deep learning

4月 042019

According to the World Cancer Research Fund, Breast cancer is one of the most common cancers worldwide, with 12.3% of new cancer patients in 2018 suffering from breast cancer. Early detection can significantly improve treatment value, however, the interpretation of cancer images heavily depends on the experience of doctors and technicians. The [...]

Malignant or benign? Cancer detection with SAS Viya and NVIDIA GPUs was published on SAS Voices by David Tareen

3月 182019

Artificial intelligence (AI) is a natural evolution of analytics. Over the years, we have seen AI add learning and automation capabilities to the predictive and prescriptive jobs of analytics. We have been building AI systems for decades, but a few things have changed to make today’s AI systems more powerful. [...]

Advancing AI with deep learning and GPUs was published on SAS Voices by Oliver Schabenberger

3月 182019

Artificial intelligence (AI) is a natural evolution of analytics. Over the years, we have seen AI add learning and automation capabilities to the predictive and prescriptive jobs of analytics. We have been building AI systems for decades, but a few things have changed to make today’s AI systems more powerful. [...]

Advancing AI with deep learning and GPUs was published on SAS Voices by Oliver Schabenberger

10月 102018

Deep learning (DL) is a subset of neural networks, which have been around since the 1960’s. Computing resources and the need for a lot of data during training were the crippling factor for neural networks. But with the growing availability of computing resources such as multi-core machines, graphics processing units (GPUs) accelerators and hardware specialized, DL is becoming much more practical for business problems.

Financial institutions use a large number of computations to evaluate portfolios, price securities, and financial derivatives. For example, every cell in a spreadsheet potentially implements a different formula. Time is also usually of the essence so having the fastest possible technology to perform financial calculations with acceptable accuracy is paramount.

In this blog, we talk to Henry Bequet, Director of High-Performance Computing and Machine Learning in the Finance Risk division of SAS, about how he uses DL as a technology to maximize performance.

Henry discusses how the performance of numerical applications can be greatly improved by using DL. Once a DL network is trained to compute analytics, using that DL network becomes drastically faster than more classic methodologies like Monte Carlo simulations.

We asked him to explain deep learning for numerical analysis (DL4NA) and the most common questions he gets asked.

Can you describe the deep learning methodology proposed in DL4NA?

Yes, it starts with writing your analytics in a transparent and scalable way. All content that is released as a solution by the SAS financial risk division uses the "many task computing" (MTC) paradigm. Simply put, when writing your analytics using the many task computing paradigm, you organize code in SAS programs that define task inputs and outputs. A job flow is a set of tasks that will run in parallel, and the job flow will also handle synchronization.

Fig 1.1 A Sequential Job Flow

The job flow in Figure 1.1 visually gives you a hint that the two tasks can be executed in parallel. The addition of the task into the job flow is what defines the potential parallelism, not the task itself. The task designer or implementer doesn’t need to know that the task is being executed at the same time as other tasks. It is not uncommon to have hundreds of tasks in a job flow.

Fig 1.2 A Complex Job Flow

Using that information, the SAS platform, and the Infrastructure for Risk Management (IRM) is able to automatically infer the parallelization in your analytics. This allows your analytics to run on tens or hundreds of cores. (Most SAS customers run out of cores before they run out of tasks to run in parallel.) By running SAS code in parallel, on a single machine or on a grid, you gain orders of magnitude of performance improvements.

This methodology also has the benefit of expressing your analytics in the form of Y= f(x), which is precisely what you feed a deep neural network (DNN) to learn. That organization of your analytics allows you to train a DNN to reproduce the results of your analytics originally written in SAS. Once you have the trained DNN, you can use it to score tremendously faster than the original SAS code. You can also use your DNN to push your analytics to the edge. I believe that this is a powerful methodology that offers a wide spectrum of applicability. It is also a good example of deep learning helping data scientists build better and faster models.

Fig 1.3 Example of a DNN with four layers: two visible layers and two hidden layers.

The number of neurons of the input layer is driven by the number of features. The number of neurons of the output layer is driven by the number of classes that we want to recognize, in this case, three. The number of neurons in the hidden layers as well as the number of hidden layers is up to us: those two parameters are model hyper-parameters.

How do I run my SAS program faster using deep learning?

In the financial risk division, I work with banks and insurance companies all over the world that are faced with increasing regulatory requirements like CCAR and IFRS17. Those problems are particularly challenging because they involve big data and big compute.

The good news is that new hardware architectures are emerging with the rise of hybrid computing. Computers are increasing built as a combination of traditional CPUs and innovative devices like GPUs, TPUs, FPGAs, ASICs. Those hybrid machines can run significantly faster than legacy computers.

The bad news is that hybrid computers are hard to program and each of them is specific: you write code for GPU, it won’t run on an FPGA, it won’t even run on different generations of the same device. Consequently, software developers and software vendors are reluctant to jump into the fray and data scientist and statisticians are left out of the performance gains. So there is a gap, a big gap in fact.

To fill that gap is the raison d’être of my new book, Deep Learning for Numerical Applications with SAS. Check it out and visit the SAS Risk Management Community to share your thoughts and concerns on this cross-industry topic.

Deep learning for numerical analysis explained was published on SAS Users.

1月 062018

Deep learning is not synonymous with artificial intelligence (AI) or even machine learning. Artificial Intelligence is a broad field which aims to "automate cognitive processes." Machine learning is a subfield of AI that aims to automatically develop programs (called models) purely from exposure to training data.

