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This article was published as a part of the Data Science Blogathon

IntroductionIn today’s article, I will talk about developing a convolutional neural network employing TensorFlow Functional API. It will dispense the capability of functional API, which allows us to produce hybrid model architecture surpassing the ability of a primary sequential model.

Photo by Rita Morais from Unsplash

About: TensorFlowTensorFlow is a popular library, something you perpetually hear probably in Deep Learning and Artificial Intelligence society. There are numerous open-source packages and projects for deep learning.

TensorFlow, an open-source artificial intelligence library managing data flow graphs, is the most prevalent deep-learning library. It is used to generate large-scale neural networks with countless layers.

TensorFlow is practiced for deep learning or machine learning predicaments such as Classification, Perception, Perception, Discovery, forecast, and Production.

So, when we interpret a classification problem, we apply a convolutional neural network model. Still, most developers were intimate with modeling sequential models. The layers accompany each other one by one.

The sequential API empowers you to design models layer-by-layer for most significant problems.

The difficulty is restricted in that it does not allow you to produce models that share layers or have added inputs or outputs.

Because of this, we can practice Tensorflows Functional API as Multi-Output Model.

Functional API (tf.Keras)The functional API in tf.Keras is an alternative way of building more flexible models, including formulating a further complex model.

For example, when implementing an insignificantly more complicated example with machine learning, you may rarely face the state when you demand added models for the same data.

So we would need to produce two outputs. The most manageable option would be to build two separate models based on the corresponding data to make predictions.

This would be gentle, but what if, in a present scenario, we need to have 50 outputs. It could be a discomfort to maintain all those separate models.

Alternatively, it is more fruitful to construct a single model with increased outcomes.

In the open API method, models are determined by forming layers and correlating them straight to each other in sets, then establishing a Model that defines the layers to function as the input and output.

What is different in Sequential API?Sequential API enables you to generate models layer-by-layer for most top queries. It is regulated because it does not allow you to design models that share layers or have added inputs or outputs.

Let us understand how to create an object of sequential API model below:

model = tf.keras.models.Sequential([ tf.keras.layers.Flatten(input_shape=(28, 28)), tf.keras.layers.Dense(128, activation=’relu’), tf.keras.layers.Dropout(0.2), tf.keras.layers.Dense(10, activation=’softmax’) ])

In functional API, you can design models that produce a lot more versatility. You can undoubtedly fix models where layers relate to more than just the preceding and succeeding layers.

You can combine layers with several other layers. As a consequence, producing heterogeneous networks such as siamese networks and residual networks becomes feasible.

Let’s begin to develop a CNN model practicing a Functional APIIn this post, we utilize the MNIST dataset to build the convolutional neural network for image classification. The MNIST database comprises 60,000 training images and 10,000 testing images secured from American Census Bureau workers and American high school juniors.

# import libraries import numpy as np import tensorflow as tf from tensorflow.keras.layers import Dense, Dropout, Input from tensorflow.keras.layers import Conv2D, MaxPooling2D, Flatten from tensorflow.keras.models import Model from tensorflow.keras.datasets import mnist # load data (x_train, y_train), (x_test, y_test) = mnist.load_data() # convert sparse label to categorical values num_labels = len(np.unique(y_train)) y_train = to_categorical(y_train) y_test = to_categorical(y_test) # preprocess the input images image_size = x_train.shape[1] x_train = np.reshape(x_train,[-1, image_size, image_size, 1]) x_test = np.reshape(x_test,[-1, image_size, image_size, 1]) x_train = x_train.astype('float32') / 255 x_test = x_test.astype('float32') / 255In the code above,

I distributed these two groups as train and test and distributed the labels and the inputs.

Independent variables (x_train and x_test) hold greyscale RGB codes of 0 to 255, whereas dependent variables (y_train and y_test) carry labels of 0 to 9, describing which number they genuinely are.

It is a good practice to normalize our data as it is constantly required in deep learning models. We can accomplish this by dividing the RGB codes by 255.

Next, we initialize parameters for the networks.

# parameters for the network input_shape = (image_size, image_size, 1) batch_size = 128 kernel_size = 3 filters = 64 dropout = 0.3In the code above,

input_shape: variable represents a need to plan and style a standalone Input layer that designates input data. The input layer accepts a shape argument that is a tuple that describes the dimensions of the input data.

batch_size: is a hyperparameter that determines the number of samples to run through before refreshing the internal model parameters.

kernel_size: relates to the dimensions (height x width) of the filter mask. Convolutional neural networks (CNN) are essentially a pile of layers marked by various filters’ operations on the input. Those filters are ordinarily called kernels.

filter: is expressed by a vector of weights among which we convolve the input.

Dropout: is a process where randomly picked neurons are neglected throughout training. This implies that their participation in the activation of downstream neurons is temporally dismissed on the front pass.

Let us define a simplistic Multilayer Perceptron, a convolutional neural network:

# utiliaing functional API to build cnn layers inputs = Input(shape=input_shape) y = Conv2D(filters=filters, kernel_size=kernel_size, activation='relu')(inputs) y = MaxPooling2D()(y) y = Conv2D(filters=filters, kernel_size=kernel_size, activation='relu')(y) y = MaxPooling2D()(y) y = Conv2D(filters=filters, kernel_size=kernel_size, activation='relu')(y) # convert image to vector y = Flatten()(y) # dropout regularization y = Dropout(dropout)(y) outputs = Dense(num_labels, activation='softmax')(y) # model building by supplying inputs/outputs model = Model(inputs=inputs, outputs=outputs) In the code above,

We specify a multilayer Perceptron model toward binary classification.

The model holds an input layer, 3 hidden layers beside 64 neurons, and a product layer with 1 output.

Rectified linear activation functions are applied in all hidden layers, and a softmax activation function is adopted in the product layer for binary classification.

And you can observe the layers in the model are correlated pairwise. This is achieved by stipulating where the input comes from while determining each new layer.

As with every Sequential API, the model is the information we can summarize, fit, evaluate, and apply to execute predictions.

TensorFlow presents a Model class that you can practice to generate a model from your developed layers. It demands that you only define the input and output layers—mapping the structure and model graph of the network architecture.

Lastly, we train the model.

optimizer=’adam’, metrics=[‘accuracy’]) model.fit(x_train, y_train, validation_data=(x_test, y_test), epochs=20, batch_size=batch_size) # accuracy evaluation score = model.evaluate(x_test, y_test, batch_size=batch_size, verbose=0) print(“nTest accuracy: %.1f%%” % (100.0 * score[1]))

Now we have successfully developed a convolutional neural network to distinguish handwritten digits with Tensorflow’s Functional API. We have obtained an accuracy of above 99%, and we can save the model & design a digit-classifier web application.

References:

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## Introduction To Saliency Map In An Image With Tensorflow 2.X Api

This article was published as a part of the Data Science Blogathon.

Introduction to Tensorflow 2.xSuppose we want to focus on a particular part of an image than what concept will help us. Yes, it is a saliency map. It mainly focuses on specific pixels of images while ignoring others.

Saliency MapThe saliency map of an image represents the most prominent and focused pixel of an image. Sometimes, the brighter pixels of an image tell us about the salient of the pixels. This means the brightness of the pixel is directly proportional to the saliency of an image.

