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统计代写|统计与机器学习作业代写Statistical and Machine Learning代考|Use Case: Bad Debt
One of the major problems in telecommunications is bad debt, whether it is unintentional or intentional. There are many reasons for a customer to have unintentional bad debt, like unemployment, unexpected expenditures, and so on. There are also many ways companies can handle this bad debt: renegotiating the debt, partially collecting the debt, or partially suspending the services. For intentional bad debt, there is nothing to do, unless it can be prevented. In certain markets, like many in South America, there is also an aggravating circumstance. Companies providing utility services pay sales taxes to the government when they issue the bill. When those customers do not pay their bills, the utility companies do not get the revenue associated with the invoices, but even worse, they do not get back the taxes already paid to the government. It is a double loss.
This type of problem can be tackled by using an accurate supervised model, even though it is not possible to interpret it. A neural network can be trained on the historical invoices to capture the relationship of the usage and the intentional bad debt. Thinking about just the top percentage of cases based on the predictive probability, there is a huge opportunity here to save money in terms of taxes. This model runs right before the billing process and creates a list of the invoices most likely not to be paid. Even if the threshold is raised to the top $5 \%$ or just the cases where the predictive probability is greater than $92 \%$, the savings in taxes can be substantial. What does the company do in this case? It does not issue the bill. It sounds weird. However, for the top cases in terms of predictive probability, the company does not issue the bill and that can save millions of dollars. Of course, there are always errors in models, such as misclassified cases. Unfortunately, these customers will have their services temporarily disconnected, until they contact the Call Center to complain. This is the moment when the company realizes the misclassification. Fraudsters usually do not complain to the Call Center. When a misclassified customer complains about the service, the company immediately needs to reactivate the services and replace the customer’s loss. However, considering all losses and savings, the model still can avoid millions in taxes.
The simulation in Figure $4.6$ shows the possible financial return by deploying a bad debt model. For example, in some markets, telecommunications companies need to pay taxes when they issue a customer bill, sometimes around $33 \%$. If customers do not pay their bills, the company cannot recoup the taxes. This is the risk of the business. However, some of the bad debt is fraud. What if the company identifies the fraud before issuing the bill? The damage by the fraud is already done. But the company can at least avoid the taxes. The predictive model evaluates all bills before issuing them. Every bill has an associated likelihood identifying the risk of that bill associated with fraud or not. Considering the top $5 \%$ of the bills with higher predictive probability, the overall accuracy is $92 \%$. That means, the model can lead to a wrong decision in $8 \%$ of the cases. Considering an average bill of USD 41 and a population of possible intentional bad dept (on the top $5 \%$ ) of 480,954 , the total billing amount is about USD $19.7$ million. Making the right decision in $92 \%$ of the cases would avoid USD $5.5$ million in taxes. Making a wrong decision in $8 \%$ of the cases would cost to the company USD 1 million. The savings would still reach over USD $4.5$ million at the end. In a real scenario of fraud, all these customers identified as fraudsters would not have their bills issued and would have their services cutoff. The good customers, the $8 \%$ included in the model’s mistake, would be in touch with the company to determine what happened. The services would be resumed, and the bill would be reissued, reducing the loss caused by the predictive model.
统计代写|统计与机器学习作业代写Statistical and Machine Learning代考|Support Vector Machines
Support vector machines (SVM) are one of the newest machine learning models presented to solve real-world problems. SVM was created in the 90 s, and it is a robust model to classify categorical or continuous targets. Like neural networks, these models tend to be black boxes, but they are very flexible. Support vector machines automatically discover any relationship between the input variables and the target. Data scientists do not need to specify the functional form, or the relationship between the inputs and the target before fitting the model.
Support vector machines were originally developed for pure classification tasks to solve pattern recognition problems. In other words, the model makes decision predictions instead of ranks or estimates. In that way, the SVM separates the outcomes of a binary target into two classes, for example, squares and circles. Support vector machines can now be used for regression tasks as well. In the simple example shown in Figure 5.1, the goal is to classify dark squares versus light circles. There are many classification rules or “regression lines” that can be used to separate the square and circle cases. In fact, if the data is linearly separable, as shown in the figure, there are a limitless number of solutions, or lines, to separate squares and circles or any cases in a binary target. Is there an optimal solution considering all possible lines that split the squares and circles? Given two input variables, the SVM is a line. Given three input variables, the support vector is a plane. With more than three input variables, the support vector is a hyperplane.
For mathematical convenience, the binary target is defined by values $+1$ and $-1$, rather than the usual 1 and 0 in logistic regression. Because the linear separator equals 0 , classification is determined by a point falling on the positive or negative side of the line. In other words, if the outcome is positive, then the case fits to one class. If the outcome is negative, then the case fits to the other class.
This is a quite simple linear problem to start with. Finding the best solution to a linear classification problem is an optimization problem. The SVM gets more complicated when the problem is not linearly separable. In Figure 5.1, think of the vector $\mathrm{W}$ as the mechanism that affects the slope of $\mathrm{H}$ (the optimal line that correctly classifies the observations).
