力。

A notable disadvantage of ANNs is that it is a “black box” algorithm. It does not give an explanation to why and how it came to its final selected model. An appropriate network structure can be achieved through a trial and error approach.

人工神經網絡的顯著缺點是它是一種“黑匣子”算法。 它沒有說明為什么以及如何涉及最終選擇的模型。 適當的網絡結構可以通過反復試驗的方法來實現。

4.模型精度指標 (4. Model Accuracy Metrics)

There are plenty of different Accuracy Metrics one can use to compare models. We will briefly go over which metrics we are using.

有許多不同的準確性度量標準可用于比較模型。 我們將簡要介紹一下正在使用的指標。

4.1分類 ： (4.1 Classification:)

We are going to look at 3 different accuracy metrics for classification. For our binary task, we will highlight all 3 as each one is important. Sensitivity is the most important out of the 3. For our multi-value task, we will focus on the overall accuracy.

我們將研究3種不同的分類精度指標 。 對于我們的二進制任務，我們將突出顯示所有三個，因為每個都很重要。 靈敏度是三者中最重要的。對于我們的多值任務，我們將專注于整體準確性。

Imagine Source想象來源

Accuracy (all correct / all) = TP + TN / TP + TN + FP + FN

精度(全部正確 /全部)= TP + TN / TP + TN + FP + FN

Sensitivity aka Recall (true positives / all actual positives) = TP / TP + FN

靈敏度又稱為召回率( 真實陽性/所有實際陽性)= TP / TP + FN

Specificity (true negatives / all actual negatives) =TN / TN + FP

特異性( 真陰性/所有實際陰性)= TN / TN + FP

• Sensitivity tells us what percentage of NBA players that won MVP was correctly identified.

  敏感性告訴我們正確確定了贏得MVP的NBA球員的百分比。

• Specificity tells us what percentage of NBA players who did not end up winning the MVP award were correctly identified.

  特殊性告訴我們正確識別未最終獲得MVP獎的NBA球員的百分比。

Our Testing data set will have 20% MVPs and 80% Not MVPs. We prefer a model that has high sensitivity % as were are concerned with predicting who will win MVP.

我們的測試數據集將具有20％的MVP和80％的非MVP。 我們更喜歡具有高靈敏度％的模型，因為該模型與預測誰將贏得MVP有關。

4.2回歸： (4.2 Regression:)

For our regression task, we will use 3 accuracy metrics when inferring the results from the different models.

對于我們的回歸任務，在從不同模型推斷結果時，我們將使用3個準確性指標 。

RMSE (Root Mean Squared Error)is the square root of the averaged squared difference between the target value and the value predicted by the model. The lower the value is, the better the model is. RMSE gives a relatively high weight to large errors. This means the RMSE should be more useful when large errors are particularly undesirable.

RMSE (均方根誤差)是目標值與模型預測的值之間的均方差的平方根。 值越低，模型越好。 RMSE對較大的錯誤給予相對較高的權重。 這意味著當特別不希望出現大錯誤時，RMSE應該會更加有用。

The formula for RMSERMSE的公式

R-squared (Coefficient of determination) shows the proportion of variance in the outcome variable that is explained by the predictions. Typically, the higher the value is, the better the model is.

R平方 (確定系數)顯示了預測所解釋的結果變量中方差的比例。 通常，值越高，模型越好。

Image Source圖片來源

MAE (Mean absolute error) represents the difference between the original and predicted values extracted by averaged the absolute difference over the data set. The lower the value is, the better the model is.

MAE (平均絕對誤差)表示原始值和預測值之間的差值，該值是通過對數據集上的絕對差值進行平均而得出的。 值越低，模型越好。

Imagine Source想象來源

5.二進制分類 (5. Binary Classification)

Barplot of MVP data distributionMVP數據分布圖

In our binary data, there is 80 non-MVPs and only 20 MVPs. If our machine learning models simply predict “No” it would still have high prediction accuracy (80%). This class imbalance will be addressed after we examine our target variable in more depth.