Suppose we want to give attention to a particular part of an image, like wanting to focus on the image of a bird rather than the other parts like the sky, nest etc. Then by computing the saliency map, we will achieve this. It will crucially assist in reducing the computational cost. It is usually a grayscale image but can be converted into another format of a coloured image depending upon our visual comfortability. Saliency maps are also termed “heat maps” since the hotness/brightness of the image has an impactful effect on identifying the class of the object. The saliency map aims to determine the areas in the fovea that are salient or observable at every place and to influence the decision of attentive regions based on the spatial pattern of saliency. It is employed in a variety of Visual Attention models. The “ITTI and Koch” Computational Framework of Visual Attention is built on the notion of a saliency map.

How to Compute Saliency Map with Tensorflow?The saliency map can be calculated by taking the derivatives of the class probability Pk with respect to the input image X.

saliency_map = dpk/dX

Hang on a minute! That seems quite familiar! Yes, it’s the same backpropagation which we use for training the model. We only need to take one more step: the gradient does not stop at the first layer of our network. Rather, we must return it to the input image X.

As a result, saliency maps provide a suitable characterization for each input pixel in accordance with a specific class prediction Pi. Pixels that are significant for flower prediction should cluster around flower pixels. Otherwise, something really strange is going on with the trained model.

Different Types of the Saliency Map1. Static Saliency: It focuses on every static pixel of the image to calculate the important area of interest for saliency map analysis.

2. Motion Saliency: It focuses on the dynamic features of video data. The saliency map in a video is computed by calculating the optical flow of a video. The moving entities/objects are considered salient objects.

CodeWe will perform step-by-step investigations of the ResNet50 architecture, which has been pre-trained on ImageNet. But you can take other pretrained deep learning models or bring your own trained model. We will illustrate how to develop a basic saliency map utilizing the most famous DL model in TensorFlow 2.x. We used the Wikimedia image as a test image during the tutorials.

We begin by creating a ResNet50 with ImageNet weights. With the simple helper functions, we import the image on the disc and prepare it for feeding to the ResNet50.

# Import necessary packages import tensorflow as tf import numpy as np import matplotlib.pyplot as plt def input_img(path): image = tf.image.decode_png(tf.io.read_file(path)) image = tf.expand_dims(image, axis=0) image = tf.cast(image, tf.float32) image = tf.image.resize(image, [224,224]) return image def normalize_image(img): def get_image(): import urllib.request filename = 'image.jpg' urll )fig1: Input_image

test_model = tf.keras.applications.resnet50.ResNet50() #test_model.summary() get_image() img_path = "image.jpg" input_img = input_img(img_path) input_img = tf.keras.applications.densenet.preprocess_input(input_img) plt.imshow(normalize_image(input_img[0]), cmap = "ocean") result = test_model(input_img) max_idx = tf.argmax(result,axis = 1) tf.keras.applications.imagenet_utils.decode_predictions(result.numpy())

with tf.GradientTape() as tape: tape.watch(input_img) result = test_model(input_img) max_score = result[0,max_idx[0]]

fig2: (1) Saliency_map, (2) input_image, (3) overlayed_image

ConIn this blog, we have defined the saliency map in different aspects. We have added a pictorial representation to understand the term “saliency map” deeply. Also, we have understood it by implementing it in python using TensorFlow API. The results seem promising and can be easily understandable.

In this article, you have learned about the saliency map for an image with tensorflow.

A python code is also implemented on an image t

The mathematical background of the saliency map is also covered in this article.

That’s it! Congratulations, you just computed a saliency map.

github_repo.

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## Building A Blockchain In Python

This article was published as a part of the Data Science Blogathon.

Introduction on BlockchainEach block in a blockchain is unique and contains a hash value, which can be used for differentiating each block. Fingerprinting is the concept used for linking blocks on a blockchain. As new blocks keep getting added to the end of the blockchain, the hash of the penultimate block is used for building the hash for a new block, which makes the blocks in a blockchain tamper-proof.

In this article, we will be building a simple blockchain in python that will store some text information from users. The blockchain technology used in the industry is far more complex than the blockchain that we will be building in this article, but this is enough to understand blockchain technology from an implementation perspective.

Each block on our blockchain will have the following properties:

Index – This is an auto-incremented number used to recognize a block in the blockchain.

Sender – The user who created the block on the blockchain.

Timestamp – The time at which the block was created.

Previous hash – The hash value of the preceding block in the chain. This is useful in verifying the integrity of a blockchain by fingerprinting and linking the blocks in the blockchain.

Hash – This is a hash generated using all the above-mentioned properties present in a block. This property uniquely identifies a block in a blockchain.

Nonce – This is a number that helps in creating the hash as per the difficulty requirement set for the blockchain.

The first block of a blockchain is called the genesis block. From the above explanation, it can be derived that the preceding hash cannot be extracted from the blockchain as the blockchain is empty. In such a case, the preceding hash is generated using some secret specified by the creator of that blockchain. This ensures that all the blocks in a blockchain have a similar structural schema. Each blockchain has a difficulty level associated with it. It specifies the number of digits that need to be 0 in the hash. To satisfy this condition, we have the nonce property, which is a whole number that helps in generating the hash with the specified number of preceding zeros. Since the hashing algorithm used in most blockchain technology is SHA256, it is almost impossible to find the nonce by pre-calculating the hash value. Trial-and-error is the only way to calculate the nonce, which makes it computationally expensive and time-consuming. We need to run a for loop to calculate the nonce value. The process of guessing the nonce that generates the hash as per the requirements is called blockchain mining and is computationally expensive and time-consuming but is necessary to add a block to the blockchain. We will set the difficulty level to 4 for our blockchain and so the first 4 letters of each hash should have ‘0000’. For mining bitcoin, the difficulty level is set to 30, and mining each block in bitcoin roughly takes 10 minutes.

Now that we have a basic understanding of the blockchain that we will be building in this article, let’s get our hands dirty and start building.

Importing ModulesThere is nothing fancy here; all the modules used in building the blockchain are native python modules and can be directly imported without having to install them using pip. We will be using the hashlib module for performing SHA256 hashing while the time module will be useful to fetch the block generation time.

import hashlib from time import time from pprint import pprint Building the BlockchainWe will define a class called blockchain with two properties, namely blocks and secret. The blocks property will store all the blocks on the blockchain while the secret variable will be used for building the previous hash for the genesis block. We will define three functions, namely create_block, validate_blockchain, and show_blockchain. The create_block function will be used to create a new block and append it to the block’s property in the blockchain. The properties of each block explained earlier will be implemented here. The nonce that satisfies the blockchain requirement of having four zeros preceding each hash will be calculated. The validate_blockchain function will be used to validate the integrity of the blockchain. This means that it will check the fingerprinting on each block on the blockchain and tell us if the blockchain is stable or not. Each block should contain the correct hash of the previous block. If there are any discrepancies, it is safe to assume that someone has meddled with the blocks on the blockchain. This property makes blockchains immutable and tamper-proof. Finally, the show_blockchain function will be used to display all the blocks on the blockchain.

class blockchain(): def __init__(self): self.blocks = [] self.__secret = '' self.__difficulty = 4 # guessing the nonce i = 0 secret_string = '/*SECRET*/' while True: _hash = hashlib.sha256(str(secret_string+str(i)).encode('utf-8')).hexdigest() if(_hash[:self.__difficulty] == '0'*self.__difficulty): self.__secret = _hash break i+=1 def create_block(self, sender:str, information:str): block = { 'index': len(self.blocks), 'sender': sender, 'timestamp': time(), 'info': information } if(block['index'] == 0): block['previous_hash'] = self.__secret # for genesis block else: block['previous_hash'] = self.blocks[-1]['hash'] # guessing the nonce i = 0 while True: block['nonce'] = i _hash = hashlib.sha256(str(block).encode('utf-8')).hexdigest() if(_hash[:self.__difficulty] == '0'*self.__difficulty): block['hash'] = _hash break i+=1 self.blocks.append(block) def validate_blockchain(self): valid = True n = len(self.blocks)-1 i = 0 while(i<n): if(self.blocks[i]['hash'] != self.blocks[i+1]['previous_hash']): valid = False break i+=1 if valid: print('The blockchain is valid...') else: print('The blockchain is not valid...') def show_blockchain(self): for block in self.blocks: pprint(block) print()Now that we have built the blockchain class, let’s use it to create our blockchain and add some blocks to it. I will add 3 blocks to the blockchain and will validate the blockchain and finally print the blocks and look at the output.