Deep Learning and AI

Deep learning is one of many branches of machine learning, where the models are long chains of geometric functions, applied one after the other to form stacks of layers. It is one among many approaches to machine learning but not on equal footing with the others.

What makes deep learning exceptional

Why is deep learning unequaled among machine learning techniques? Well, deep learning has achieved tremendous success in a wide range of tasks that have historically been extremely difficult for computers, especially in the areas of machine perception. This includes extracting useful information from images, videos, sound, and others.

Given sufficient training data (in particular, training data appropriately labelled by humans), it’s possible to extract from perceptual data almost anything that a human could extract. Large corporations and businesses are deriving value from deep learning by enabling human-level speech recognition, smart assistants, human-level image classification, vastly improved machine translation, and more. Google Now, Amazon Alexa, ad targeting used by Google, Baidu and Bing are all powered by deep learning. Think of superhuman Go playing and near-human-level autonomous driving.

In the summer of 2016, an experimental short movie, Sunspring, was directed using a script written by a long short-term memory (LSTM) algorithm a type of deep learning algorithm.

How to build deep learning models

Given all this success recorded using deep learning, it's important to stress that building deep learning models is more of an art than science. To build a deep learning or any machine learning model for that matter one need to consider the following steps:

  • Define the problem: What data does the organisation have? What are we trying to predict? Do we need to collect more data? How can we manually label the data? Make sure to work with domain expert because you can’t interpret what you don’t know!
  • What metrics can we use to reliably measure the success of our goals.
  • Prepare validation process that will be used to evaluate the model.
  • Data exploration and pre-processing: This is where most time will be spent such as normalization, manipulation, joining of multiple data sources and so on.
  • Develop an initial model that does better than a baseline model. This gives some indication of whether machine learning is ideal for the problem.
  • Refine model architecture by tuning hyperparameters and adding regularization. Make changes based on validation data.
  • Avoid overfitting.
  • Once happy with the model, deploy it into production environment. This may be difficult to achieve for many organisations giving that a deep learning score code is large. This is where SAS can help. SAS has developed a scoring mechanism called "astore" which allows deep learning method to be pushed into production with just a click.

Is the deep learning hype justified?

We're still in the middle of deep learning revolution trying to understand the limitations of this algorithm. Due to its unprecedented successes, there has been a lot of hype in the field of deep learning and AI. It’s important for managers, professionals, researchers and industrial decision makers to be able to distill this hype from reality created by the media.

Despite the progress on machine perception, we are still far from human level AI. Our models can only perform local generalization, adapting to new situations that must be similar to past data, whereas human cognition is capable of extreme generalization, quickly adapting to radically novel situations and planning for long-term future situations. To make this concrete, imagine you’ve developed a deep network controlling a human body, and you wanted it to learn to safely navigate a city without getting hit by cars, the net would have to die many thousands of times in various situations until it could infer that cars are dangerous, and develop appropriate avoidance behaviors. Dropped into a new city, the net would have to relearn most of what it knows. On the other hand, humans are able to learn safe behaviors without having to die even once—again, thanks to our power of abstract modeling of hypothetical situations.

Lastly, remember deep learning is a long chain of geometrical functions. To learn its parameters via gradient descent one key technical requirements is that it must be differentiable and continuous which is a significant constraint.

Looking beyond the AI and deep learning hype was published on SAS Users.

12月 222017
In keras, we can visualize activation functions' geometric properties using backend functions over layers of a model.

We all know the exact function of popular activation functions such as 'sigmoid', 'tanh', 'relu', etc, and we can feed data to these functions to directly obtain their output. But how to do that via keras without explicitly specifying their functional forms?

This can be done following the four steps below:

1. define a simple MLP model with a one dimension input data, a one neuron dense network as the hidden layer, and the output layer will have a 'linear' activation function for one neuron.
2. Extract layers' output of the model (fitted or not) via iterating through model.layers
3. Using backend function K.function() to obtain calculated output for a given input data
4. Feed desired data to the above functions to obtain the output from appropriate activation function.

The code below is a demo:

from keras.layers import Dense, Activation
from keras.models import Sequential
import keras.backend as K
import numpy as np
import matplotlib.pyplot as plt

# 以下设置显示中文文方法根据
plt.rcParams['font.sans-serif'] = ['SimHei'] #指定默认字体
plt.rcParams['axes.unicode_minus'] = False #解决图像中中文符号显示为方块的问题

def NNmodel(activationFunc='linear'):
if (activationFunc=='softplus') | (activationFunc=='sigmoid'):
elif activationFunc=='hard_sigmoid':
model = Sequential()
model.add(Dense(1, input_shape=(1,), activation=activationFunc,

model.add(Dense(1, activation='linear', name='Output'))
model.compile(loss='mse', optimizer='sgd')
return model

def VisualActivation(activationFunc='relu', plot=True):
x = (np.arange(100)-50)/10
y = np.log(x+x.max()+1)

model = NNmodel(activationFunc = activationFunc)

inX = model.input
outputs = [layer.output for layer in model.layers if'Hidden']
functions = [K.function([inX], [out]) for out in outputs]

layer_outs = [func([x.reshape(-1, 1)]) for func in functions]
activationLayer = layer_outs[0][0]

activationDf = pd.DataFrame(activationLayer)
result=pd.concat([pd.DataFrame(x), activationDf], axis=1)
result.columns=['X', 'Activated']
result.set_index('X', inplace=True)
if plot:

return result

# Now we can visualize them (assuming default settings) :
actFuncs = ['linear', 'softmax', 'sigmoid', 'tanh', 'softsign', 'hard_sigmoid', 'softplus', 'selu', 'elu']

from keras.layers import LeakyReLU
figure = plt.figure()
for i, f in enumerate(actFuncs):
# 依次画图
figure.add_subplot(3, 3, i+1)
out=VisualActivation(activationFunc=f, plot=False)
plt.plot(out.index, out.Activated)

This figure is the output from above code. As we can see, the geometric property of each activation function is well captured.

