cs代写|机器学习代写machine learning代考|Neural networks and Keras

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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|Neural networks and Keras

cs代写|机器学习代写machine learning代考|Neurons and the threshold perceptron

The brain is composed of specialized cells. These cells include neurons, which are thought to be the main information-processing units, and glia, which have a variety of supporting roles. A schematic example of a neuron is shown in Fig. 4.1a. Neurons are specialized in electrical and chemical information processing. They have an extensions called an axon to send signals, and receiving extensions called dendrites. The contact zone between the neurons is called a synapse. A sending neuron is often referred to as the presynaptic neuron and the receiving cell is a postsynaptic neuron. When an neuron becomes active it sends a spike down the axon where it can release chemicals called neurotransmitters. The neurotransmitters can then bind to receiving receptors on the dendrite that trigger the opening of ion channels. Ion channels are specialized proteins that form gates in the cell membrane. In this way, electrically charged ions can enter or leave the neuron and accordingly change the voltage (membrane potential) of the neuron. The dendrite and cell body acts like a cable and a capacitor that integrates (sums) the potentials of all synapses. When the combined voltage at the axon reaches a certain threshold, a spike is generated. The spike can then travel down the axon and affect further neurons downstream.

This outline of the functionality of a neuron is, of course, a major simplification. For example, we ignored the description of the specific time course of opening and closing of ion channels and hence some of the more detailed dynamics of neural activity. Also, we ignored the description of the transmission of the electric signals within the neuron; this is why such a model is called a point-neuron. Despite these simplifications, this model captures some important aspects of a neuron functionality. Such a model suffices for us at this point to build simplified models that demonstrate some of the informationprocessing capabilities of such a simplified neuron or a network of simplified neurons. We will now describe this model in mathematical terms so that we can then simulate such model neurons with the help of a computer.

Warren McCulloch and Walter Pitts were among the first to propose such a simple model of a neuron in 1943 which they called the threshold logical unit. It is now often

referred to as the McCulloch-Pitts neuron. Such a unit is shown in Fig. 4.2A with three input channels, although neurons have typically a much larger number of input channels. Input values are labeled by $x$ with a subscript for each channel. Each channel has an associated weight parameter, $w_{i}$, representing the “strength” of a synapse.
The McCulloch-Pitts neuron operates in the following way. Each input value is multiplied with the corresponding weight value, and these weighted values are then summed together, mimicking the superposition of electric charges. Finally, if the weighted summed input is larger than a certain threshold value, $w_{0}$, then the output is set to 1 , and 0 otherwise. Mathematically this can be written as
y(\mathbf{x} ; \mathbf{w})=\left{\begin{array}{cc}
1 & \text { if } \sum_{i}^{n} w_{i} x_{i}=\mathbf{w}^{T} \mathbf{x}>w_{0} \
0 & \text { otherwise }
This simple neuron model can be written in a more generic form that we will call the perceptron. In this more general model, we calculate the output of a neuron by applying an gain function $g$ to the weighted summed input,
y(\mathbf{x} ; \mathbf{w})=g\left(\mathbf{w}^{T} \mathbf{x}\right)
where $w$ are parameters that need to be set to specific values or, in other words, they are the parameters of our parameterized model for supervised learning. We will come back to this point later regarding how precisely to chose them. The original McCulloch-Pits neuron is in these terms a threshold perceptron with a threshold gain function,
1 \text { if } x>0 \
0 \text { otherwise }
This threshold gain function is a first example of a non-linear function that transforms the sum of the weighted inputs. The gain function is sometimes called the activation function, the transfer function, or the output function in the neural network literature. Non-linear gain functions are an important part of artificial neural networks as further discussed in later chapters.

cs代写|机器学习代写machine learning代考|Multilayer perceptron (MLP) and Keras

To represent more complex functions with perceptron-like elements we are now building networks of artificial neurons. We will start with a multilayer perceptron (MLP) as

shown in Fig.4.3. This network is called a two-layer network as it basically has two processing layers. The input layer simply represents the feature vector of a sensory input, while the next two layers are composed of the perceptron-like elements that sum up the input from previous layers with their associate weighs of the connection channels and apply a non-linear gain function $\sigma(x)$ to this sum,
y_{i}=\sigma\left(\sum_{j} w_{i j} x_{j}\right)
We used here the common notation with variables $x$ representing input and $y$ representing the output. The synaptic weights are written as $w_{i j}$. The above equation corresponds to a single-layer perceptron in the case of a single output node. Of course, with more layers, we need to distinguish the different neurons and weights, for example with superscipts for the weights as in Fig.4.3. The output of this network is calculated as
y_{i}=\sigma\left(w_{i j}^{\mathrm{o}} \sigma\left(\sum_{k} w_{j k}^{\mathrm{h}} x_{k}\right)\right) .
where we used the superscript “o” for the output weights and the superscript ” $h$ ” for the hidden weights. These formulae represent a parameterized function that is the model in the machine learning context.