在我們的二進制數據中，有80個非MVP，只有20個MVP。 如果我們的機器學習模型僅預測“否”，它仍將具有較高的預測準確性(80％)。 在更深入地檢查目標變量之后，將解決此類班級失衡問題。

Boxplot for binary data二進制數據的箱線圖

Ideally, the boxplots would be distinguishable. From an eye test, the below look like variables which might have clear distinction among classes.

理想情況下，箱線圖將是可區分的。 通過眼睛測試，下面看起來像變量，可能在類之間有明顯的區別。

• Seed, Sum, W, WS, WS48
  種子，總和，W，WS，WS48

Synthetic Minority Oversampling Technique (SMOTE) creates new synthetic observations. Thew newly generated instances are relatively close in feature space to existing examples in the minority class (aka they’re made up, but similar to the real ones). The increase in observations allows for the machine learning algorithm to learn more, which leads to a better understanding of the data. A standard approach for implementing SMOTE is to only increase the minority class, but since our data set has such few observations we increased both the minority and majority classes to 75 observations. This number was selected based off experimenting with several iterations. We will just be showing the 75/75 split. (150 in total)

綜合少數族裔過采樣技術 (SMOTE)創建了新的綜合觀察。 這些新生成的實例在特征空間上與少數類中的現有實例相對較近(aka它們是組成的，但與真實實例相似)。 觀察值的增加允許機器學習算法學習更多，從而可以更好地理解數據。 實施SMOTE的標準方法是僅增加少數派類別，但是由于我們的數據集具有很少的觀察值，因此我們將少數派和多數派類別都增加到了75個。 這個數字是根據多次迭代實驗選擇的。 我們將僅顯示75/75分割 。 (共150個)

# SMOTE
over_2 <- SMOTE(Results ~., Train_C2, perc.over = 400, perc.under = 125, k = 5)over_2$Results <- factor(over_2$Results, levels = c("MVP", "Not_MVP"))# Check target variable's distribution
table(over_2$Results)75 75 SMOTE for the binary TRAINING data set二進制培訓數據集的SMOTE

Now our over_2 training dataset contains 150 target observations. 75 MVP observations and 75 Not_MVP observations.

現在我們的over_2訓練數據集包含150個目標觀察值。 75個MVP觀測值和75個Not_MVP觀測值。

• Important to emphasize that we are only applying the SMOTE algorithm to the training data set.
  需要強調的是，我們僅將SMOTE算法應用于訓練數據集。

5.1 Logistic回歸 (5.1 Logistic Regression)

Logistic Regression is a binary classification algorithm that belongs to the family of generalized linear models(GLM). The model makes a prediction by returning a probability of the target class. It uses a threshold value to determine which group of the target class the prediction belongs to.

Logistic回歸是一種二進制分類算法，屬于廣義線性模型(GLM)族。 該模型通過返回目標類別的概率進行預測。 它使用閾值確定預測屬于目標類別的哪一組。

c_logistic_model2 <- glm(Results ~ ., data = Train_C2[,3:15],
family = binomial)

Our basic model uses glm() from the glmnet library. We use all variables to predict our target variable (Results).

我們的基本模型使用glmnet庫中的glm()。 我們使用所有變量來預測目標變量(結果)。

upgraded_c_logistic_model2 <- train(Results ~ .,data= over_2[,3:15],
method = "glmboost",
trControl = fitControl)

Fit a glm using a boosting algorithm (as opposed to MLE). Unlike the glm function, glmboost will perform variable selection.

使用提升算法(而不是MLE)來擬合glm。 與glm函數不同，glmboost將執行變量選擇。

Improvements include

改進包括

• Smote data
  遠程數據
• 10 fold cross-validation
  10倍交叉驗證
• Boosting
  提升

Results:

結果：

Our “basic” vs “upgraded” logistic regression results我們的“基本”與“升級”邏輯回歸結果

While our upgraded model had a worse specificity it is important to note that the overall accuracy and sensitivity both increased.

盡管我們升級后的模型的特異性較差，但需要注意的是總體準確性和敏感性均提高了。

Below is another way to visualize the confusion matrix for the logistic regression models. The visualizations below are valuable to stakeholders (NBA fans) because they can intuitively understand what this machine learning algorithm considers an “MVP”.