 Posted by at 4:44 下午
9月 072017
In many introductory to image recognition tasks, the famous MNIST data set is typically used. However, there are some issues with this data:

1. It is too easy. For example, a simple MLP model can achieve 99% accuracy, and a 2-layer CNN can achieve 99% accuracy.

2. It is over used. Literally every machine learning introductory article or image recognition task will use this data set as benchmark. But because it is so easy to get nearly perfect classification result, its usefulness is discounted and is not really useful for modern machine learning/AI tasks.

Therefore, there appears Fashion-MNIST dataset. This dataset is developed as a direct replacement for MNIST data in the sense that:

1. It is the same size and style: 28x28 grayscale image
2. Each image is associated with 1 out of 10 classes, which are:
       9:Ankle boot
3. 60000 training sample and 10000 testing sample Here is a snapshot of some samples:
Since its appearance, there have been multiple submissions to benchmark this data, and some of them are able to achieve 95%+ accuracy, most noticeably Residual network or separable CNN.
I am also trying to benchmark against this data, using keras. keras is a high level framework for building deep learning models, with selection of TensorFlow, Theano and CNTK for backend. It is easy to install and use. For my application, I used CNTK backend. You can refer to this article on its installation.

Here, I will benchmark two models. One is a MLP with layer structure of 256-512-100-10, and the other one is a VGG-like CNN. Code is available at my github:

The first model achieved accuracy of [0.89, 0.90] on testing data after 100 epochs, while the latter achieved accuracy of >0.94 on testing data after 45 epochs. First, read in the Fashion-MNIST data:

import numpy as np
import io, gzip, requests
train_image_url = ""
train_label_url = ""
test_image_url = ""
test_label_url = ""

def readRemoteGZipFile(url, isLabel=True):
response=requests.get(url, stream=True)
gzip_content = response.content
fObj = io.BytesIO(gzip_content)
content = gzip.GzipFile(fileobj=fObj).read()
if isLabel:
result = np.frombuffer(content, dtype=np.uint8, offset=offset)

train_labels = readRemoteGZipFile(train_label_url, isLabel=True)
train_images_raw = readRemoteGZipFile(train_image_url, isLabel=False)

test_labels = readRemoteGZipFile(test_label_url, isLabel=True)
test_images_raw = readRemoteGZipFile(test_image_url, isLabel=False)

train_images = train_images_raw.reshape(len(train_labels), 784)
test_images = test_images_raw.reshape(len(test_labels), 784)
Let's first visual it using tSNE. tSNE is said to be the most effective dimension reduction tool.This plot function is borrowed from sklearn example.

from sklearn import manifold
from time import time
import matplotlib.pyplot as plt
from matplotlib import offsetbox
plt.rcParams['figure.figsize']=(20, 10)
# Scale and visualize the embedding vectors
def plot_embedding(X, Image, Y, title=None):
x_min, x_max = np.min(X, 0), np.max(X, 0)
X = (X - x_min) / (x_max - x_min)

ax = plt.subplot(111)
for i in range(X.shape[0]):
plt.text(X[i, 0], X[i, 1], str(Y[i]),[i] / 10.),
fontdict={'weight': 'bold', 'size': 9})

if hasattr(offsetbox, 'AnnotationBbox'):
# only print thumbnails with matplotlib > 1.0
shown_images = np.array([[1., 1.]]) # just something big
for i in range(X.shape[0]):
dist = np.sum((X[i] - shown_images) ** 2, 1)
if np.min(dist) < 4e-3:
# don't show points that are too close
shown_images = np.r_[shown_images, [X[i]]]
imagebox = offsetbox.AnnotationBbox(
plt.xticks([]), plt.yticks([])
if title is not None:

tSNE is very computationally expensive, so for impatient people like me, I used 1000 samples for a quick run. If your PC is fast enough and have time, you can run tSNE against the full dataset.

samples=np.random.choice(range(len(Y_train)), size=sampleSize)
tsne = manifold.TSNE(n_components=2, init='pca', random_state=0)
t0 = time()
sample_images = train_images[samples]
sample_targets = train_labels[samples]
X_tsne = tsne.fit_transform(sample_images)
t1 = time()
plot_embedding(X_tsne, sample_images.reshape(sample_targets.shape[0], 28, 28), sample_targets,
"t-SNE embedding of the digits (time %.2fs)" %
(t1 - t0))
We see that several features, including mass size, split on bottom and semetricity, etc, separate the categories. Deep learning excels here because you don't have to manually engineering the features but let the algorithm extracts those.

