cs代写|机器学习代写machine learning代考|Bagging and data augmentation

如果你也在 怎样代写机器学习machine learning这个学科遇到相关的难题,请随时右上角联系我们的24/7代写客服。


statistics-lab™ 为您的留学生涯保驾护航 在代写机器学习machine learning方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写机器学习machine learning代写方面经验极为丰富,各种代写机器学习machine learning相关的作业也就用不着说。

我们提供的机器学习machine learning及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
cs代写|机器学习代写machine learning代考|Bagging and data augmentation

cs代写|机器学习代写machine learning代考|Bagging and data augmentation

Having enough training data is often a struggle for machine learning practitioners. The problems of not having enough training data are endless. For one, this might reinforce the problem with overfitting or even prevent using a model of sufficient complexity at the start. Support vector machines are fairly simple (shallow) models that have the advantage of needing less data than deep learning methods. Nevertheless, even for these methods we might only have a limited amount of data to train the model.

A popular workaround has been a method called bagging, which stands for “bootstrap aggregating.” The idea is therefore to use the original dataset to create several more training datasets by sampling from the original dataset with replacement. Sampling with replacement, which is also called boostrapping, means that we could have several copies of the same training data in the dataset. The question then is what good they can do. The answer is that if we are training several models on these different datasets we can propose a final model as the model with the averaged parameters. Such a regularized model can help with overfitting or challenges of shallow minima in the learning algorithm. We will discuss this point further when discussing the learning algorithms in more detail later.

While bagging is an interesting method with some practical benefits, the field of data augmentation now often uses more general ideas. For example, we could just add some noise in the duplicate data of the bootstrapped training sets which will give the training algorithms some more information on possible variations of the data. We will later see that other transformation of data, such as rotations or some other form of systematic distortions for image data is now a common way to train deep neural networks for computer vision. Even using some form of other models to transfom the data can be helpful, such as generating training data synthetically from physics-based simulations. There are a lot of possibilities that we can not all discuss in this book, but we want to make sure that such techniques are kept in mind for practical applications.

cs代写|机器学习代写machine learning代考|Balancing data

We have already mentioned balancing data, but it is worthwhile pausing again to look at this briefly. A common problem for many machine learning algorithms is a situation in which we have much more data for one class than another. For example, say we have data from 100 people with a decease and data from 100,000 healthy controls. Such ratios of positive and negative class are not uncommon in many applications. A trivial classifier that always predicts the majority class would then get $99.9$ per cent correct. In mathematical terms, this is just the prior probability of finding the class, which sets the baseline somewhat for better classifications. The problem is that many learning methods that are guided by simple loss measures such as this accuracy will mostly find this trivial solution. There have been many methods proposed to prevent such trivial solutions of which we will only mention a few here.

One of the simplest methods to counter imbalance of data is simply to use as many data from the positive class as the negative class in the training set. This systematic under-sampling of the majority class is a valid procedure as long as the sub-sampled data still represent sufficiently the important features of this class. However, it also means that we lose some information that is available to us and the machine. In the example above this means that we would only utilize 100 of the healthy controls in the training data. Another way is then to somehow enlarge the minority class by repeating some examples. This seems to be a bad idea as repeating examples does not seem to add any information. Indeed, it has been shown that this technique does not usually improve the performance of the classifier or prevent the majority overfitting problem. The only reason that this might sometimes work is that it can at least make sure the learning algorithms is incremented the same number of times for the majority and the minority class.

Another method is to apply different weights or learning rates to learn examples with different sizes to the training set. One problem with this is to find the right scaling of increase or decrease in the training weight, but this technique has been applied successfully in many case, including deep learning.

In practice it has been shown that a combination of both strategies under-sampling the majority class and over-sampling the minority class can be most beneficial, in particular when augmenting the over-sampling with some form of augmentation of the data. This is formalized in a method called SMOTE: synthetic minority over-sampling technique. The idea is therefore to change some characteristics of the over-sampled data such as adding noise. In this way there is at least a benefit of showing the learner variations that can guide the learning process. This is very similar to the bagging and data augmentation idea discussed earlier.

cs代写|机器学习代写machine learning代考|Validation for hyperparameter learning

Thus far we have mainly assumed that we have one training set, which we use to learn the parameters of the parameterized hypothesis function (model), and a test set, to evaluate the performance of the resulting model. In practice, there is an important step in applying machine learning methods which have to do with tuning hyperparameters. Hyperparameters are algorithmic parameters beyond the parameters of the hypothesis functions. Such parameters include, for example, the number of neurons in a neural network, or which split criteria to use in decision trees, discussed later. SVMs also have several parameters such as one to tune the softness of the classifier, usually called $C$, or the width of the Gaussian kernel $\gamma$. We can even specify the number of iterations of some training algorithms. We will later shed more light on these parameters, but for now it is important only to know that there are many parameters of the algorithms itself beyond the parameters of the parameterized hypothesis function (model), which can be tunes. To some extent we could think of all these parameters as those of the final model, but it is common to make the distinction between the main model parameters and the hyperparaemeters of the algorithms.