Python Code:

We can see the blocks present on the blockchain and that the validate_blockchain function returns true. Now let’s meddle with our blockchain and add a new block somewhere in-between the blocks of the blockchain and run the validate_blockchain function to see what it returns.

block = { 'index': 2, 'sender': 'Arjun', 'timestamp': time(), 'info': 'I am trying to tamper with the blockchain...' } block['previous_hash'] = b.blocks[1]['hash'] i = 0 while True: block['nonce'] = i _hash = hashlib.sha256(str(block).encode('utf-8')).hexdigest() if(_hash[:4] == '0'*4): block['hash'] = _hash break i+=1 b.blocks.insert(2, block) b.show_blockchain() b.validate_blockchain()This is the output we get.

{'hash': '0000bfffcda53dc1c98a1fbaeab9b8da4e410bbcc24690fbe648027e3dadbee4', 'index': 0, 'info': 'Python is the best programming language!!', 'nonce': 91976, 'previous_hash': '000023ae8bc9821a09c780aaec9ac20714cbc4a829506ff765f4c82a302ef439', 'sender': 'Ram', 'timestamp': 1654930841.4248617} {'hash': '00006929e45271c2ac38fb99780388709fa0ef9822c7f84568c22fa90683c15f', 'index': 1, 'info': 'I love cybersecurity', 'nonce': 171415, 'previous_hash': '0000bfffcda53dc1c98a1fbaeab9b8da4e410bbcc24690fbe648027e3dadbee4', 'sender': 'Vishnu', 'timestamp': 1654930842.8172457} {'hash': '000078a974ba08d2351ec103a5ddb2d66499a639f90f9ae98462b9644d140ca9', 'index': 2, 'info': 'I am trying to tamper with the blockchain...', 'nonce': 24231, 'previous_hash': '00006929e45271c2ac38fb99780388709fa0ef9822c7f84568c22fa90683c15f', 'sender': 'Arjun', 'timestamp': 1654930848.2898204} {'hash': '0000fe124dad744f17dd9095d61887881b2cbef6809ffd97f9fca1d0db055f2a', 'index': 2, 'info': 'AI is the future', 'nonce': 173881, 'previous_hash': '00006929e45271c2ac38fb99780388709fa0ef9822c7f84568c22fa90683c15f', 'sender': 'Sanjay', 'timestamp': 1654930845.594902} The blockchain is not valid...We can see that the validate_blockchain function returns false because there is some mismatch in the fingerprinting and hence the integrity of our blockchain has been compromised.

In this article, we discussed the following:

What is blockchain and how to build a blockchain using Python?

Properties of blockchain

Fingerprinting in blockchain

Difficulty level and nonce in blockchain

Building our own blockchain

Tampering with the blocks

Checking for the integrity of the tampered blockchain

To continue this project further, the blockchain can be hosted and deployed as a REST API server on the cloud that can be used by the users to store information on the blockchain. Obviously, our blockchain is not distributed for the sake of simplicity. If you are really interested in using blockchain technology for your database, feel free to look at BigchainDB, which is a decentralized blockchain database. It provides support for both python and nodejs. Alternatively, GunDB is a popular graph-based decentralized database engine being used in web3 applications in recent times.

That’s it for this article (building blockchain using Python). Hope you enjoyed reading this article and learned something new. Thanks for reading and happy learning!

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## Building A Diverse, Strong Climate Workforce

Building a Diverse, Strong Climate Workforce Climate leaders from Boston University and around the country brief Congress on how they are working to train the next generation for careers solving the climate crisis

Pamela Templer (center), a BU College of Arts & Sciences professor of biology, participated in a virtual Congressional briefing event titled Building the Next Generation Climate Workforce, along with Shawn Jones (left), head of energy storage development at BlueWave Solar, and PhD candidate Yasmin Romitti (Pardee’12, GRS’25).

Climate Change

Building a Diverse, Strong Climate Workforce Climate leaders from Boston University and around the country briefed Congressional staff on how they are working to train the next generation for careers solving the climate crisisClimate change is throwing problems at society that are unlike any we’ve experienced before—from battling extreme heat to combating flooding from sea level rise. It’s forcing us to not only build adaptations for a changing world, but take on the monumental tasks of creating green infrastructure and transitioning from carbon-emitting fossil fuels to renewable energy. And every piece of solving the climate puzzle will require more and more involvement by people from all walks of life.

In the face of unfolding climate challenges, many universities, community organizations, and private companies are training people who want to build a career in the climate workforce, whether in science, management, policy, communication, or governance fields. On June 9, Boston University brought together leaders in climate change solutions and research for a Congressional briefing on how to build a workforce centered on meeting the global challenges from climate change, a panel called Building the Next Generation Climate Workforce: Innovative Solutions from Around the Country.

The briefing was hosted by BU Federal Relations and featured four different panelists with expertise in science-backed policymaking, expanding diversity in STEM, and preparing to meet energy demands from renewable sources like solar and wind.

“The media often latches on to the darkest and worst side of an issue and climate change is no different,” said panel moderator Melissa Varga, science network community and partnerships manager for the Union of Concerned Scientists Center for Science and Democracy, in her opening remarks. ”Don’t get me wrong, the situation is dire. Marginalized and communities of color are the worst and first hit, and immediate action is needed. But rarely do we hear about the innovative efforts that are actually working for communities.” Each speaker at the virtual panel shared how their work contributes to training a diverse climate workforce.

Varga introduced US Rep. Suzanne Bonamici (D-Ore.), who spoke about how Congress has a role to play supporting that workforce, including through legislation that can expand job training opportunities to communities who have historically been left behind. “Here in the Pacific Northwest, we feel these effects [of climate change] acutely,” she said. “Our only option moving forward is to implement sweeping adaptation measures and decarbonize as rapidly as possible.”

The panelists included Shawn Jones, the head of energy storage development at BlueWave Solar, a solar energy developer based in Boston, Pamela Padilla, president of the Society for the Advancement of Chicanos/Hispanics and Native Americans in Science and University of North Texas vice president of research and innovation, BU PhD student Yasmin Romitti (Pardee’12, GRS’25), and Pamela Templer, a College of Arts & Sciences professor of biology and the director of BU’s URBAN Program.

“To me, a climate workforce means successfully preparing our graduates to tackle climate challenges,” Templer told The Brink prior to the event. “We know that temperatures are rising, weather events are becoming more extreme, and these are all impacting human health and well-being. Having graduates understand how we can both reduce the greenhouse gas emissions that lead to climate change and create solutions to help humans adapt to the ways that climate is already changing is essential.”

The URBAN Program (Urban Biogeoscience and Environmental Health), funded by a $3 million National Science Foundation Research Traineeship Program grant, helps graduate students gain expertise in fields that include environmental health, biology, engineering, statistics, and more, as well as the skills needed to work across disciplines. The program offers professional development workshops, training students in science communication, the workings of municipal governments, and collaborating effectively with city leaders.