In order to build your own networks, we first import some libraries

from keras.models import Sequential
from keras.layers.convolutional import Conv2D, MaxPooling2D, AveragePooling2D
from keras.layers.advanced_activations import LeakyReLU
from keras.layers import Activation
We also do standard data preprocessing:

X_train = train_images.reshape(train_images.shape[0], 28, 28, 1).astype('float32')
X_test = test_images.reshape(test_images.shape[0], 28, 28, 1).astype('float32')

X_train /= 255
X_test /= 255

X_train -= 0.5
X_test -= 0.5

X_train *= 2.
X_test *= 2.

Y_train = train_labels
Y_test = test_labels
Y_train2 = keras.utils.to_categorical(Y_train).astype('float32')
Y_test2 = keras.utils.to_categorical(Y_test).astype('float32')
Here is the simple MLP implemented in keras:

mlp = Sequential()
mlp.add(Dense(256, input_shape=(784,)))
mlp.add(Dense(10, activation='softmax'))
mlp.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])

This model achieved almost 90% accuracy on test dataset at about 100 epochs. Now, let's build a VGG-like CNN model. We use an architecture that is similar to VGG but still very different. Because the figure data is small, if we use original VGG architecture, it is very likely to overfit and won't perform very well in testing data which is observed in publically submitted benchmarks listed above. To build such a model in keras is very natural and easy:

num_classes = len(set(Y_train))
model3.add(Conv2D(filters=32, kernel_size=(3, 3), padding="same",
input_shape=X_train.shape[1:], activation='relu'))
model3.add(Conv2D(filters=64, kernel_size=(3, 3), padding="same", activation='relu'))
model3.add(MaxPooling2D(pool_size=(2, 2)))
model3.add(Conv2D(filters=128, kernel_size=(3, 3), padding="same", activation='relu'))
model3.add(Conv2D(filters=256, kernel_size=(3, 3), padding="valid", activation='relu'))
model3.add(MaxPooling2D(pool_size=(3, 3)))
model3.add(Dense(num_classes, activation='softmax'))
model3.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])
This model has 1.5million parameters. We can call 'fit' method to train the model:, Y_train2, validation_data = (X_test, Y_test2), epochs=50, verbose=1, batch_size=500)
After 40 epochs, this model archieves accuracy of 0.94 on testing data.Obviously, there is also overfitting problem for this model. We will address this issue later.

 Posted by at 8:48 上午
9月 032017


## 什么是KERAS

KEARS是Google工程师François Chollet为主创人员,基于Python开发和维护的一个抽象的神经网络建模环境,提供了一系列的API供用户调用构造自己的深度学习网络。KERAS的出发点就是为用户提供一个能够快速实现模型的手段,从而缩短建模迭代的时间,加快模型试验的频率。用KERAS开发者的话说,就是要做好的科研必须尽可能地缩短从想法到实现结果的时间。在业界工作中这也是成功的关键要素之一。


 1. 设计初衷就是方便以模块化地方式快速构造深度学习模型的原型;

2. 可以很方便地在CPU和GPU之间切换

3. KERAS本身只是描述模型的环境,其计算平台目前依赖于TensorFlow,CNTK和Theano这三种,以后会拓展到其他流行的计算平台上,比如mxNet等;

4. KERAS的拓展性既可以通过自定义KERAS里的激活函数或者损失函数等能自定义的部分进行,也可以通过引用对应的计算平台的自定义部分进行,具有一定的灵活性;



1. 首先要将原始数据处理成KERAS的API能够接受的格式,一般是一个张量的形式,通常在维度上表示为(批量数,[单一样本对应张量的维度])。这里[单一样本对应张量的维度] 是一个通用的说法,对应于不同类型的模型,数据有不同的要求。 通常,如果是一个简单的全链接模型,则单一样本对应张量的维度就是特征个数; 如果是一维的时间序列数据,并要用循环神经网络模型训练的话,则单一样本对应张量的维度是时间步和每个时间步对应的回看序列长度; 如果输入数据是图像,并使用卷积神经网络模型进行训练,则单一样本张量对应图像的高,宽和色彩频道三个维度。但是如果是使用全连接模型训练图像数据,则单一样本对应张量是该图像扁化(Flatten)以后的向量长度,其为高,宽和色彩频道各个维度数量的乘积。一般卷积神经网络最靠近输出层的那层都设置一个全连接层,因此也需要扁化输入张量。

2. 其次要构造需要的深度学习模型。这一步又分为模型的选择和模型的细化两个步骤:
   - 选择模型的类型。KERAS里定义了两大类模型

Figure 1。MLP是一个典型的序列模型,[图片来源]( 可以看到从左到右,输入层到隐含层到输出层每一层之间都是前后依次相连的简单关系。这个简单的网络结构可以用三句KERAS命令实现:

model.add(Dense(5, input_shape=(4,), activation=’sigmoid’))
model.add(Dense(1, activation=’sigmoid’))

而通用模型则是对应更广义的模型,具备更大的灵活性。上面提到的序列模型也可以用通用模型来表达,这个我们在后一节详解。 当然通用模型更能用来描述层与层之间有较复杂关系的情况,比如非相邻的层之间进行连接,或者多个神经网络的合并等。比如我们可以使用通用模型进行矩阵分解:

user_in = Input(shape=(1,), dtype='int64', name='user_in')
u = Embedding(n_users, n_factors, input_length=1)(user_in)
movie_in = Input(shape=(1,), dtype='int64', name='movie_in')
v = Embedding(n_movies, n_factors, input_length=1)(movie_in)
x = merge([u, v], mode='dot')
x = Flatten()(x)
model = Model([user_in, movie_in], x)
model.compile(Adam(0.001), loss='mse')