The formula for $\mathrm{H}$ is shown below. The bias parameter $\mathrm{b}$ is the measure of offset of the separating line from the origin, or the plane in three dimensions or hyperplane in higher dimensions. The quantity $\langle w, x\rangle$ is the dot product between the vectors $w$ and $x$. A dot product is a way to multiply vectors that result in a scalar, or a single number, as the answer. It is an element-by-element multiplication and then a sum across the products. The algorithm of support vector machines selects values for $w$ and $\mathbf{b}$ that define the optimal line that correctly classifies the cases.
$$
H={\langle w, x\rangle+b=0}
$$
统计与机器学习代考
统计代写|统计与机器学习作业代写统计和机器学习代考|用例:坏账
电信行业的主要问题之一是坏账，无论是无意的还是有意的。客户产生意外坏账的原因有很多，比如失业、意外支出等等。公司也有很多方法可以处理这些坏账:重新协商债务，部分收回债务，或部分暂停服务。对于有意的坏账，没有办法，除非它可以预防。在某些市场，比如南美洲的许多市场，情况也很糟糕。提供公用事业服务的公司在开出账单时向政府支付销售税。当这些客户不支付他们的账单时，公用事业公司得不到与发票相关的收入，但更糟糕的是，他们不能拿回已经支付给政府的税款。这是双重损失。
这类问题可以通过使用精确的监督模型来解决，尽管不可能解释它。通过对历史发票进行神经网络训练，可以捕捉到票据使用与故意坏账之间的关系。考虑到基于预测概率的最高比例的案例，在税收方面有很大的机会来节省资金。该模型在账单处理之前运行，并创建最可能未支付的发票列表。即使将阈值提高到顶部$5 \%$或仅在预测概率大于$92 \%$的情况下，也可以节省大量的税收。在这种情况下，公司会怎么做?它不发行票据。听起来很奇怪。然而，在预测概率最高的情况下，公司不发行账单，这可以节省数百万美元。当然，模型中总会有错误，比如错误分类的案例。不幸的是，这些客户的服务将暂时中断，直到他们联系呼叫中心投诉为止。这时公司才意识到分类错误。骗子通常不会向呼叫中心投诉。当分类错误的客户投诉该服务时，公司需要立即重新激活该服务，并弥补客户的损失。但是，考虑到所有的损失和节省，该模型仍然可以避免数百万美元的税收
图$4.6$中的模拟显示了通过部署坏账模型可能获得的财务回报。例如，在某些市场中，电信公司在签发客户账单时需要交税，有时在$33 \%$左右。如果顾客不支付他们的账单，公司就不能收回税款。这就是生意的风险所在。然而，一些坏账是欺诈。如果公司在开出账单之前就发现了欺诈行为，该怎么办?欺诈造成的损害已经造成。但该公司至少可以避免这些税收。预测模型在发行票据之前对所有票据进行评估。每一张票据都有一个相关的可能性，以确定该票据是否与欺诈相关的风险。考虑到预测概率较高的账单中最前面的$5 \%$，整体准确率为$92 \%$。这意味着，在$8 \%$的情况下，该模型可能导致错误的决定。考虑到平均账单41美元和可能的故意不良部门(在顶部$5 \%$)的人口480,954，总账单金额约为$19.7$万美元。在$92 \%$的案例中做出正确的决定将避免$5.5$万美元的税收。如果在$8 \%$案例中做出错误的决定，公司将损失100万美元。最终节省的资金仍将超过$4.5$万美元。在真实的欺诈场景中，所有这些被确定为诈骗者的客户的账单都不会被签发，他们的服务也会被切断。好客户，包括模型错误中的$8 \%$，将与公司联系，以确定发生了什么。业务将恢复，账单将重新发放，减少了预测模型造成的损失。
统计代写|统计与机器学习作业代写统计与机器学习代考|支持向量机
支持向量机(SVM)是用于解决现实世界问题的最新机器学习模型之一。支持向量机诞生于90年代，是一种对类别或连续目标进行分类的鲁棒模型。像神经网络一样，这些模型往往是黑盒，但它们非常灵活。支持向量机自动发现输入变量和目标之间的任何关系。在拟合模型之前，数据科学家不需要指定函数形式或输入和目标之间的关系。支持向量机最初是为纯分类任务开发的，目的是解决模式识别问题。换句话说，模型做出决策预测，而不是排序或估计。通过这种方式，支持向量机将二进制目标的结果分为两类，例如，正方形和圆形。支持向量机现在也可以用于回归任务。在图5.1所示的简单示例中，目标是将暗方形与亮圆形进行分类。有许多分类规则或“回归线”可用于分离方形和圆形情况。事实上，如果数据是线性可分的，如图所示，有无限多的解，或线，来分离正方形和圆或二进制目标中的任何情况。考虑到所有可能分割正方形和圆形的线，是否存在一个最佳解决方案?给定两个输入变量，SVM是一条直线。给定三个输入变量，支持向量是一个平面。当输入变量多于三个时，支持向量是一个超平面。为了便于数学计算，二元目标由值$+1$和$-1$定义，而不是逻辑回归中通常的1和0。因为线性分隔符等于0，所以分类是由落在直线正或负一侧的点决定的。换句话说，如果结果是积极的，那么这个案例适合于一个类别。如果结果是负面的，那么这个案例就适合另一类人。这是一个非常简单的线性问题。寻找线性分类问题的最佳解是一个优化问题。当问题不是线性可分的时候，支持向量机变得更加复杂。在图5.1中，可以将向量$\mathrm{W}$视为影响$\mathrm{H}$(正确分类观察结果的最优直线)斜率的机制
$\mathrm{H}$的公式如下所示。偏置参数$\mathrm{b}$是分离线与原点、三维平面或高维超平面的偏移量的度量。数量$\langle w, x\rangle$是向量$w$和$x$之间的点积。点积是一种向量相乘的方法，结果是一个标量，或一个数字，作为答案。它是一个元素对元素的乘法然后是乘积的和。支持向量机的算法为$w$和$\mathbf{b}$选择值，定义正确分类案例的最佳行。
$$
H={\langle w, x\rangle+b=0}
$$
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