The 2023 Nebraska high school state volleyball tournament begins today in Lincoln! Today's first-round matches in Classes A, B and C-1 will be played at Pinnacle Bank Arena. Two matches will be played at a time starting at 9 a.m., with matches starting approximately every two hours until the last two of the day begin around 7 p.m.

Nebraska high school state volleyball live scoreboard, Nov. 1

LINCOLN — Elkhorn North opened the Class B state volleyball tournament with a 25-12, 25-15, 25-14 win over Seward at Pinnacle Bank Arena. The Wolves (29-7), who lost to Omaha Skutt in five sets in the 2022 final, will meet the winner of the Skutt-Waverly quarterfinal at 7 p.m. Friday at PBA. Seward finished 26-8.

Class B: Elkhorn North sweeps Seward in first round of Nebraska state volleyball tournament

Finally, in girl golf, history was made Tuesday night as South Brunswick claimed its first ever individual girls golf state title.              With the cross country state championships and the first round of the football playoffs this weekend,

Wilmington-area playoff top performers for Oct. 30-Nov. 4

We'll update this page all postseason long with the latest scores and updates from all six area sports. Brackets, if released, are below.             Boys soccer             NCHSAA 4A Second Round: Nov.

Wilmington-area fall high school playoffs: NCHSAA boys soccer brackets revealed

A close four-quarter game against Lumberton on Friday in which Purnell Swett was upset 15-12 by the Pirates wasn’t the end of the suspense around the Rams program. The next 16 hours

Rams ready for postseason return

Eight games into the season, Georgia Tech is in fourth place in the ACC with a 3-2 conference record, and North Carolina and Miami find themselves in fifth and sixth place respectively.

Georgia Tech is a Perfect Chaos Team for the 2023 College Football Season

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Girls volleyball: Updated 2023 NJSIAA State Tournament Brackets, Nov. 1

Flames' Jacob Markstrom: Set to start Wednesday

The PAL singles and doubles girls’ tennis tournaments got underway Monday and there were no big surprises on Day 1 as most of the top seeds in both brackets advanced to Wednesday’s semifinals. The one mild upset came in the singles bracket, where Half ...

Most of top seeds advance at PAL tennis tournament

Forget multiple clicks or hard-to-read brackets with inconsistent information. You want the HS football playoff schedule? We've got it for you right here.

Forget the hard-to-read brackets. We've got the RIIL football playoff schedule right here.

Get the most recent info and news about Bracketz on HackerNoon, where 10k+ technologists publish stories for 4M+ monthly readers.