下面是可視化邏輯回歸模型的混淆矩陣的另一種方法。 下面的可視化對利益相關者(NBA球迷)很有價值，因為他們可以直觀地理解該機器學習算法認為的“ MVP”。

Accuracy of our binary logistic regression models. These are the same results as our confusion matrices above!

我們的二進制邏輯回歸模型的準確性。 這些結果與我們上面的混淆矩陣相同！

Our basic model incorrectly predicted that Jason Kidd in 2002 and Lebron in 2011 & 2017 were MVPs. It also predicted that Allen Iverson 2001 and Tim Duncan 2002 were not MVPs when they actually were MVPs.

我們的基本模型錯誤地預測2002年的Jason Kidd和2011＆2017年的Lebron是MVP。 它還預測，艾倫·艾弗森(Allen Iverson)2001和蒂姆·鄧肯(Tim Duncan 2002)并不是MVP，而實際上他們是MVP。

Our upgraded logistic model was more generous with predicting an observation would be an MVP. It incorrectly predicted Nash ’07, Lebron ’11, KD ’13 and Lebron ’17 as MVPs when they were not MVPs. It also predicted that A.I was not an MVP in 2001 when he was, in fact, the MVP.

我們升級后的邏輯模型更加慷慨，可以預測觀察將是MVP。 當它們不是MVP時，它錯誤地將Nash '07，Lebron '11，KD '13和Lebron '17預測為MVP。 它還預測A??I在2001年并不是MVP，而實際上他是MVP。

5.2決策樹 (5.2 Decision Tree)

c_tree_model2 <- rpart(Results ~ ., data = Train_C2[,3:15])

Our basic decision tree uses the rpart library to predict Results. The decision tree automatically does variable selection. Below is our final tree:

我們的基本決策樹使用rpart庫預測結果。 決策樹自動進行變量選擇。 下面是我們的最后一棵樹：

upgraded_c_tree_model2 <- train(Results ~ ., data = over_2[,3:15],
method = "rpart",
tuneLength = 10,
trControl = fitControl)

Our upgraded model is implemented with caret, but behind the scenes, it uses the rpart library. For our upgraded model we incorporated tuneLength. The tuneLength parameter tells the algorithm to try different default values for the main parameter.

我們的升級模型是使用插入符號實現的，但在后臺，它使用了rpart庫。 對于我們的升級模型，我們合并了tuneLength。 tuneLength參數告訴算法嘗試對main參數使用不同的默認值。

Improvements include

改進包括

• Smote data
  遠程數據
• 10 fold cross-validation
  10倍交叉驗證
• TuneLength
  音調長度

Results:

結果：

Our “basic” vs “upgraded” decision tree results我們的“基本”與“升級”決策樹結果

Our upgraded model improved on overall accuracy and sensitivity while remaining consistent with specificity.

我們升級后的模型改善了總體準確性和敏感性，同時保持了特異性。

5.3人工神經網絡 (5.3 Artificial Neural Networks)

From the neuralnet package, we implement a simple neuralnet using all the available explanatory variables. With the complexity of neural networks, there are lots of options to explore in the neuralnet package.

從Neuronet包中，我們使用所有可用的解釋變量來實現一個簡單的Neuronet。 由于神經網絡的復雜性，在Neuronet軟件包中有很多可供探索的選擇。

c_ann_model2 <- neuralnet(Results ~ ., data = Train_C2[,3:15],
hidden = c(2,1))

While the ANN model is expected to perform better, as you can see by the plot above it is much less interpretable.

雖然人工神經網絡模型有望表現更好，但如上圖所示，它的可解釋性要差得多。

When you train a neural network (nnet) using Caret you need to specify two hyper-parameters: size and decay. Decay is the weight decay, and there are three tuning values. This is the regularization parameter to avoid over-fitting. Size is the number of units in the hidden layer.