“I think about the droughts in the Southwest, and how the Navajo Nation is addressing this. It’s important that we communicate knowledge to families and our elders in the community so they understand and know how they can participate,” Padilla said. She also discussed how government agencies can bolster her organization’s work in increasing participation from Chicano, Hispanic, and Native American people in science and technology. “They can move the needle with dollars, as well as support.”

On the private industry side of the climate workforce, Jones is working to transform access to renewable energy with community solar projects and storage solutions, while volunteering in the community and offering students mentoring opportunities.

“You don’t need a science degree to tackle climate change,” Jones said. He also echoed the need to bring diverse talent and individuals from all backgrounds into climate-centered careers.

“Everyone understands what a doctor does, what lawyers and engineers do, but the climate work? I still don’t think people understand what we actually do, so we have to bring a little bit more transparency to our process, so [more people] understand what skills are needed,” he said.

Asked how Congress can further support efforts to train students working in climate, Templer said that “Congress can continue to support graduate training grants—like the National Science Foundation Research Traineeship Program—that enable universities like BU to create new interdisciplinary hands-on, solutions-oriented training programs. It would be helpful if Congress could allocate more funds to ensure that successful graduate programs like ours continue.”

Romitti, a climate, energy, and health student who’s researching how people adapt to heat in cities, said the URBAN Program has been invaluable, providing her with a community and experience creating policy-relevant research. “Looking ahead, I’m very excited to be part of this next-generation climate workforce,” Romitti said. “What’s next for me, I don’t exactly know, but I think that’s a good thing, because it just shows that because of the training and opportunities I’ve had with URBAN, I feel like I have the tools and the resources to be a competitive applicant across different sectors.”

All the panelists shared their hope for more investment at the federal level in training students interested in climate-focused careers that can elevate diversity and bring more opportunities for communities that are impacted the most by climate change.

Varga closed by saying: “There’s so much to be optimistic about, and yet still so much more work to do.”

Explore Related Topics:

## Linear Regression Tutorial With Tensorflow

What is Linear Regression?

Linear Regression is an approach in statistics for modelling relationships between two variables. This modelling is done between a scalar response and one or more explanatory variables. The relationship with one explanatory variable is called simple linear regression and for more than one explanatory variables, it is called multiple linear regression.

TensorFlow provides tools to have full control of the computations. This is done with the low-level API. On top of that, TensorFlow is equipped with a vast array of APIs to perform many machine learning algorithms. This is the high-level API. TensorFlow calls them estimators

Low-level API: Build the architecture, optimization of the model from scratch. It is complicated for a beginner

High-level API: Define the algorithm. It is easer-friendly. TensorFlow provides a toolbox called estimator to construct, train, evaluate and make a prediction.

In this tutorial, you will use the estimators only. The computations are faster and are easier to implement. The first part of the tutorial explains how to use the gradient descent optimizer to train a Linear regression in TensorFlow. In a second part, you will use the Boston dataset to predict the price of a house using TensorFlow estimator.

Download Boston DataSet

In this TensorFlow Regression tutorial, you will learn:

How to train a linear regression modelBefore we begin to train the model, let’s have a look at what is a linear regression.

Imagine you have two variables, x and y and your task is to predict the value of knowing the value of . If you plot the data, you can see a positive relationship between your independent variable, x and your dependent variable y.

You may observe, if x=1,y will roughly be equal to 6 and if x=2,y will be around 8.5.

This is not a very accurate method and prone to error, especially with a dataset with hundreds of thousands of points.

A linear regression is evaluated with an equation. The variable y is explained by one or many covariates. In your example, there is only one dependent variable. If you have to write this equation, it will be:

With:

is the bias. i.e. if x=0, y=

is the weight associated to x

is the residual or the error of the model. It includes what the model cannot learn from the data

Imagine you fit the model and you find the following solution for:

= 3.8

= 2.78

You can substitute those numbers in the equation and it becomes:

y= 3.8 + 2.78x

You have now a better way to find the values for y. That is, you can replace x with any value you want to predict y. In the image below, we have replace x in the equation with all the values in the dataset and plot the result.

The red line represents the fitted value, that is the values of y for each value of x. You don’t need to see the value of x to predict y, for each x there is any which belongs to the red line. You can also predict for values of x higher than 2!

If you want to extend the linear regression to more covariates, you can by adding more variables to the model. The difference between traditional analysis and linear regression is the linear regression looks at how y will react for each variable x taken independently.

Let’s see an example. Imagine you want to predict the sales of an ice cream shop. The dataset contains different information such as the weather (i.e rainy, sunny, cloudy), customer informations (i.e salary, gender, marital status).

Traditional analysis will try to predict the sale by let’s say computing the average for each variable and try to estimate the sale for different scenarios. It will lead to poor predictions and restrict the analysis to the chosen scenario.

If you use linear regression, you can write this equation:

The algorithm will find the best solution for the weights; it means it will try to minimize the cost (the difference between the fitted line and the data points).

How the algorithm worksThe algorithm will choose a random number for each

and and replace the value of x to get the predicted value of y. If the dataset has 100 observations, the algorithm computes 100 predicted values.

andand replace the value of x to get the predicted value of y. If the dataset has 100 observations, the algorithm computes 100 predicted values.

We can compute the error, noted

of the model, which is the difference between the predicted value and the real value. A positive error means the model underestimates the prediction of y, and a negative error means the model overestimates the prediction of y.

Your goal is to minimize the square of the error. The algorithm computes the mean of the square error. This step is called minimization of the error. For linear regression is the Mean Square Error, also called MSE. Mathematically, it is:

Where:

is the weights so refers to the predicted value

y is the real values

m is the number of observations

Note that

means it uses the transpose of the matrices. The is the mathematical notation of the mean.

means it uses the transpose of the matrices. Theis the mathematical notation of the mean.

The goal is to find the best

that minimize the MSE

that minimize the MSE

If the average error is large, it means the model performs poorly and the weights are not chosen properly. To correct the weights, you need to use an optimizer. The traditional optimizer is called Gradient Descent.

The gradient descent takes the derivative and decreases or increases the weight. If the derivative is positive, the weight is decreased. If the derivative is negative, the weight increases. The model will update the weights and recompute the error. This process is repeated until the error does not change anymore. Each process is called an iteration. Besides, the gradients are multiplied by a learning rate. It indicates the speed of the learning.

If the learning rate is too small, it will take very long time for the algorithm to converge (i.e requires lots of iterations). If the learning rate is too high, the algorithm might never converge.

You can see from the picture above, the model repeats the process about 20 times before to find a stable value for the weights, therefore reaching the lowest error.

Note that, the error is not equal to zero but stabilizes around 5. It means, the model makes a typical error of 5. If you want to reduce the error, you need to add more information to the model such as more variables or use different estimators.

You remember the first equation

The final weights are 3.8 and 2.78. The video below shows you how the gradient descent optimize the loss function to find this weights

How to train a Linear Regression with TensorFlow

Now that you have a better understanding of what is happening behind the hood, you are ready to use the estimator API provided by TensorFlow to train your first linear regression using TensorFlow.

You will use the Boston Dataset, which includes the following variables

crim per capita crime rate by town

zn proportion of residential land zoned for lots over 25,000 sq.ft.

indus proportion of non-retail business acres per town.

nox nitric oxides concentration

rm average number of rooms per dwelling

age proportion of owner-occupied units built before 1940

dis weighted distances to five Boston employment centers

tax full-value property-tax rate per dollars 10,000

ptratio pupil-teacher ratio by town

medv Median value of owner-occupied homes in thousand dollars

You will create three different datasets:

dataset objective shape

Training Train the model and obtain the weights 400, 10

Evaluation Evaluate the performance of the model on unseen data 100, 10

Predict Use the model to predict house value on new data 6, 10

The objectives is to use the features of the dataset to predict the value of the house.

