### 统计代写|机器学习代写machine learning代考|Reinforcement Learning

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

## 统计代写|机器学习代写machine learning代考|Reinforcement Learning

The problem of reinforcement learning is to learn what to do-how to map situations to actions-so as to maximize a given reward. In contrast to the supervised learning task, the learning algorithm is not told which actions to take in a given situation. Instead, the learner is assumed to gain information about the actions taken by some reward not necessarily arriving immediately after the action is taken. One example of such a problem is learning to play chess. Each board configuration, i.e., the position of all figures on the $8 \times 8$ board, is a given state; the actions are the possible moves in a given position. The reward for a given action (chess move) is winning the game, losing it or achieving a draw. Note that this reward is delayed which is very typical for reinforcement learning. Since a given state has no “optimal” action, one of the biggest challenges of a reinforcement learning algorithm is to find a trade-off between exploration and exploitation. In order to maximize reward a learning algorithm must choose actions which have been tried out in the past and found to be effective in producing reward-it must exploit its current knowledge. On the other hand, to discover those actions the learning algorithm has to choose actions not tried in the past and thus explore the state space. There is no general solution to this dilemma, but that neither of the two options can lead exclusively to an optimal strategy is clear. As this learning problem is only of partial relevance to this book, the interested reader should refer Sutton and Barto (1998) for an excellent introduction to this problem.

## 统计代写|机器学习代写machine learning代考|Learning Kernel Classifiers

Here is a typical classification learning problem. Suppose we want to design a system that is able to recognize handwritten zip codes on mail envelopes. Initially, we use a scanning device to obtain images of the single digits in digital form. In the design of the underlying software system we have to decide whether we “hardwire” the recognition function into our program or allow the program to learn its recognition function. Besides being the more flexible approach, the idea of learning the recognition function offers the additional advantage that any change involving the scanning can be incorporated automatically; in the “hardwired” approach we would have to reprogram the recognition function whenever we change the scanning device. This flexibility requires that we provide the learning

algorithm with some example classifications of typical digits. In this particular case it is relatively easy to acquire at least $100-1000$ images and label them manually (see Figure $1.5$ (left)).

Our next decision involves the representation of the images in the computer. Since the scanning device supplies us with an image matrix of intensity values at fixed positions, it seems natural to use this representation directly, i.e., concatenate the rows of the image matrix to obtain a long data vector for each image. As a consequence, the data can be represented by a matrix $\mathbf{X}$ with as many rows as number of training samples and as many columns are there are pixels per image (see Figure $1.5$ (right)). Each row $\mathbf{x}_{i}$ of the data matrix $\mathbf{X}$ represents one image of a digit by the intensity values at the fixed pixel positions.

Now consider a very simple learning algorithm where we just store the training examples. In order to classify a new test image, we assign it to the class of the training image closest to it. This surprisingly easy learning algorithm is also known as the nearest-neighbor classifier and has almost optimal performance in the limit of a large number of training images. In our example we see that nearest neighbor classification seems to perform very well (see Figure 1.6). However, this simple and intuitive algorithm suffers two major problems:

1. It requires a distance measure which must be small between images depicting the same digit and large between images showing different digits. In the example shown in Figure 1.6 we use the Euclidean distance
$$|\mathbf{x}-\overline{\mathbf{x}}| \stackrel{\text { def }}{=} \sqrt{\sum_{j=1}^{N}\left(x_{j}-\tilde{x}_{j}\right)^{2}}$$where $N=784$ is the number of different pixels. From Figure $1.6$ we already see that not all of the closest images seem to be related to the correct class, which indicates that we should look for a better representation.

## 统计代写|机器学习代写machine learning代考|The Purposes of Learning Theory

The first part of this book may lead the reader to wonder-after learning so many different learning algorithms-which one to use for a particular problem. This legitimate question is one that the results from learning theory try to answer. Learning theory is concerned with the study of learning algorithms’ performance. By casting the learning problem into the powerful framework of probability theory, we aim to answer the following questions:

1. How many training examples do we need to ensure a certain performance?
2. Given a fixed training sample, e.g., the forty-nine images in Figure 1.5, what performance of the function learned can be guaranteed?
1. Given two different learning algorithms, which one should we choose for a given training sample so as to maximize the performance of the resulting learning algorithm?

I should point out that all these questions must be followed by the additional phrase “with high probability over the random draw of the training sample”. This requirement is unavoidable and reflects the fact that we model the training sample as a random sample. Thus, in any of the statements about the performance of learning algorithms we have the inherent duality between precision and confidence: The more precise the statement on the algorithm’s performance is, e.g., the prediction error is not larger than $5 \%$, the less confident it is. In the extreme case, we can say that the prediction error is exactly $5 \%$, but we have absolutely no (mathematical) confidence in this statement. The performance measure is most easily defined when considering supervised learning tasks. Since we are given a target value for each object, we need only to measure by how much the learned function deviates from the target value at all objects-in particular for the unseen objects. This quantity is modeled by the expected loss of a function over the random draw of object-target pairs. As a consequence our ultimate interest is in (probabilistic) upper bounds on the expected loss of the function learned from the random training sample, i.e., $\mathbf{P}$ (training samples s.t. the expected loss of the function learned $\leq \varepsilon(\delta)) \geq 1-\delta$.

## 统计代写|机器学习代写machine learning代考|Learning Kernel Classifiers

1. 它需要一个距离度量，在描绘相同数字的图像之间必须很小，而在显示不同数字的图像之间必须很大。在图 1.6 所示的示例中，我们使用欧几里得距离
|X−X¯|= 定义 ∑j=1ñ(Xj−X~j)2在哪里ñ=784是不同像素的数量。从图1.6我们已经看到，并非所有最接近的图像似乎都与正确的类相关，这表明我们应该寻找更好的表示。

## 统计代写|机器学习代写machine learning代考|The Purposes of Learning Theory

1. 我们需要多少训练样例才能保证一定的性能？
2. 给定一个固定的训练样本，例如图 1.5 中的 49 张图像，可以保证所学函数的性能如何？
3. 给定两种不同的学习算法，我们应该为给定的训练样本选择哪一种，以最大限度地提高学习算法的性能？

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## MATLAB代写

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