使用Caret訓練神經網絡(nnet)時，您需要指定兩個超參數：大小和衰減。 衰減是重量衰減，有三個調整值。 這是避免過度擬合的正則化參數。 大小是隱藏層中的單位數。

*For our upgraded model we are using the nnet package instead of the neural network package, which means we don’t have access to the same plots. We will not be plotting the nnet ANN as it is not as user friendly. This is also the case for section 6 and 7 ANN models

*對于我們的升級模型，我們使用nnet軟件包而不是神經網絡軟件包，這意味著我們無法訪問相同的圖。 我們不會繪制nnet ANN，因為它不那么用戶友好。 第6節和第7節ANN模型也是如此

nnetGrid <- expand.grid(size = seq(from = 1, to = 10, by = 1),
decay = seq(from = 0.1, to = 0.5, by = 0.1))set.seed(4321)
## ANN model
upgraded_c_ann_model2 <- train(Results ~ ., data = over_2[,3:15],
method = "nnet",
trControl = fitControl,
preProcess = c('center', 'scale'),
tuneGrid = nnetGrid)

Improvements include

改進包括

• Smote data
  遠程數據
• 10 fold cross-validation
  10倍交叉驗證
• preProcess
  預處理
• nnetGrid
  nnetGrid

Results:

結果：

Our “basic” vs “upgraded” ANN results我們的“基本”與“升級”人工神經網絡結果

Our upgraded model improved on overall accuracy and sensitivity while remaining consistent with specificity.

我們升級后的模型改善了總體準確性和敏感性，同時保持了特異性。

6.多值分類 (6. Multi-value Classification)

In our multi-value data set, there are 5 groups; 1st place, 2nd place, 3rd place, 4th place and 5th place. Each group has 20 instances. Since the target data is distributed evenly then we will focus more on accuracy as a metric. Accuracy is a good measure when the target variable classes in the data are nearly balanced.

在我們的多值數據集中，共有5組； 第一名，第二名，第三名，第四名和第五名。 每個組有20個實例。 由于目標數據分布均勻，因此我們將更多地關注準確性作為度量標準。 當數據中的目標變量類別接近平衡時，準確性是一個很好的度量。

From an eye test, the below look like variables which might have a clear distinction.

從眼睛測試來看，下面的變量看起來可能有明顯的區別。

• Seed, Sum, WS, WS48
  種子，總和，WS，WS48

For our ‘upgraded’ models we implemented the SMOTE technique again. The justification for this is that do to the small number of observations, we felt that creating more observations would help the machine learning algorithms pick up on the underlying relationships.

對于我們的“升級”模型，我們再次實施了SMOTE技術。 這樣做的理由是只對少量的觀察結果進行處理，我們認為創建更多的觀察結果將有助于機器學習算法掌握潛在的關系。

# SMOTE
set.seed(4321)
over_5 <- SMOTE(Rank ~., Train_C5, perc.over = 200, perc.under = 420, k = 5)Original training data is 75 obs while SMOTE_5 is 171原始訓練數據為75磅，而SMOTE_5為171

SMOTE randomly generates synthetic observations, which means we didn’t intentionally make the distribution look like this. If you wanted to modify the distribution then change the “perc.under” or “perc.over” in the SMOTE() formula. (or change the set.seed() as it’s randomly generated)

SMOTE 隨機生成綜合觀測值，這意味著我們沒有故意使分布看起來像這樣。 如果要修改分布，請在SMOTE()公式中更改“ perc.under”或“ perc.over”。 (或更改set.seed()，因為它是隨機生成的)

This is a rather large increase in training data, but this came after experimenting with different results. Our more conservative datasets produced ~100 & ~140 observations but their accuracy were significantly worse.

訓練數據的增加是相當大的，但這是在試驗了不同結果之后得出的。 我們更保守的數據集產生了約100和?140個觀測值，但其準確性明顯差。

6.1多項式Lo??gistic回歸 (6.1 Multinomial Logistic Regression)

From the nnet package, we use the multinom function. This fits a multinomial log-linear models via neural networks.

從nnet包中，我們使用multinom函數。 這通過神經網絡擬合多項式對數線性模型。

c_log_model5 <- multinom(Rank ~ ., data = Train_C5[,3:15])

For our upgraded model we are using the same technique as our basic model.