During the second part of the tutorial, you will learn how to use TensorFlow with three different way to import the data:

With Pandas

With Numpy

Only TF

Note that, all options provide the same results.

You will learn how to use the high-level API to build, train an evaluate a TensorFlow linear regression model. If you were using the low-level API, you had to define by hand the:

Loss function

Optimize: Gradient descent

Matrices multiplication

Graph and tensor

This is tedious and more complicated for beginner.

PandasYou need to import the necessary libraries to train the model.

import pandas as pd from sklearn import datasets import tensorflow as tf import itertoolsStep 1) Import the data with panda.

You define the column names and store it in COLUMNS. You can use pd.read_csv() to import the data.

COLUMNS = ["crim", "zn", "indus", "nox", "rm", "age", "dis", "tax", "ptratio", "medv"]training_set = pd.read_csv(“E:/boston_train.csv”, skipinitialspace=True,skiprows=1, names=COLUMNS)

test_set = pd.read_csv(“E:/boston_test.csv”, skipinitialspace=True,skiprows=1, names=COLUMNS)

prediction_set = pd.read_csv(“E:/boston_predict.csv”, skipinitialspace=True,skiprows=1, names=COLUMNS)

You can print the shape of the data.

print(training_set.shape, test_set.shape, prediction_set.shape) Output (400, 10) (100, 10) (6, 10)Note that the label, i.e. your y, is included in the dataset. So you need to define two other lists. One containing only the features and one with the name of the label only. These two lists will tell your estimator what are the features in the dataset and what column name is the label

It is done with the code below.

FEATURES = ["crim", "zn", "indus", "nox", "rm", "age", "dis", "tax", "ptratio"] LABEL = "medv"Step 2) Convert the data

You need to convert the numeric variables in the proper format. Tensorflow provides a method to convert continuous variable: tf.feature_column.numeric_column().

In the previous step, you define a list a feature you want to include in the model. Now you can use this list to convert them into numeric data. If you want to exclude features in your model, feel free to drop one or more variables in the list FEATURES before you construct the feature_cols

Note that you will use Python list comprehension with the list FEATURES to create a new list named feature_cols. It helps you avoid writing nine times tf.feature_column.numeric_column(). A list comprehension is a faster and cleaner way to create new lists

feature_cols = [tf.feature_column.numeric_column(k) for k in FEATURES]Step 3) Define the estimator

In this step, you need to define the estimator. Tensorflow currently provides 6 pre-built estimators, including 3 for classification task and 3 for TensorFlow regression task:

Regressor

DNNRegressor

LinearRegressor

DNNLineaCombinedRegressor

Classifier

DNNClassifier

LinearClassifier

DNNLineaCombinedClassifier

In this tutorial, you will use the Linear Regressor. To access this function, you need to use tf.estimator.

The function needs two arguments:

feature_columns: Contains the variables to include in the model

model_dir: path to store the graph, save the model parameters, etc

Tensorflow will automatically create a file named train in your working directory. You need to use this path to access the Tensorboard as shown in the below TensorFlow regression example.

estimator = tf.estimator.LinearRegressor( feature_columns=feature_cols, model_dir="train") Output INFO:tensorflow:Using default config.The tricky part with TensorFlow is the way to feed the model. Tensorflow is designed to work with parallel computing and very large dataset. Due to the limitation of the machine resources, it is impossible to feed the model with all the data at once. For that, you need to feed a batch of data each time. Note that, we are talking about huge dataset with millions or more records. If you don’t add batch, you will end up with a memory error.

For instance, if your data contains 100 observations and you define a batch size of 10, it means the model will see 10 observations for each iteration (10*10).

When the model has seen all the data, it finishes one epoch. An epoch defines how many times you want the model to see the data. It is better to set this step to none and let the model performs iteration number of time.

A second information to add is if you want to shuffle the data before each iteration. During the training, it is important to shuffle the data so that the model does not learn specific pattern of the dataset. If the model learns the details of the underlying pattern of the data, it will have difficulties to generalize the prediction for unseen data. This is called overfitting. The model performs well on the training data but cannot predict correctly for unseen data.

TensorFlow makes this two steps easy to do. When the data goes to the pipeline, it knows how many observations it needs (batch) and if it has to shuffle the data.

To instruct Tensorflow how to feed the model, you can use pandas_input_fn. This object needs 5 parameters:

x: feature data

y: label data

batch_size: batch. By default 128

num_epoch: Number of epoch, by default 1

shuffle: Shuffle or not the data. By default, None

You need to feed the model many times so you define a function to repeat this process. all this function get_input_fn.

def get_input_fn(data_set, num_epochs=None, n_batch = 128, shuffle=True): return tf.estimator.inputs.pandas_input_fn( x=pd.DataFrame({k: data_set[k].values for k in FEATURES}), y = pd.Series(data_set[LABEL].values), batch_size=n_batch, num_epochs=num_epochs, shuffle=shuffle)The usual method to evaluate the performance of a model is to:

Train the model

Evaluate the model in a different dataset

Make prediction

Tensorflow estimator provides three different functions to carry out this three steps easily.

Step 4): Train the model

You can use the estimator train to evaluate the model. The train estimator needs an input_fn and a number of steps. You can use the function you created above to feed the model. Then, you instruct the model to iterate 1000 times. Note that, you don’t specify the number of epochs, you let the model iterates 1000 times. If you set the number of epoch to 1, then the model will iterate 4 times: There are 400 records in the training set, and the batch size is 128

128 rows

128 rows

128 rows

16 rows

Therefore, it is easier to set the number of epoch to none and define the number of iteration as shown in th below TensorFlow classification example.

estimator.train(input_fn=get_input_fn(training_set, num_epochs=None, n_batch = 128, shuffle=False), steps=1000) Output INFO:tensorflow:Calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Create CheckpointSaverHook. INFO:tensorflow:Graph was finalized. INFO:tensorflow:Running local_init_op. INFO:tensorflow:Done running local_init_op. INFO:tensorflow:Saving checkpoints for 1 into train/model.ckpt. INFO:tensorflow:loss = 83729.64, step = 1 INFO:tensorflow:global_step/sec: 238.616 INFO:tensorflow:loss = 13909.657, step = 101 (0.420 sec) INFO:tensorflow:global_step/sec: 314.293 INFO:tensorflow:loss = 12881.449, step = 201 (0.320 sec) INFO:tensorflow:global_step/sec: 303.863 INFO:tensorflow:loss = 12391.541, step = 301 (0.327 sec) INFO:tensorflow:global_step/sec: 308.782 INFO:tensorflow:loss = 12050.5625, step = 401 (0.326 sec) INFO:tensorflow:global_step/sec: 244.969 INFO:tensorflow:loss = 11766.134, step = 501 (0.407 sec) INFO:tensorflow:global_step/sec: 155.966 INFO:tensorflow:loss = 11509.922, step = 601 (0.641 sec) INFO:tensorflow:global_step/sec: 263.256 INFO:tensorflow:loss = 11272.889, step = 701 (0.379 sec) INFO:tensorflow:global_step/sec: 254.112 INFO:tensorflow:loss = 11051.9795, step = 801 (0.396 sec) INFO:tensorflow:global_step/sec: 292.405 INFO:tensorflow:loss = 10845.855, step = 901 (0.341 sec) INFO:tensorflow:Saving checkpoints for 1000 into train/model.ckpt. INFO:tensorflow:Loss for final step: 5925.9873.You can check the Tensorboard will the following command:

activate hello-tf # For MacOS tensorboard --logdir=./train # For Windows tensorboard --logdir=trainStep 5) Evaluate your model