The question is then how we tune the hyperparameters. This in itself is a learning problem for which we need a special learning set that we will call a validation set. The name indicates that it is used for some form of validation, although it is most often used to test a specific hyperparameters setting that can be used to compare different settings and to choose the better one. Choosing the hyperparameters itself is therefore a type of learning problem, and some form of learning algorithms have been proposed. A simple learning algorithm for hyperparameters would be a grid search where we vary the parameters in constant increments over some ranges of values. Other algorithms, like simulated annealing or genetic algorithms, have also been used. A dominant mode that is itself often effective when used by experienced machine learners is the handtuning of parameters. Whatever method we choose, we need a way to evaluate our choice with some of our data.

Therefore, we have to split our training data again into a set for training the main model parameters and a set for training the hyperparameters. The former we still call the training set, but the second is commonly called the validation set. Thus, the question arises again how to split the original training data into a training set for model parameters and the validation set for the hyperparameter tuning. Now, we can of course use the cross-validation procedure as explained earlier for this. Indeed, it is very common to use cross-validation for hyperparameter tuning, and somehow the name of the cross-validation coincides with the name of the validation step. But notice that the cross-validation procedure is a method to split data and that this can be used for both hyperparameter tuning and evaluating the predicted performance of our final model.

cs代写|机器学习代写machine learning代考|Bagging and data augmentation


cs代写|机器学习代写machine learning代考|Bagging and data augmentation


一种流行的解决方法是一种称为 bagging 的方法,它代表“引导聚合”。因此,我们的想法是使用原始数据集通过从原始数据集进行采样并替换来创建更多的训练数据集。替换抽样,也称为提升,意味着我们可以在数据集中拥有多个相同训练数据的副本。那么问题是他们能做什么好事。答案是,如果我们在这些不同的数据集上训练多个模型,我们可以提出一个最终模型作为具有平均参数的模型。这种正则化模型可以帮助解决学习算法中的过拟合或浅最小值的挑战。我们将在稍后更详细地讨论学习算法时进一步讨论这一点。

虽然 bagging 是一种有趣的方法,具有一些实际的好处,但数据增强领域现在经常使用更一般的想法。例如,我们可以在自举训练集的重复数据中添加一些噪声,这将为训练算法提供更多关于数据可能变化的信息。稍后我们将看到其他数据转换,例如图像数据的旋转或其他形式的系统失真,现在是训练计算机视觉深度神经网络的常用方法。即使使用某种形式的其他模型来转换数据也会有所帮助,例如从基于物理的模拟中综合生成训练数据。有很多可能性我们无法在本书中全部讨论,但我们希望确保在实际应用中牢记这些技术。

cs代写|机器学习代写machine learning代考|Balancing data

我们已经提到了平衡数据,但值得再次停下来简要地看一下。许多机器学习算法的一个常见问题是我们拥有一个类的数据比另一个类多得多的情况。例如,假设我们有来自 100 名死者的数据和来自 100,000 名健康对照者的数据。这种正负类的比率在许多应用中并不少见。一个总是预测多数类的平凡分类器会得到99.9百分百正确。用数学术语来说,这只是找到类别的先验概率,它为更好的分类设置了一些基线。问题是,许多以简单损失度量(例如这种准确性)为指导的学习方法大多会找到这个微不足道的解决方案。已经提出了许多方法来防止这种琐碎的解决方案,我们在这里只提到一些。

对抗数据不平衡的最简单方法之一就是在训练集中使用与负类一样多的正类数据。只要二次抽样的数据仍然充分代表该类的重要特征,这种对多数类的系统性欠采样是一个有效的过程。但是,这也意味着我们丢失了一些对我们和机器可用的信息。在上面的示例中,这意味着我们将仅在训练数据中使用 100 个健康对照。另一种方法是通过重复一些例子以某种方式扩大少数群体。这似乎是一个坏主意,因为重复示例似乎不会添加任何信息。事实上,已经表明这种技术通常不会提高分类器的性能或防止多数过拟合问题。


实践表明,对多数类进行欠采样和对少数类进行过采样这两种策略的组合可能是最有益的,特别是在通过某种形式的数据增强来增强过采样时。这在一种称为 SMOTE 的方法中被形式化:合成少数过采样技术。因此,这个想法是改变过采样数据的一些特征,例如添加噪声。通过这种方式,至少有一个好处是可以展示可以指导学习过程的学习者变化。这与前面讨论的 bagging 和数据增强想法非常相似。

cs代写|机器学习代写machine learning代考|Validation for hyperparameter learning

到目前为止,我们主要假设我们有一个训练集,我们用它来学习参数化假设函数(模型)的参数,以及一个测试集,来评估结果模型的性能。在实践中,应用机器学习方法有一个重要步骤,这与调整超参数有关。超参数是超出假设函数参数的算法参数。例如,这些参数包括神经网络中神经元的数量,或者在决策树中使用哪些分割标准,稍后将讨论。支持向量机也有几个参数,例如一个用于调整分类器的柔软度的参数,通常称为C,或高斯核的宽度C. 我们甚至可以指定一些训练算法的迭代次数。我们稍后会更深入地了解这些参数,但现在重要的是只知道算法本身的许多参数超出了可以调整的参数化假设函数(模型)的参数。在某种程度上,我们可以将所有这些参数视为最终模型的参数,但通常会区分主要模型参数和算法的超参数。



cs代写|机器学习代写machine learning代考 请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。







术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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。