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**MAJURO, Marshall Islands, May 15th, 2024/Chainwire/--**Multipool, a leading innovator in the blockchain and cryptocurrency industry, announces the close of its $650k VC investment round led by NxGen, and the announcement of its Fjord Foundry LBP on May 21st-23rd. In the past month, Multipool has brought together the best of the crypto investment scene and connected them with the next big thing, receiving an overwhelmingly positive response from the community. “We’re thrilled to have raised $650k from VC & private investors. With NxGen, we aim to take the Multipool project of a DEX with CEX appeal to new heights and bounds, revolutionizing the crypto space. The LBP launches on Fjord Foundry, May 21st, stay tuned! ” Wojciech Kaszycki, a Core Contributor at Multipool Partnered with Professionals The Multipool LBP launches with industry professionals including NxGen, a group of private investors and advisers. These stakeholders provide Multipool with all the skillsets and regulatory support needed to reshape the industry offering compliance, flawless technological development and widespread awareness. The Big Launch With the close of the VC round, Multipool will launch their LBP on Fjord Foundry May 21st - 23rd, where crypto enthusiasts from all around the world can participate, joining a community of vibrant experts on the cutting edge of crypto tech. To learn more about Multipool and the upcoming LBP, users can visit: Website - www.multipool.finance Telegram - t.me/multipoolfi X - https://twitter.com/multipoolfi About Multipool Multipool is a cutting-edge decentralized exchange (DEX) transforming the trading landscape for real-world assets (RWAs) and cryptocurrencies. Multipool is designed for fairness and equality, featuring a fully decentralized on-chain order book, deep liquidity through dynamic bracket pools, and seamless trading of RWAs and cryptocurrencies. Utilizing world-class innovations including industry-first FIX APIs, low latency networks, zero price impact auctions, trustless RFQs, peer-to-peer repo lending, and MEV bot protection, Multipool sets a new standard in DeFi trading. Experience unparalleled efficiency and security in your trading journey with Multipool – The DEX with CEX appeal. https://www.multipool.finance/ Contact Public Relations Manager Angie Hermosa Multipool press@multipool.finance This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. **MAJURO, Marshall Islands, May 15th, 2024/Chainwire/--**Multipool, a leading innovator in the blockchain and cryptocurrency industry, announces the close of its $650k VC investment round led by NxGen, and the announcement of its Fjord Foundry LBP on May 21st-23rd. In the past month, Multipool has brought together the best of the crypto investment scene and connected them with the next big thing, receiving an overwhelmingly positive response from the community. “We’re thrilled to have raised $650k from VC & private investors. With NxGen, we aim to take the Multipool project of a DEX with CEX appeal to new heights and bounds, revolutionizing the crypto space. The LBP launches on Fjord Foundry, May 21st, stay tuned! ” Wojciech Kaszycki, a Core Contributor at Multipool “We’re thrilled to have raised $650k from VC & private investors. With NxGen, we aim to take the Multipool project of a DEX with CEX appeal to new heights and bounds, revolutionizing the crypto space. The LBP launches on Fjord Foundry, May 21st, stay tuned! ” Wojciech Kaszycki, a Core Contributor at Multipool Partnered with Professionals The Multipool LBP launches with industry professionals including NxGen, a group of private investors and advisers. These stakeholders provide Multipool with all the skillsets and regulatory support needed to reshape the industry offering compliance, flawless technological development and widespread awareness. The Big Launch With the close of the VC round, Multipool will launch their LBP on Fjord Foundry May 21st - 23rd, where crypto enthusiasts from all around the world can participate, joining a community of vibrant experts on the cutting edge of crypto tech. To learn more about Multipool and the upcoming LBP, users can visit: Website - www.multipool.finance www.multipool.finance www.multipool.finance Telegram - t.me/multipoolfi t.me/multipoolfi t.me/multipoolfi X - https://twitter.com/multipoolfi https://twitter.com/multipoolfi https://twitter.com/multipoolfi About Multipool Multipool is a cutting-edge decentralized exchange (DEX) transforming the trading landscape for real-world assets (RWAs) and cryptocurrencies. Multipool is designed for fairness and equality, featuring a fully decentralized on-chain order book, deep liquidity through dynamic bracket pools, and seamless trading of RWAs and cryptocurrencies. Utilizing world-class innovations including industry-first FIX APIs, low latency networks, zero price impact auctions, trustless RFQs, peer-to-peer repo lending, and MEV bot protection, Multipool sets a new standard in DeFi trading. Experience unparalleled efficiency and security in your trading journey with Multipool – The DEX with CEX appeal. https://www.multipool.finance/ https://www.multipool.finance/ https://www.multipool.finance/ Contact Public Relations Manager Angie Hermosa Multipool press@multipool.finance This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here . here here