You can evaluate the fit of your model on the test set with the code below:

ev = estimator.evaluate( input_fn=get_input_fn(test_set, num_epochs=1, n_batch = 128, shuffle=False)) Output INFO:tensorflow:Calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Starting evaluation at 2023-05-13-01:43:13 INFO:tensorflow:Graph was finalized. INFO:tensorflow:Restoring parameters from train/model.ckpt-1000 INFO:tensorflow:Running local_init_op. INFO:tensorflow:Done running local_init_op. INFO:tensorflow:Finished evaluation at 2023-05-13-01:43:13 INFO:tensorflow:Saving dict for global step 1000: average_loss = 32.15896, global_step = 1000, loss = 3215.896You can print the loss with the code below:

loss_score = ev["loss"] print("Loss: {0:f}".format(loss_score)) Output Loss: 3215.895996The model has a loss of 3215. You can check the summary statistic to get an idea of how big the error is.

training_set['medv'].describe() Output count 400.000000 mean 22.625500 std 9.572593 min 5.000000 25% 16.600000 50% 21.400000 75% 25.025000 max 50.000000 Name: medv, dtype: float64From the summary statistic above, you know that the average price for a house is 22 thousand, with a minimum price of 9 thousand and maximum of 50 thousand. The model makes a typical error of 3k dollars.

Step 6) Make the prediction

Finally, you can use the estimator TensorFlow predict to estimate the value of 6 Boston houses.

y = estimator.predict( input_fn=get_input_fn(prediction_set, num_epochs=1, n_batch = 128, shuffle=False))To print the estimated values of , you can use this code:

predictions = list(p["predictions"] for p in itertools.islice(y, 6))print("Predictions: {}".format(str(predictions))) Output INFO:tensorflow:Calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Graph was finalized. INFO:tensorflow:Restoring parameters from train/model.ckpt-1000 INFO:tensorflow:Running local_init_op. INFO:tensorflow:Done running local_init_op. Predictions: [array([32.297546], dtype=float32), array([18.96125], dtype=float32), array([27.270979], dtype=float32), array([29.299236], dtype=float32), array([16.436684], dtype=float32), array([21.460876], dtype=float32)]The model forecast the following values:

House Prediction

1 32.29

2 18.96

3 27.27

4 29.29

5 16.43

7 21.46

Note that we don’t know the true value of . In the tutorial of deep learning, you will try to beat the linear model

Numpy SolutionThis section explains how to train the model using a numpy estimator to feed the data. The method is the same exept that you will use numpy_input_fn estimator.

training_set_n = pd.read_csv(“E:/boston_train.csv”).values

test_set_n = pd.read_csv(“E:/boston_test.csv”).values

prediction_set_n = pd.read_csv(“E:/boston_predict.csv”).values

Step 1) Import the data

First of all, you need to differentiate the feature variables from the label. You need to do this for the training data and evaluation. It is faster to define a function to split the data.

def prepare_data(df): X_train = df[:, :-3] y_train = df[:,-3] return X_train, y_trainYou can use the function to split the label from the features of the train/evaluate dataset

X_train, y_train = prepare_data(training_set_n) X_test, y_test = prepare_data(test_set_n)You need to exclude the last column of the prediction dataset because it contains only NaN

x_predict = prediction_set_n[:, :-2]Confirm the shape of the array. Note that, the label should not have a dimension, it means (400,).

print(X_train.shape, y_train.shape, x_predict.shape) Output (400, 9) (400,) (6, 9)You can construct the feature columns as follow:

feature_columns = [ tf.feature_column.numeric_column('x', shape=X_train.shape[1:])]The estimator is defined as before, you instruct the feature columns and where to save the graph.

estimator = tf.estimator.LinearRegressor( feature_columns=feature_columns, model_dir="train1") Output INFO:tensorflow:Using default config.You can use the numpy estimapor to feed the data to the model and then train the model. Note that, we define the input_fn function before to ease the readability.

# Train the estimatortrain_input = tf.estimator.inputs.numpy_input_fn( x={"x": X_train}, y=y_train, batch_size=128, shuffle=False, num_epochs=None) estimator.train(input_fn = train_input,steps=5000) Output INFO:tensorflow:Calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Create CheckpointSaverHook. INFO:tensorflow:Graph was finalized. INFO:tensorflow:Running local_init_op. INFO:tensorflow:Done running local_init_op. INFO:tensorflow:Saving checkpoints for 1 into train1/model.ckpt. INFO:tensorflow:loss = 83729.64, step = 1 INFO:tensorflow:global_step/sec: 490.057 INFO:tensorflow:loss = 13909.656, step = 101 (0.206 sec) INFO:tensorflow:global_step/sec: 788.986 INFO:tensorflow:loss = 12881.45, step = 201 (0.126 sec) INFO:tensorflow:global_step/sec: 736.339 INFO:tensorflow:loss = 12391.541, step = 301 (0.136 sec) INFO:tensorflow:global_step/sec: 383.305 INFO:tensorflow:loss = 12050.561, step = 401 (0.260 sec) INFO:tensorflow:global_step/sec: 859.832 INFO:tensorflow:loss = 11766.133, step = 501 (0.117 sec) INFO:tensorflow:global_step/sec: 804.394 INFO:tensorflow:loss = 11509.918, step = 601 (0.125 sec) INFO:tensorflow:global_step/sec: 753.059 INFO:tensorflow:loss = 11272.891, step = 701 (0.134 sec) INFO:tensorflow:global_step/sec: 402.165 INFO:tensorflow:loss = 11051.979, step = 801 (0.248 sec) INFO:tensorflow:global_step/sec: 344.022 INFO:tensorflow:loss = 10845.854, step = 901 (0.288 sec) INFO:tensorflow:Saving checkpoints for 1000 into train1/model.ckpt. INFO:tensorflow:Loss for final step: 5925.985. Out[23]:You replicate the same step with a different estimator to evaluate your model

eval_input = tf.estimator.inputs.numpy_input_fn( x={"x": X_test}, y=y_test, shuffle=False, batch_size=128, num_epochs=1) estimator.evaluate(eval_input,steps=None) Output INFO:tensorflow:Calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Starting evaluation at 2023-05-13-01:44:00 INFO:tensorflow:Graph was finalized. INFO:tensorflow:Restoring parameters from train1/model.ckpt-1000 INFO:tensorflow:Running local_init_op. INFO:tensorflow:Done running local_init_op. INFO:tensorflow:Finished evaluation at 2023-05-13-01:44:00 INFO:tensorflow:Saving dict for global step 1000: average_loss = 32.158947, global_step = 1000, loss = 3215.8945 Out[24]: {'average_loss': 32.158947, 'global_step': 1000, 'loss': 3215.8945}Finaly, you can compute the prediction. It should be the similar as pandas.

test_input = tf.estimator.inputs.numpy_input_fn( x={"x": x_predict}, batch_size=128, num_epochs=1, shuffle=False) y = estimator.predict(test_input) predictions = list(p["predictions"] for p in itertools.islice(y, 6)) print("Predictions: {}".format(str(predictions))) Output INFO:tensorflow:Calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Graph was finalized. INFO:tensorflow:Restoring parameters from train1/model.ckpt-1000 INFO:tensorflow:Running local_init_op. INFO:tensorflow:Done running local_init_op. Predictions: [array([32.297546], dtype=float32), array([18.961248], dtype=float32), array([27.270979], dtype=float32), array([29.299242], dtype=float32), array([16.43668], dtype=float32), array([21.460878], dtype=float32)] Tensorflow solutionThe last section is dedicated to a TensorFlow solution. This method is sligthly more complicated than the other one.