 Figure 2。矩阵分解的深度学习模型

      - 细化模型的结构。其实上面已经展示了模型结构细化之后的情况。一般来说,确定了模型类型以后,其结构不外乎每层的类型是什么,是全连接层还是卷积层还是放弃(Dropout)层;每层的其他参数是什么,比如如果需要指定激活函数,那么使用什么样的激活函数,如果是卷积层,那么需要多少过滤器,每个过滤器的大小是怎样的?等等这些都可以通过设定不同的参数进行细化。

3. 然后对模型进行编译,编译完成以后可以查看模型的基本信息,特别是参数的数量;

4. 最后带入数据对模型进行拟合。一般来讲,如果数据是静态的张量数据,通过使用fit方法。如果数据特别大,可是使用可迭代的data generator对象,并使用fit_generator方法来拟合。

## KERAS和深度学习模型的对应关系

KERAS既然是开发出来快速构造深度学习模型的工具,那么它的API和深度学习模型的要素都有很强的对应关系。 正如上面所说,目前的深度学习模型都可以纳入序列模型或者通用模型的,那么我们用图示的方式来表示这个对应关系,方便读者理解。这里网络图为了方便与按行排列的代码对应,对每一层都进行了标注。 下图展示的是一个典型的全连接序列模型:
Figure 3。全连接序列模型,修改自[博客](


Model = Sequential()
Model.add(Dense(10, activation=’sigmoid’,
input_shape=(8, )) 【隐含层1+输入层】
Model.add(Dense(8, activation=’relu’)) 【隐含层2】
Model.add(Dense(10, activation=’relu’)) 【隐含层3】
Model.add(Dense(5, activation=’softmax’)) 【输出层】


x = Input(shape=(8,)) 【输入层】
b = Dense(10, activation=’sigmoid’)(x) 【隐含层1】
c = Dense(8, activation=’relu’)(b) 【隐含层2】
d = Dense(10, activation=’relu’)(c ) 【隐含层3】
out = Dense(5, activation=’softmax’)(d) 【输出层】
model = Model(inputs=x, outputs=out)

上面也举了另外的比较复杂的例子。在后面的具体案例中,我们也会强调网络结构和对应的KERAS命令,使读者能建立起较强的联系。 ##使用KERAS构造深度推荐系统 推荐系统是机器学习最广泛的应用领域之一,大家熟悉的亚马逊、迪士尼、谷歌、Netflix 等公司都在网页上有其推荐系统的界面,帮助用户更快、更方便地从海量信息中找到有价值的信息。比如亚马逊(会给你推荐书、音乐等,迪士尼(给你推荐最喜欢的卡通人物和迪士尼电影,谷歌搜索更不用说了, Google Play、 Youtube 等也有自己的推荐引擎、推荐视频和应用等。下面是我登陆亚马逊之后的一个推荐页面,可见我之前应该是购买了咖啡机,所以会有相关的产品推荐出来。
 Figure 4。亚马逊的推荐页面局部



Figure 5。深度模型

有了这个示意图,我们就可以很方便地用KERAS依次构造。这里我们假设已经将用户和电影产品做了按照One Hot编码形式组织好了。


k = 128
model1 = Sequential()
model1.add(Embedding(n_users + 1, k, input_length = 1))
model2 = Sequential()
model2.add(Embedding(n_movies + 1, k, input_length = 1))

这里的k是映射到的空间的维度。在一般的业务系统中我们可能有上百万的用户和产品,经过嵌入映射到128维的实数域上以后显著地降低了整个系统的维度和大小。 以上几句命令实现了上图从最低下到“用户嵌入”和“电影嵌入”这一阶段的编程。


model = Sequential()
model.add(Merge([model1, model2], mode = 'concat'))

至此完成了到第一个粗箭头的网络构造。两个网络已经合并为一个网络。 下面的命令依次完成“隐含层128”和“隐含层32”的构造:

model.add(Dense(k, activation = 'relu'))
model.add(Dense(int(k/4), activation = 'relu'))


model.add(Dense(int(k/16), activation = 'relu'))


model.add(Dense(1, activation = 'linear'))

model.compile(loss = 'mse', optimizer = "adam")
这里使用了均方差(MSE)作为损失函数,并使用了ADAM优化算法。 下面,为了能训练模型,需要将数据构造为[users, movies]的形式:

users = ratings['user_id'].values
movies = ratings['movie_id'].values
X_train = [users, movies]
最后训练模型:, y_train, batch_size = 100, epochs = 50)