Multipool Announces LBP After Raising $650k In VC Round Led By NxGen

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com];
(2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za];
(3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za];
(4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction
Methodology
Neural Network Methodology
Numerical results, implementation and discussion
Conclusion, Acknowledgments, and Funding
Availability of data, code and materials, Contributions and Declarations
References 3. Neural Network Methodology The neural network (NN) algorithm is used for solving problems relating to dimensionality reduction [42, 49], visualization of data [31], clustering [11, 52] and classification issues [37, 40]. It is also used in regression [2, 21, 45] in solving regression problems since they do not require prior knowledge about the distribution of the data. The NN algorithm often has the tendency to predict with higher accuracy than other techniques due to the NN’s capability to fit any continuous functions [18]. Mathematically, the NN can be referred to as a directed graph having neurons as vertices and links as edges. Different forms of NN depend on the connectivity of their neurons, and the simplest one is the Multi-layer perceptron, also known as the feedforward NN. Basically, a NN can have only one input and one output layer in its simplest form, and this can be written as: where m is the number of input variables, Φ is the activation function, wi,k is the weight of the input layer i with respect to the output k, b is the bias, and the input vector x is connected to the output k (denoting the kth neuron in the output layer) through a biased weighted sum. In the presence of hidden layers positioned between the input layers and the output layers, the output can be written as: where m1 is the number of input variables, m2 is the number of nodes in the hidden layer, Φ : R → R refers to non-linear activation functions for each of the layers in the brackets, and Φout is the possibly new output function. Recently, the NN has become an indispensable tool for learning the solutions of differential equations, and this section will utilize the potential of the NN in solving PDE-related problems [1, 10, 20, 50]. Also, the NN has been implemented in solving equations without analytical solutions. For instance, Nwankwo et al. [38] considered the solution of the American options PDE by incorporating the Landau transformation and solving the corresponding transformed function via a neural network approach. In many scientific and industrial contexts, there is a need to solve parametric PDEs using NN techniques and Khoo et al. [24] developed such a technique which solves PDE with inhomogeneous coefficient fields. For high-dimensional parametric PDE, [14] analyzed the deep parametric PDE method to solve high-dimensional parametric PDEs with much emphasis on financial applications. In the following, we describe the Bitcoin options with the corresponding Black-Scholes pricing PDE: The above equation which is a non-homogeneous PDE can be re-written as Standard theorems guarantee a classical smooth solution exists for the pricing PDE (3.13) given the assumed dynamics. The continuity and linear growth conditions on the coefficient functions ensure they satisfy Lipschitz continuity. Contingent claims theory shows that Lipschitz continuity is sufficient for existence and uniqueness under the stochastic process specifications. In particular, the smooth past price dependence in the diffusion coefficient allows the application results for delayed Black-Scholes equations. Therefore, the Cauchy problem is well-posed under the model assumptions, and a smooth pricing solution is guaranteed to exist based on the theorems. This provides the theoretical foundation for using a neural network to approximate the price function numerically. Thus, employing the ANN to solve the PDE, we introduce an approximating function ζ(t, S : θ) with parameter set θ. The loss or cost function associated with this training is measured by how well the approximation function satisfies the differential operator, boundary conditions and the terminal condition of the option pricing PDE. These are given respectively as Suppose L(ζ) = 0, then ζ(t, S : θ) is a solution of the PDE in equation (3.13). The major aim is to obtain a set of parameters θ such that the function ζ(t, S : θ) minimizes the observed error of L(ζ). The procedure for seeking a good parameter set by minimizing this loss function using the stochastic gradient descent (SGD) optimizer is called “training”. Thus, using a Machine Learning approach, and in this case, the artificial NN, it will be feasible to minimize the function L(ζ) by applying the SGD approach on the sequence of asset and time points which are drawn at random. A part of the input samples, fully dependent on the mini-batch size, is drawn within each iteration to estimate the gradient of the given objective function. The gradient is then estimated over these mini-batches due to the limitations of the computer memory [30]. The training of NN is classified into first identifying the network’s hyperparameters, that is, the architectural structure and the loss function of the network. Next, use the SGD to optimize or estimate the loss minimizer, and then the derivatives of the loss function are computed using the backpropagation techniques. Essentially, the process of searching and identifying the best θ parameter by minimizing the loss function using the gradient descent-based optimizers is referred to as “training”. The whole procedure is well illustrated in the algorithm below [46], and can be implemented in solving the PDE in equation (3.13): The learning rate α is employed to scale the intensity of the parameter updates during the gradient descent. Choosing the learning rate, as the descent parameter α, in the network training is crucial since this factor plays a significant role in aiding the algorithm’s convergence to the true solution in the gradient descent. It equally affects the pace at which the algorithm learns and whether or not the cost function is minimized. When α implies divergence, and thus, the optimal point can be missed. Also, a fixed value of α can most likely make the local optima overshoot after some iterations, leading to divergence. Defining the learning rate as a dynamic decreasing function is preferable since it allows the algorithm to identify the needed point rapidly. Another limitation in employing the gradient descent method is obtaining the value of the initial parameters of the loss function. If the value is significantly close to the local optimum, then the slope of the loss function reduces, thereby leading to the optimal convergence. Otherwise, there will be no convergence as the solution explodes abnormally. 