對于我們的升級模型，我們使用與基本模型相同的技術。

upgraded_c_log_model5 <- train(Rank ~ ., data = over_5[,3:15],
method = 'multinom',
trControl = fitControl)

Improvements include

改進包括

• Smote data
  遠程數據
• 10 fold cross-validation
  10倍交叉驗證

Results:

結果：

Our upgraded model resulted in a major increase in overall accuracy.

我們升級后的模型大大提高了整體準確性。

6.2決策樹 (6.2 Decision Trees)

c_tree_model5 <- rpart(Rank ~ ., data = Train_C5[,3:15])

Our basic decision tree uses the rpart library to predict Results. The decision tree automatically does variable selection. Below is our final tree:

我們的基本決策樹使用rpart庫預測結果。 決策樹自動進行變量選擇。 下面是我們的最后一棵樹：

~~Zoom in~~~~放大~~ upgraded_c_tree_model5 <- train(Rank ~ ., data = over_5[,3:15],
method = "ctree",
trControl = fitControl)

Our upgraded model is implemented with Caret, but behind the scenes, it uses the party library. Since it’s not using the rpart package we won’t be able to plot the decision tree. Ctree does have a plot function, but it’s not as user friendly.

我們的升級模型是使用Caret實現的，但在后臺使用了聚會庫。 由于未使用rpart包，因此我們無法繪制決策樹。 Ctree確實具有繪圖功能，但是它不那么用戶友好。

Improvements include

改進包括

• ctree instead of rpart (party library instead of rpart library)
  用ctree代替rpart(用方庫代替rpart庫)
• Smote data
  遠程數據
• 10 fold cross-validation
  10倍交叉驗證

Results:

結果：

Our upgraded model resulted in a major increase in overall accuracy.

我們升級后的模型大大提高了整體準確性。

6.3人工神經網絡 (6.3 Artificial Neural Networks)

c_ann_model5 <- nnet(Rank ~ ., data = Train_C5[,3:15], size = 1)

Our basic ann model uses the neural nnet package to model our data.

我們的基本ann模型使用神經網絡nnet包對數據進行建模。

nnetGrid <- expand.grid(size = seq(from = 1, to = 10, by = 1),
decay = seq(from = 0.1, to = 0.5, by = 0.1))set.seed(4321)
# ANN model
upgraded_c_ann_model5 <- train(Rank ~ ., data = over_5[,3:15],
method = "nnet",
preProcess = c('center', 'scale'),
tuneGrid = nnetGrid,
trControl = fitControl)

Improvements include

改進包括

• Smote data
  遠程數據
• 10 fold cross-validation
  10倍交叉驗證
• preprocessing
  預處理
• nnetGrid
  nnetGrid

Results:

結果：

Our upgraded model resulted in a major increase in overall accuracy.

我們升級后的模型大大提高了整體準確性。

7回歸 (7 Regression)

Our target variable for our regression task is Points_Won. In the below graphic the Y-axis is how many points a candidate won while the X-axis is showing a different statistic. You can find out what the X-axis is by looking at the title (top-middle) of each sub-plot.

我們回歸任務的目標變量是Points_Won。 在下面的圖形中，Y軸是候選人在X軸顯示不同的統計數據時贏得的積分。 您可以通過查看每個子圖的標題(中上)來找出X軸是什么。

Question: If you inspect each sub-plot, do you find any with a linear relationship?

問題：如果檢查每個子圖，是否發現它們之間存在線性關系？

To be absolutely sure of linear relationship variables we will also use the correlation matrix (on top of the scatter plot above). The results will help us decide which variables to select for our MLR model.

為了絕對確定線性關系變量，我們還將使用相關矩陣(在上面的散點圖上方)。 結果將幫助我們確定為MLR模型選擇哪些變量。

# Correlation Matrix - Visual first
ggcorr(Train_r[,3:15], label = TRUE, label_size = 2.9, hjust = 1, layout.exp = 2)Correlation Matrix on our Training Data我們的訓練數據的相關矩陣

The way to read this visual is closer to 1 or -1 the more correlated the variables are to each other. A correlation number close to zero implies the absence of a linear relationship. Our focus is to find variables that are correlated to “Points_Won”. We do that by going down the last row and looking for boxes with #’s closest to 1 or -1.