Note that if you use Jupyter notebook, you need to Restart and clean the kernel to run this session.

TensorFlow has built a great tool to pass the data into the pipeline. In this section, you will build the input_fn function by yourself.

Step 1) Define the path and the format of the data

First of all, you declare two variables with the path of the csv file. Note that, you have two files, one for the training set and one for the testing set.

import tensorflow as tf df_train = "E:/boston_train.csv" df_eval = "E:/boston_test.csv"Then, you need to define the columns you want to use from the csv file. We will use all. After that, you need to declare the type of variable it is.

Floats variable are defined by [0.]

COLUMNS = ["crim", "zn", "indus", "nox", "rm", "age", "dis", "tax", "ptratio", "medv"]RECORDS_ALL = [[0.0], [0.0], [0.0], [0.0],[0.0],[0.0],[0.0],[0.0],[0.0],[0.0]]Step 2) Define the input_fn function

The function can be broken into three part:

Import the data

Create the iterator

Consume the data

Below is the overal code to define the function. The code will be explained after

def input_fn(data_file, batch_size, num_epoch = None): # Step 1 def parse_csv(value): columns = tf.decode_csv(value, record_defaults= RECORDS_ALL) features = dict(zip(COLUMNS, columns)) #labels = features.pop('median_house_value') labels = features.pop('medv') return features, labels # Extract lines from input files using the Dataset API. dataset = (tf.data.TextLineDataset(data_file) # Read text file .skip(1) # Skip header row .map(parse_csv)) dataset = dataset.repeat(num_epoch) dataset = dataset.batch(batch_size) # Step 3 iterator = dataset.make_one_shot_iterator() features, labels = iterator.get_next() return features, labels** Import the data**

This method calls a function that you will create in order to instruct how to transform the chúng tôi a nutshell, you need to pass the data in the TextLineDataset object, exclude the header and apply a transformation which is instructed by a chúng tôi explanation

tf.data.TextLineDataset(data_file): This line read the csv file

.skip(1) : skip the header

.map(parse_csv)): parse the records into the tensorsYou need to define a function to instruct the map object. You can call this function parse_csv.

This function parses the csv file with the method tf.decode_csv and declares the features and the label. The features can be declared as a dictionary or a tuple. You use the dictionary method because it is more chúng tôi explanation

tf.decode_csv(value, record_defaults= RECORDS_ALL): the method decode_csv uses the output of the TextLineDataset to read the csv file. record_defaults instructs TensorFlow about the columns type.

dict(zip(_CSV_COLUMNS, columns)): Populate the dictionary with all the columns extracted during this data processing

features.pop(‘median_house_value’): Exclude the target variable from the feature variable and create a label variable

The Dataset needs further elements to iteratively feeds the Tensors. Indeed, you need to add the method repeat to allow the dataset to continue indefinitely to feed the model. If you don’t add the method, the model will iterate only one time and then throw an error because no more data are fed in the pipeline.

After that, you can control the batch size with the batch method. It means you tell the dataset how many data you want to pass in the pipeline for each iteration. If you set a big batch size, the model will be slow.

Step 3) Create the iterator

Now you are ready for the second step: create an iterator to return the elements in the dataset.

The simplest way of creating an operator is with the method make_one_shot_iterator.

After that, you can create the features and labels from the iterator.

Step 4) Consume the data

You can check what happens with input_fn function. You need to call the function in a session to consume the data. You try with a batch size equals to 1.

Note that, it prints the features in a dictionary and the label as an array.

It will show the first line of the csv file. You can try to run this code many times with different batch size.

next_batch = input_fn(df_train, batch_size = 1, num_epoch = None) with tf.Session() as sess: first_batch = sess.run(next_batch) print(first_batch) Output ({'crim': array([2.3004], dtype=float32), 'zn': array([0.], dtype=float32), 'indus': array([19.58], dtype=float32), 'nox': array([0.605], dtype=float32), 'rm': array([6.319], dtype=float32), 'age': array([96.1], dtype=float32), 'dis': array([2.1], dtype=float32), 'tax': array([403.], dtype=float32), 'ptratio': array([14.7], dtype=float32)}, array([23.8], dtype=float32))Step 4) Define the feature column

You need to define the numeric columns as follow:

X1= tf.feature_column.numeric_column('crim') X2= tf.feature_column.numeric_column('zn') X3= tf.feature_column.numeric_column('indus') X4= tf.feature_column.numeric_column('nox') X5= tf.feature_column.numeric_column('rm') X6= tf.feature_column.numeric_column('age') X7= tf.feature_column.numeric_column('dis') X8= tf.feature_column.numeric_column('tax') X9= tf.feature_column.numeric_column('ptratio')Note that you need to combined all the variables in a bucket

base_columns = [X1, X2, X3,X4, X5, X6,X7, X8, X9]Step 5) Build the model

You can train the model with the estimator LinearRegressor.

model = tf.estimator.LinearRegressor(feature_columns=base_columns, model_dir='train3') OutputYou need to use a lambda function to allow to write the argument in the function inpu_fn. If you don’t use a lambda function, you cannot train the model.

# Train the estimatormodel.train(steps =1000, input_fn= lambda : input_fn(df_train,batch_size=128, num_epoch = None))Output

INFO:tensorflow:Calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Create CheckpointSaverHook. INFO:tensorflow:Graph was finalized. INFO:tensorflow:Running local_init_op. INFO:tensorflow:Done running local_init_op. INFO:tensorflow:Saving checkpoints for 1 into train3/model.ckpt. INFO:tensorflow:loss = 83729.64, step = 1 INFO:tensorflow:global_step/sec: 72.5646 INFO:tensorflow:loss = 13909.657, step = 101 (1.380 sec) INFO:tensorflow:global_step/sec: 101.355 INFO:tensorflow:loss = 12881.449, step = 201 (0.986 sec) INFO:tensorflow:global_step/sec: 109.293 INFO:tensorflow:loss = 12391.541, step = 301 (0.915 sec) INFO:tensorflow:global_step/sec: 102.235 INFO:tensorflow:loss = 12050.5625, step = 401 (0.978 sec) INFO:tensorflow:global_step/sec: 104.656 INFO:tensorflow:loss = 11766.134, step = 501 (0.956 sec) INFO:tensorflow:global_step/sec: 106.697 INFO:tensorflow:loss = 11509.922, step = 601 (0.938 sec) INFO:tensorflow:global_step/sec: 118.454 INFO:tensorflow:loss = 11272.889, step = 701 (0.844 sec) INFO:tensorflow:global_step/sec: 114.947 INFO:tensorflow:loss = 11051.9795, step = 801 (0.870 sec) INFO:tensorflow:global_step/sec: 111.484 INFO:tensorflow:loss = 10845.855, step = 901 (0.897 sec) INFO:tensorflow:Saving checkpoints for 1000 into train3/model.ckpt. INFO:tensorflow:Loss for final step: 5925.9873. Out[8]:You can evaluate the fit of you model on the test set with the code below:

results = model.evaluate(steps =None,input_fn=lambda: input_fn(df_eval, batch_size =128, num_epoch = 1)) for key in results: print(" {}, was: {}".format(key, results[key])) Output INFO:tensorflow:Calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Starting evaluation at 2023-05-13-02:06:02 INFO:tensorflow:Graph was finalized. INFO:tensorflow:Restoring parameters from train3/model.ckpt-1000 INFO:tensorflow:Running local_init_op. INFO:tensorflow:Done running local_init_op. INFO:tensorflow:Finished evaluation at 2023-05-13-02:06:02 INFO:tensorflow:Saving dict for global step 1000: average_loss = 32.15896, global_step = 1000, loss = 3215.896 average_loss, was: 32.158958435058594 loss, was: 3215.89599609375 global_step, was: 1000The last step is predicting the value of based on the value of , the matrices of the features. You can write a dictionary with the values you want to predict. Your model has 9 features so you need to provide a value for each. The model will provide a prediction for each of them.