图像识别是深度学习最典型的应用之一。关于深度学习的图像识别可以追溯很长的历史,其中最具有代表性的例子是手写字体识别和图片识别。手写字体识别主要是用机器正确区别手写体数字 0~9。银行支票上的手写体识别技术就是基于这个技术。图片识别的代表作就是 ImageNet。这个比赛需要团队识别图片中的动物或者物体,把它们正确地分到一千个类别中的其中一个。 图像识别有很多种技术可以实现,目前最主流的技术是深度神经网络,其中尤以卷积神经网络(CNN)最为出名。卷积神经网络(见图1)是一种自动化特征提取的机器学习模型。从数学的角度看,任何一张图片都可以对应到 224 × 224 × 3 或者 32 × 32 × 3 等三维向量,这取决于像素。我们的目标是把这个三维向量(又被称为张量)映射到 N个类别中的一类。神经网络就是建立了这样一个映射关系,或者称为函数。它通过建立网状结构,辅以矩阵的加、乘等运算,最后输出每个图像属于每个类别的概率,并且取概率最高的作为我们的决策依据。 下面是一个典型的序列卷积神经网络模型的结构:
Figure 6。卷积神经网络结构。来源于CNTK教程

- 输入层的图像;
- 卷积操作;
- 激活函数的应用;
- 池化操作;
- 将数据展平(Flatten),为输出到全连接层做准备;
- 全连接层准备输出;
- softmax应用于分类问题的全连接层作为输出层。


 - 首先,这是一个序列模型,因此先要声明一个序列模型的对象:

- 卷积是应用一个局部的过滤器到原始数据的过程,比如下图就展示了一个3x3的过滤器应用在一个7x7的图像上过程。假设在当前步,这个过滤器的权重经过学习得到如图所示的权重结果,在当前步继续进行卷积操作就是将这个3x3的过滤器从左上角每次要么向右要么向下移动一格,和对应的图像局部的3x3的区域进行依元素点乘求和得到卷积的结果。因为依次移动,到最边上的时候过滤器会超出图像的边界,一般会将这些对应的卷积结果删除,从而卷积后的张量维度会少于原始图像。比如这个例子中原图为7x7,使用一个3x3的过滤器卷积之后最后两列和两行进行卷积的时候会使过滤器超过边界,因此最后的卷积结果是一个5x5的图像。这里可以使用多个过滤器,每个过滤器应用一次,每次应用产生的卷积结果构成隐含层的一层。比如采用16个过滤器,如果不删除边界的过滤结果,则得到新的[7x7x16]的张量。
Figure 7.卷积演示,来源于CNTK教程

1. 首先指定过滤器数量 filter,是一个整数;
2. 第二是要指定二维过滤器的大小,比如(3,3);
3. 第三要指定步长,即延某轴移动的时候是依次移动一个像素还是多个像素,默认为1;
4. 第四要指定补齐策略padding,即是否要将在边界的卷积结果去掉。如果值为”same”,则不去掉,卷积结果和输入图像有同样的高和宽;如果值为”valid”,则不会处理过滤器会超出边界的像素。
5. 最后,如果卷积层是第一层,那么还需要指明输入数据的维度input\_shape。因为一般用TensorFlow或者CNTK做后台,输入数据要求是channel_last,因此输入的原始维度为[样本量,高,宽,频道],那么这里的维度只需要去掉样本量即可,即为[高,宽,频道数],一般用X.shape[1:]即可得到。

    model.add(Conv2D(filters=16, kernel_size=(3, 3),
    strides=1, padding=”valid”,
- 再次要添加激活层引入激活函数,通常是一个非线性的函数。激活函数既可以通过在Conv2D里面指定activation=参数引入,也可以通过单独添加Activation层引入。

卷积神经网络常用的激活函数是Rectified Linear Unit, 简称relu。该函数其实就是max(0, x),在层次较深的网络中比以前常用的取值区间在(0,1)或者(-1, 1)之间的sigmoid类激活函数效果好,因为不存在梯度消失的问题。

    model.add(Conv2D(filters=16, kernel\_size=(3, 3),
    strides=1, padding=”valid”,

- 然后进行的池化操作是在卷积神经网络中对图像特征的一种处理,通常在卷积操作和激活函数之后进行。池化操作是将原有输入按照一定大小切分成互不交叉的局部区域,目的是为了计算特征在局部的充分统计量,从而降低总体的特征数量,防止过度拟合和减少计算量。下图展示了最大池化方法的应用。在一个6x6的图像上应用3x3的池化操作,将原输入矩阵切割为不相交叉的2x2区域,每个区域的取值是对应原输入局部的最大值。
Figure 8。最大池化操作 对应于图像的最大池化层通过MaxPooling2D,KERAS也支持平均池化层,区别在于取对应局部的平均值作为池化后结果,方法为AveragePooling2D。对应上面的例子,KERAS的命令如下:

    model.add(MaxPooling2D(pool_size=(3, 3))
- 为了输出到全连接层,先要对数据进行展平(Flatten)。这是因为全连接层只处理包含样本数在内一共二维的数据,要求第一维是样本数,第二维是所有特征的个数。因此对于一个包含2000个样本,每个样本是28x28x3的小图像的数据,展平之后是一个2000x2352的矩阵,其中2352是28,28,3的乘积。在KERAS里进行展平非常简单,在上面的MaxPooling2D层之后添**model.add(Flatten())** 即可,KERAS能自己分析出输入和输出的维度。

 - 在前面这些处理之后,但是在输出之前,通常会添加一个或者多个全连接层进一步处理数据。全连接层可以通过Dense指出,指明输出神经元个数和激活函数即可:
model.add(Dense(1000, activation=’relu’))