變量之間的相關性越高，讀取此視覺效果的方式越接近1或-1。 接近零的相關數表示不存在線性關系。 我們的重點是找到與“ Points_Won”相關的變量。 為此，我們向下走最后一行，然后查找帶有＃的數字最接近1或-1的框。

In order to confirm which variables are the most correlated to the “Points_Won” column, we performed a correlation matrix on randomly sampled training data. As this is randomly sampled we thought it would be best to sample it 5 times and select the two variables with the highest correlation to Points_Won.

為了確認哪些變量與“ Points_Won”列最相關，我們對隨機采樣的訓練數據執行了相關矩陣。 由于這是隨機采樣，因此我們認為最好采樣5次，然后選擇與Points_Won相關性最高的兩個變量。

# Correlation Matrix - Ran 5 times randomly
cor(Train_r[,2:14])Correlation matrix ran five times相關矩陣運行了五次

Each column is a newly ran correlated matrix. The two highest are highlighted in each column. As the data in randomly sampled, there is a variance in correlation from column to column. After 5 runs it seems that win share (WS) and wins (W) will be the two variables we build our MLR model on.

每列都是一個新運行的相關矩陣。 最高的兩個在每一列中突出顯示。 由于數據是隨機抽樣的，因此各列之間的相關性存在差異。 經過5次運行之后，似乎勝利份額(WS)和勝利(W)將成為我們建立MLR模型的兩個變量。

7.1多元線性回歸 (7.1 Multi-linear Regression)

Our basic mlr model uses the lm package.

我們的基本mlr模型使用lm軟件包。

r_mlr_model <- lm(Points_Won ~ WS + W, data = Train_r)

Our upgraded model uses the glmnet package to model our upgraded mlr model. Elastic net combines the penalties of ridge regression and lasso to get the best of both worlds. Elastic Net aims at minimizing the following loss function:

我們的升級模型使用glmnet軟件包為我們的升級的mlr模型建模。 彈性網結合了嶺回歸和套索的懲罰，從而獲得了兩全其美的效果。 Elastic Net旨在最小化以下損失函數：

where α is the mixing parameter between ridge (α = 0) and lasso (α = 1).

其中α是脊( α = 0)和套索( α = 1)之間的混合參數。

# Make a custom tuning grid
tuneGrid <- expand.grid(alpha = 0:1, lambda = seq(0.0001, 1,
length = 10))upgraded_r_mlr_model <- train(Points_Won ~., data = Train_r[,3:15],
method = "glmnet",
trControl = fitControl,
tuneGrid = tuneGrid)

Improvements include

改進包括

• 10 fold cross-validation
  10倍交叉驗證
• tuneGrid
  tuneGrid
• Elastic net
  彈力網

Results:

結果：

Our upgraded model resulted in a much better RMSE, R-squared and MAE.

我們升級后的模型產生了更好的RMSE，R平方和MAE。

7.2決策樹 (7.2 Decision Tree)

Our basic decision tree model uses the rpart package.

我們的基本決策樹模型使用rpart包。

r_tree_model <- rpart(Points_Won ~., data = Train_r[,3:15])

Our upgraded model uses the same rpart package but adds 10-fold cross-validation through the caret package. Both models use the same explanatory variables.

我們的升級模型使用相同的rpart包，但通過插入符號包添加了十倍的交叉驗證。 兩種模型使用相同的解釋變量。

upgraded_r_tree_model <- train(Points_Won ~., data = Train_r[,3:15],
method = "rpart",
trControl = fitControl)

Improvements include

改進包括

• 10 fold cross-validation
  10倍交叉驗證

Results:

結果：

Our upgraded model resulted in a much better RMSE, R-squared and MAE.

我們升級后的模型產生了更好的RMSE，R平方和MAE。

7.3人工神經網絡 (7.3 Artificial Neural Network)

Our Original ANN Model uses the nnet package

我們的原始 ANN模型使用nnet包

r_ann_model <- nnet(Points_Won ~ ., data = Train_r[,3:15], size =1)

Our upgraded model uses the same nnet package but adds a few modifications through the caret package. Both models use the same explanatory variables.