In the code below, you wrote the values of each features that is contained in the df_predict csv file.

You need to write a new input_fn function because there is no label in the dataset. You can use the API from_tensor from the Dataset.

prediction_input = { 'crim': [0.03359,5.09017,0.12650,0.05515,8.15174,0.24522], 'zn': [75.0,0.0,25.0,33.0,0.0,0.0], 'indus': [2.95,18.10,5.13,2.18,18.10,9.90], 'nox': [0.428,0.713,0.453,0.472,0.700,0.544], 'rm': [7.024,6.297,6.762,7.236,5.390,5.782], 'age': [15.8,91.8,43.4,41.1,98.9,71.7], 'dis': [5.4011,2.3682,7.9809,4.0220,1.7281,4.0317], 'tax': [252,666,284,222,666,304], 'ptratio': [18.3,20.2,19.7,18.4,20.2,18.4] } def test_input_fn(): dataset = tf.data.Dataset.from_tensors(prediction_input) return dataset # Predict all our prediction_inputpred_results = model.predict(input_fn=test_input_fn)Finaly, you print the predictions.

for pred in enumerate(pred_results): print(pred) Output INFO:tensorflow:Calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Graph was finalized. INFO:tensorflow:Restoring parameters from train3/model.ckpt-1000 INFO:tensorflow:Running local_init_op. INFO:tensorflow:Done running local_init_op. (0, {'predictions': array([32.297546], dtype=float32)}) (1, {'predictions': array([18.96125], dtype=float32)}) (2, {'predictions': array([27.270979], dtype=float32)}) (3, {'predictions': array([29.299236], dtype=float32)}) (4, {'predictions': array([16.436684], dtype=float32)}) (5, {'predictions': array([21.460876], dtype=float32)}) INFO:tensorflow:Calling model_fn. INFO:tensorflow:Done calling model_fn. INFO:tensorflow:Graph was finalized. INFO:tensorflow:Restoring parameters from train3/model.ckpt-5000 INFO:tensorflow:Running local_init_op. INFO:tensorflow:Done running local_init_op. (0, {'predictions': array([35.60663], dtype=float32)}) (1, {'predictions': array([22.298521], dtype=float32)}) (2, {'predictions': array([25.74533], dtype=float32)}) (3, {'predictions': array([35.126694], dtype=float32)}) (4, {'predictions': array([17.94416], dtype=float32)}) (5, {'predictions': array([22.606628], dtype=float32)}) SummaryTo train a model, you need to:

Define the features: Independent variables: X

Define the label: Dependent variable: y

Construct a train/test set

Define the initial weight

Define the loss function: MSE

Optimize the model: Gradient descent

Define:

Learning rate

Number of epoch

Batch size

In this tutorial, you learned how to use the high level API for a linear regression TensorFlow estimator. You need to define:

Feature columns. If continuous: tf.feature_column.numeric_column(). You can populate a list with python list comprehension

The estimator: tf.estimator.LinearRegressor(feature_columns, model_dir)

A function to import the data, the batch size and epoch: input_fn()

After that, you are ready to train, evaluate and make prediction with train(), evaluate() and predict()

## How To Use Tensorflow Normalize?

Introduction to TensorFlow normalize

Tensorflow normalize is the method available in the tensorflow library that helps to bring out the normalization process for tensors in neural networks. The main purpose of this process is to bring the transformation so that all the features work on the same or similar level of scale. Normalization plays a vital role in boosting the training stability as well as the performance of the model. The main techniques that are used internally for normalization include log scaling, scaling to a specified range, z score, and clipping.

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In this article, we will have a discussion over the points tensorflow normalize overviews, how to use tensorflow normalize, tensorflow Normalize features, tensorflow normalize examples, and finally concluding our statement.

Overview of TensorFlow normalizeNormalization is the process where we try to align all the parameters and features of the model on a similar scale so as to increase the overall performance and training quality for the model. The syntax of the normalized method is as shown below. Note that the normalize function works only for the data in the format of a numpy array.

Tensorflow.keras.utils.normalize(sample array, axis = -1, order = 2)

The arguments used in the above syntax are described in detail one by one here –

Sample array – It is the NumPy array data that is to be normalized.

Axis – This parameter helps to specify the axis along which we want the numpy array to normalize.

Order – This parameter specifies the order of normalization that we want to consider. The value can be a number such as here 2 stands for the L2 norm normalization.

Output value – The returned value of this method is a copy of the original numpy array which is completely normalized.

How to use TensorFlow normalize?The steps that we need to follow while making the use of the normalizing method in our python tensorflow model are as described below –

Observe and try to explore the available data set which includes finding out the connection and correlation between the data.

The training data of the model should be normalized by using normalize method following its syntax mentioned above.

The steps for the linear model including building, compiling, and evaluation of the values should be carried out.

The DNN neural network should be built, compiled, and trained properly giving out the evaluation of values.

TensorFlow Normalize featuresWhen you are trying to perform normalization, we will need to make the use of TensorFlow.estimator ad additionally we also need to mention the argument normalizer function inside the TensorFlow.feature_column in case if it’s a numeric feature then TensorFlow.feature_column.numeric_feature in case we want to supply the same parameters required while evaluating, training and serving.

The feature can be mentioned in below syntax –

Feature = tensorflow.feature_column.numeric_column (name of the feature, function of normalization = zscore)

The parameter that we pass as the function of normalizer here that is z score stands for the relation between the mean of the observations and the observations that are nothing but values.

The zscore function that we used is as shown below –

Return (x-calculatedMean)/ calculatedStandardDeviation

Let us consider one example where we will try to find the estimates by using normalization with numeric features. We will try to create standard deviation and mean values for which we have used above mentioned calculations. We will create the estimators by using the feature columns specified. Our code is as shown below –

‘number_of_people’, ‘cityPeopleCount’, ‘medianStipend’] normalization_parameters

The output of executing the above code gives the result as shown in the below image –

TensorFlow normalize examplesLet us consider one example. We will try to normalize all the data that is present in the range of -1 to 1. The TensorFlow 2.x library has come up with the experimental normalization engine which creates a way for the alternative of the manual normalization process.

The object of normalization helps us to provide the input of the set of data and also the method of NumPy which returns the matrix containing all the numbers that are normalized. This matrix can be used to prepare the pandas data frame by simply passing it which will help in plotting the histogram of the updated normalized data set. We can also observe that the data cluster around the zero value after normalization in the graph output.

dnnModel. summary()

Histogram output –

ConclusionTensorflow normalize method is used on NumPy array to make the available data set normalize. We will have to find out correlations and study the input data and then go for the manual normalization process or we can make use of the normalization technique of trial and error provided in version 2 of tensorflow.

Recommended ArticlesThis is a guide to TensorFlow normalize. Here we discuss the Introduction, overviews, How to use TensorFlow normalize? Examples with code implementation. You may also have a look at the following articles to learn more –

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