 - 最后使用一个全连接层作为输出层,同样要求使用softmax激活函数,并使用跟输出类别同样多的神经元个数。比如识别0—9十个数字,那么就应该写作:
model.add(Dense(10, activation=’relu’))


model.add(Conv2D(filters=32, kernel_size=(3, 3),
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Conv2D(filters=64, kernel_size=(3, 3), padding="valid"))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Dense(128, activation='relu'))
model.add(Dense(num_classes, activation='softmax'))
是不是很 简单? 要训练这个模型非常简单。我们先编译这个模型并显示其关键信息:

model.compile(loss='categorical_crossentropy', optimizer='adagrad', metrics=['accuracy'])

 Figure 9。模型信息 我们看到这个模型一共有421642个参数,大多来自于倒数第二层的全连接层。 拟合这个模型也很简单:, y_train,
epochs=20, verbose=1,
validation_data = (X_test, y_test))


1. 训练用特征数据X\_train,
2. 训练用结果数据y\_train,
3. 迭代次数epochs,
4. 批量大小用batch\_size指定,
5. verbose表示显示训练过程的信息,如果值为0不显示任何中间信息,如果为1显示按批量拟合的进度,如果为2则显示拟合结果信息。
6. 另外读者还可以指定验证数据集,用validation_data这个参数表示,其包含一个tuple,第一个元素是验证用特征数据,第二个是验证用结果数据。


* 首先将数据重塑为[样本数,高,宽,色彩通道数]的格式。这个可以通过numpy.reshape方法来实现。因为keras自带的MNIST数据已经是numpy的多维矩阵,并且是单色的,因此色彩通道数为1,因此数据重塑可以用下面的命令实现。读者可自行重塑验证用数据。

    X_train = X_train.reshape(X_train.shape[0],
    X_train.shape[2], 1).astype(float)

* 其次,需要将数据的取值压缩到[0, 1]之间。这有利于拟合时用的随机梯度递降算法的稳定和收敛。这可以使用X_train /= 255.0 来实现。 。

* 最后要将结果数据变为One Hot Code形式。KERAS提供了一个非常方便的方法to_categorical来实现这个功能:

    y_train = keras.utils.to_categorical(y_train, len(set(y_train)))

Figure 10。简单卷积模型在MNIST数据上的拟合结果。

 使用KERAS可以非常方便的构造自己的卷积神经网络,对于比较复杂的情况,也可以使用已经训练好的一些常见的高效模型,比如VGG16,Xception 等做迁移训练来拟合自己的数据。
Figure 11. VGG16结构,来源于:


model_vgg = VGG16(include_top = False,
weights = 'imagenet',
input_shape =(224,224,3))
model = Flatten(name = 'flatten')(model_vgg.output)
model = Dense(10, activation = 'softmax')(model)
model_vgg_mnist = Model(model_vgg.input, model,
name = 'vgg16')
这里首先引用VGG16模型,但是通过参数include_top=False指定迁移除顶层以外的其余网络结构到自己的模型中。Weights=’imagenet’表示借用的权重是用ImageNet数据训练出来的额。 其次,通过函数方法在修改过的VGG16模型上构造一个新的扁平层用来连接新构造的全连接层,这个全连接层跟前面的模型没有区别。最后把修改过的VGG16模型和新的顶层叠加起来并赋予新的名字vgg16。这样就得到了一个基于VGG16的新模型。

 ## 使用KERAS构造时间序列预测模型

 时间序列是在商业数据或者工程数据中经常出现的一种数据形式,是以时间为次序排列,用来描述和计量一系列过程或者行为的数据的统称。比如每天商店的收入流水或者某个工厂每小时的产品产出都是时间序列数据。一般研究的时间序列数据有两种类型。最常见的是跟踪单一的计量数据随时间变化的情况,即每个时间点上收集的数据是一个一维变量,这种是最常见的,通常的时间序列默认就是这种数据,也是本章研究的对象。另外一种时间序列数据是多个对象或者多个维度的计量数据随时间变化的情况,即每个时间点上收集的数据是一个多维变量,这种一般也被称为纵向数据(Longitudinal Data),但是不属于这里介绍的对象。

在这里我们介绍如何搭建一个LSTM深度学习模型来对在汉口测量的长江每月流量数据进行预测建模。该数据来源于DataMarket 的[时间序列数据库](,由澳大利亚莫纳什大学的统计学教授Rob Hyndman 创建,收集了数十个公开的时间序列数据集。

汉口长江月流量数据包含从 1865 年 1 月到 1978 年 12 月在汉口记录的长江每月的流量,总计 1368 个数据点。计量单位未知。
 Figure 12。长江月度流量时间序列 在一般的时间序列建模中,都需要检验数据的平稳性,因为传统时间序列建模都是建立在平稳数据的假设之上。这个数据具备非常强的年度周期性。使用传统的统计技术建模的时候都需要侦测周期性,并消除之,对消除周期性之后的数据运用ARIMA模型建模。
 Figure 13。长江月度流量局部和移动平滑结果