我們的升級模型使用相同的nnet軟件包，但通過插入符號軟件包進行了一些修改。 兩種模型使用相同的解釋變量。

# Make a custom tuning grid
nnetGrid <- expand.grid(size = seq(from = 1, to = 10, by = 1),
decay = seq(from = 0.0001, to = 0.5, by = 0.1))set.seed(4321)
# ANN model
# You need to add ' linout = 1' to make it a regression model or else you'll only get 1 for an output
upgraded_r_ann_model <- train(Points_Won ~ ., data = Train_r[,3:15],
method = "nnet",
trControl = fitControl,
linout = 1,
tuneGrid = nnetGrid,
preProcess = c('center', 'scale'))

When you train a neural network (nnet) using Caret you need to specify two hyper-parameters: size and decay. Size is the number of units in the hidden layer (nnet fit a single hidden layer neural network) and decay is the regularization parameter to avoid over-fitting.

使用Caret訓練神經網絡(nnet)時，您需要指定兩個超參數： size和衰減 。 大小是隱藏層中的單位數(nnet適合單個隱藏層神經網絡)，衰減是避免過度擬合的正則化參數。

Improvements include

改進包括

• Smote data
  遠程數據
• 10 fold cross-validation
  10倍交叉驗證
• preprocessing
  預處理
• nnetGrid
  nnetGrid

Results:

結果：

Our upgraded model resulted in a much better RMSE, R-squared and MAE.

我們升級后的模型產生了更好的RMSE，R平方和MAE。

8 2020年MVP候選人的預測 (8 Prediction on 2020 MVP Candidates)

The holdout test data set we will make our final predictions on !!保持測試數據集，我們將對!!做出最終預測！

We will take the best model from section 5 (Binary), 6 (Multiclass) and 7 (Regression) to predict on the Final_Test data. These are considered the “best models” because they resulted in the highest accuracy metrics (which we discussed in their respective sections).

我們將采用第5節(二進制)，第6節(多類)和第7節(回歸)中的最佳模型對Final_Test數據進行預測。 這些被認為是“最佳模型”，因為它們導致了最高的準確度指標(我們在各自的章節中進行了討論)。

Below are the results:

結果如下：

Binary (ANN) & Multi (Logistic) & Regression (MLR) model final results.二進制(ANN)和多元(物流)與回歸(MLR)模型的最終結果。

As you can Giannis is the clear favourite, followed by Lebron. According to our models, Anthony Davis will land in 3rd place for MVP voting.

Giannis顯然是最受歡迎的，其次是Lebron。 根據我們的模型，安東尼·戴維斯(Anthony Davis)將在MVP投票中排名第三。

9執行摘要(TLDR) (9 Executive Summary (TLDR))

This tutorial has given you an overview of how to implement several Machine Learning algorithms. It includes all the steps involved in achieving better results on unseen testing data. Additionally, this tutorial has highlighted a few methods related to pre-processing, SMOTE and accuracy metrics. One important take away is that just because a model is more complex doesn’t automatically mean it will yield better results.

本教程概述了如何實現幾種機器學習算法。 它包括在看不見的測試數據上獲得更好結果的所有步驟。 此外，本教程重點介紹了幾種與預處理，SMOTE和準確性指標有關的方法。 一個重要的收獲是，僅僅因為模型更加復雜，并不意味著它會自動產生更好的結果。

Here’s a list of things I look forward to investigating after publishing this blog:

這是發布此博客后我希望調查的事情清單：

Implementation of ordinal multinomial logistic regression

有序多項式邏輯回歸的實現

My next Machine Learning project will have much more data. This will lead to seeing the true value of tuning parameters.

我的下一個機器學習項目將擁有更多數據。 這將導致看到調整參數的真實值。

There are many sampling techniques for balancing data. SMOTE is just one of them. As there’s no single best technique. I would like to experiment with others in the future.

有許多用于平衡數據的采樣技術。 SMOTE只是其中之一。 因為沒有單一的最佳技術。 我想將來與其他人一起嘗試。

翻譯自: https://medium.com/swlh/applying-machine-learning-algorithms-to-nba-mvp-data-e4470a531338

機器學習算法如何應用于控制

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