cs代写|机器学习代写machine learning代考|Representational learning

Here, we are discussing feedforward neural networks which can be seen as implementing transformations or mapping functions from an input space to a latent space, and from there on to an output space. The latent space is spanned by the neurons in between the input nodes and the output nodes, which are sometime called the hidden neurons. We can of course always observe the activity of the nodes in our programs so that these are not really hidden. All the weights are learned from the data so that the transformations that are implemented by the neural network are learned from examples. However, we can guide these transformations with the architecture. The latent representations should be learned so that the final classification in the last layer is much easier than from the raw sensory space. Also, the network and hence the representation it represents should make generalizations to previously unseen examples easy and robust. It is useful to pause for a while here and discuss representations.

cs代写|机器学习代写machine learning代考|Neural networks and Keras


cs代写|机器学习代写machine learning代考|Neurons and the threshold perceptron

大脑由专门的细胞组成。这些细胞包括被认为是主要信息处理单元的神经元和具有多种支持作用的神经胶质细胞。一个神经元的示意图如图 4.1a 所示。神经元专门从事电气和化学信息处理。它们有一个称为轴突的扩展来发送信号,并接收称为树突的扩展。神经元之间的接触区称为突触。发送神经元通常被称为突触前神经元,而接收细胞是突触后神经元。当一个神经元变得活跃时,它会向轴突发送一个尖峰,在那里它可以释放称为神经递质的化学物质。然后,神经递质可以与树突上的接收受体结合,从而触发离子通道的打开。离子通道是在细胞膜中形成门的特殊蛋白质。这样,带电离子可以进入或离开神经元,从而改变神经元的电压(膜电位)。树突和细胞体就像一根电缆和一个电容器,整合(总和)所有突触的电位。当轴突处的组合电压达到某个阈值时,就会产生一个尖峰。然后,尖峰可以沿着轴突向下传播并影响下游的更多神经元。当轴突处的组合电压达到某个阈值时,就会产生一个尖峰。然后,尖峰可以沿着轴突向下传播并影响下游的更多神经元。当轴突处的组合电压达到某个阈值时,就会产生一个尖峰。然后,尖峰可以沿着轴突向下传播并影响下游的更多神经元。


Warren McCulloch 和 Walter Pitts 在 1943 年率先提出了这样一个简单的神经元模型,他们称之为阈值逻辑单元。现在经常

称为 McCulloch-Pitts 神经元。这样的单元如图 4.2A 所示,具有三个输入通道,尽管神经元通常具有更多数量的输入通道。输入值标记为X每个通道都有一个下标。每个通道都有一个相关的权重参数,在一世,代表突触的“强度”。
McCulloch-Pitts 神经元以下列方式运作。每个输入值乘以相应的权重值,然后将这些权重值相加,模拟电荷的叠加。最后,如果加权求和输入大于某个阈值,在0,则输出设置为 1 ,否则设置为 0。数学上这可以写成
y(\mathbf{x} ; \mathbf{w})=\left{

1 如果 ∑一世n在一世X一世=在吨X>在0 0 除此以外 \正确的。

y(\mathbf{x} ; \mathbf{w})=g\left(\mathbf{w}^{T} \mathbf{x}\right)


1 如果 X>0 0 除此以外 \正确的。

cs代写|机器学习代写machine learning代考|Multilayer perceptron (MLP) and Keras


如图 4.3 所示。这个网络被称为两层网络,因为它基本上有两个处理层。输入层简单地表示感官输入的特征向量,而接下来的两层由类似感知器的元素组成,它们将来自前一层的输入与其连接通道的相关权重相加,并应用非线性增益函数σ(X)到这个数目,

我们在这里使用了带变量的通用符号X表示输入和是代表输出。突触权重写为在一世j. 上式对应于单个输出节点情况下的单层感知器。当然,对于更多的层,我们需要区分不同的神经元和权重,例如使用权重的上标,如图 4.3 所示。该网络的输出计算为

我们使用上标“o”作为输出权重和上标“H” 为隐藏的权重。这些公式表示一个参数化函数,它是机器学习上下文中的模型。

cs代写|机器学习代写machine learning代考|Representational learning


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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。