我们可以通过周期图谱法(Periodogram)来得到主要的周期幅度。在Python中可以使用scipy.signal.periodogram来得到周期图谱。在这里我们不是使用原始数据,而是使用原始数据的自相关函数的周期图谱来计算主要周期,这样可以抵消噪音的影响。对读入pandas DataFrame的原始数据ts运行下面的程序我们可以得到如下的周期图谱和计算得到的主要周期长度。

import statsmodels.api as sm
from statsmodels.tsa.stattools import acf
from scipy import signal
import peakutils as peak
acf_x, acf_ci = acf(ts, alpha=0.05, nlags=36)
f, Pxx_den = signal.periodogram(acf_x, fs)
index = peak.indexes(Pxx_den)
fig = plt.figure()
ax0 = fig.add_subplot(111)
plt.vlines(f, 0, Pxx_den)
plt.plot(f, Pxx_den, marker='o', linestyle='none', color='red')
plt.title("Identified Cycle of %i" % (cycle))
plt.xlabel('frequency [Hz]')
plt.ylabel('PSD [V**2/Hz]')
print( index, f, Pxx_den)

Figure 14。周期图谱 很明显有一个周期为 12 个月的季节性。

虽然考虑到这个数据的本质是长江水文资料, 12 个月的周期是非常自然的预期,但是这个方法展示了对 ACF 序列运用周期图法(periodogram)找季节性周期的可靠性。在传统方法里,这里需要通过取间隔为12 的差分来消除周期性,得到一个尽可能平稳的时间序列,进而采用ARIMA模型建模。在Python里,单周期的时间序列数据,知道周期的长度以后可以直接使用季节性ARIMA模型(SARIMA)来训练。 但是在使用循环神经网络模型的时候我们不用考虑这些情况,可以直接使用长短记忆模型。此外,在使用LSTM这种序列模型的时候在使用LSTM对这种单一时间序列进行建模的时候,一般通过一下步骤:

1. 将数据标准化为[0,1]区间。
2. 按照LSTM的要求,将输入数据组织为[样本数,时间步,特征变量数]的三位格式来组织。
3. 定义一个LSTM深度学习模型,通常为一个序列模型对象,逐层添加LSTM层或者其他层,最后通过一个全连接层输出到输出层。
4. 最后对需要的时间段进行预测。 首先对数据进行标准化,我们使用sklearn包里的MinMaxScaler函数:

scaler = MinMaxScaler(feature_range=(0, 1))
trainstd = scaler.fit_transform(train.values.astype(float).reshape(-1, 1))
teststd = scaler.transform(test.values.astype(float).reshap

其次,我们将训练数据和测试数据组织成需要的格式,这个格式与我们将要建立的LSTM模型有关。这里我们对每个输入构造一个LSTM神经元,一个60个输入单元,每一个对应一个时间步。这60个单元的输出会作为一个全连接层的输入,这个全连接层直接产生下K个连续时间步的输出预测。作为防止过度拟合的正则化手段,我们在LSTM层和全连接层 之间加了一个Dropout层。这个Dropout层在训练的时候会随机放弃一部分权重的更新,但是在进行预测的时候所有权重都会被用到。
Figure 15。LSTM网络结构 (修改自CNTK Tutorial)


def create_dataset(dataset, timestep=1, look_back=1, look_ahead=1):
from statsmodels.tsa.tsatools import lagmat
import numpy as np
ds = dataset.reshape(-1, 1)
dataX = lagmat(dataset,
trim="both", original='ex')
dataY = lagmat(dataset[(timestep*look_back):],
trim="backward", original='ex')
dataX = dataX.reshape(dataX.shape[0],
timestep, look_back)[:-(look_ahead-1)]
return np.array(dataX), np.array(dataY[:-(look_ahead-1)])

trainX, trainY = create_dataset(trainstd,
look_back=lookback, look_ahead=lookahead)
trainX, trainY = trainX.astype('float32'), trainY.astype('float32')
truthX, truthY = create_dataset(truthstd,
look_back=lookback, look_ahead=lookahead)

model = Sequential()
model.add(LSTM(48, batch_size=batch_size, \
input\_shape=(timestep, lookback), kernel_initializer='he_uniform'))
model.compile(loss='mean_squared_error', optimizer='adam')
调用fit方法就可以快速的训练这个模型。我们指定迭代20次,小批量数为100):, trainY, epochs=20, batch_size=batch_size, verbose=1)
 Figure 16。LSTM拟合过程信息

 Figure 17。LSTM拟合结果


## 小结

在这篇短文中,我们介绍了一个目前正在流行起来的深度学习建模环境KERAS。这个建模环境相对于传统的计算环境,比如CNTK,TensorFlow,Theano等具有抽象性高,易用性好的特点,同时又依托于这几种计算环境,具有一定的可拓展性,非常适合于从事深度学习的实践者使用。 我们看到使用KERAS可以非常直观地描述神经网络结构,几乎可以达到所见即所得的情况。我们在文中还分别介绍了三种流行的应用领域,分别是:

 - 深度推荐模型,运用嵌入技术可以将不同类型的信息有机结合在一起构造一个深度神经网络推荐系统;
- 图像识别模型,运用多层卷积神经网络对图像进行切割分析,得到一个精度很好的手写数字分类器。同样的技术和模型可以直接移植到其他物体识别数据上,比如CIFAR10等。我们也介绍了运用已经训练好的现成模型进行迁移学习的手段,减少拟合的参数量,在保持一定精度的情况下提高训练速度;
- 简单时间序列预测模型,运用长短记忆(LSTM)神经网络模型来有效预测具备一定周期性的时间序列模型。一个非常简单的单层LSTM模型既可以达到定制的SARIMA模型的预测精度。

 Posted by at 3:32 下午
5月 172017

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