3.1. Solution of bitcoin option pricing PDE While the pricing PDE has a proven smooth solution under the model dynamics, obtaining the analytical form is intractable. Numerical methods must be used to approximate the solution. Neural networks provide a flexible parametric approach based on their universal approximation theoretical results. Given sufficient network capacity, neural networks can represent a wide class of functions, including solutions to PDEs like the pricing equation. However, challenges remain in finding the optimal network parameters to recover the true solution robustly. While existence is guaranteed, the non-convex optimization of neural networks does not assure convergence to global optimality. Care must be taken in specifying the network architecture, loss function, regularization, and training methodology to promote the learning of the pricing function. Subject to these caveats, neural networks present a promising computational technique for approximating smooth pricing solutions, circumventing discretization of the domain. We note the limitations of using neural networks as function approximators. However, their generalization capabilities provide a methodology for data-driven extraction of the pricing mapping across the entire domain. This avoids the constraints of methods like grid-based techniques that rely on local consistency. Future work should explore neural network training enhancements and theoretical guarantees to ensure robust solutions. This paper is available on arxiv under CC 4.0 license. Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction Methodology Neural Network Methodology Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations References Abstract and Introduction Abstract and Introduction Methodology Methodology Neural Network Methodology Neural Network Methodology Numerical results, implementation and discussion Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations Availability of data, code and materials, Contributions and Declarations References References 3. Neural Network Methodology The neural network (NN) algorithm is used for solving problems relating to dimensionality reduction [42, 49], visualization of data [31], clustering [11, 52] and classification issues [37, 40]. It is also used in regression [2, 21, 45] in solving regression problems since they do not require prior knowledge about the distribution of the data. The NN algorithm often has the tendency to predict with higher accuracy than other techniques due to the NN’s capability to fit any continuous functions [18]. Mathematically, the NN can be referred to as a directed graph having neurons as vertices and links as edges. Different forms of NN depend on the connectivity of their neurons, and the simplest one is the Multi-layer perceptron, also known as the feedforward NN. Basically, a NN can have only one input and one output layer in its simplest form, and this can be written as: where m is the number of input variables, Φ is the activation function, wi,k is the weight of the input layer i with respect to the output k, b is the bias, and the input vector x is connected to the output k (denoting the kth neuron in the output layer) through a biased weighted sum. In the presence of hidden layers positioned between the input layers and the output layers, the output can be written as: where m1 is the number of input variables, m2 is the number of nodes in the hidden layer, Φ : R → R refers to non-linear activation functions for each of the layers in the brackets, and Φout is the possibly new output function. Recently, the NN has become an indispensable tool for learning the solutions of differential equations, and this section will utilize the potential of the NN in solving PDE-related problems [1, 10, 20, 50]. Also, the NN has been implemented in solving equations without analytical solutions. For instance, Nwankwo et al. [38] considered the solution of the American options PDE by incorporating the Landau transformation and solving the corresponding transformed function via a neural network approach. In many scientific and industrial contexts, there is a need to solve parametric PDEs using NN techniques and Khoo et al. [24] developed such a technique which solves PDE with inhomogeneous coefficient fields. For high-dimensional parametric PDE, [14] analyzed the deep parametric PDE method to solve high-dimensional parametric PDEs with much emphasis on financial applications. In the following, we describe the Bitcoin options with the corresponding Black-Scholes pricing PDE: The above equation which is a non-homogeneous PDE can be re-written as Standard theorems guarantee a classical smooth solution exists for the pricing PDE (3.13) given the assumed dynamics. The continuity and linear growth conditions on the coefficient functions ensure they satisfy Lipschitz continuity. Contingent claims theory shows that Lipschitz continuity is sufficient for existence and uniqueness under the stochastic process specifications. In particular, the smooth past price dependence in the diffusion coefficient allows the application results for delayed Black-Scholes equations. Therefore, the Cauchy problem is well-posed under the model assumptions, and a smooth pricing solution is guaranteed to exist based on the theorems. This provides the theoretical foundation for using a neural network to approximate the price function numerically. Thus, employing the ANN to solve the PDE, we introduce an approximating function ζ(t, S : θ) with parameter set θ. The loss or cost function associated with this training is measured by how well the approximation function satisfies the differential operator, boundary conditions and the terminal condition of the option pricing PDE. These are given respectively as Suppose L(ζ) = 0, then ζ(t, S : θ) is a solution of the PDE in equation (3.13). The major aim is to obtain a set of parameters θ such that the function ζ(t, S : θ) minimizes the observed error of L(ζ). The procedure for seeking a good parameter set by minimizing this loss function using the stochastic gradient descent (SGD) optimizer is called “training”. Thus, using a Machine Learning approach, and in this case, the artificial NN, it will be feasible to minimize the function L(ζ) by applying the SGD approach on the sequence of asset and time points which are drawn at random. A part of the input samples, fully dependent on the mini-batch size, is drawn within each iteration to estimate the gradient of the given objective function. The gradient is then estimated over these mini-batches due to the limitations of the computer memory [30]. The training of NN is classified into first identifying the network’s hyperparameters, that is, the architectural structure and the loss function of the network. Next, use the SGD to optimize or estimate the loss minimizer, and then the derivatives of the loss function are computed using the backpropagation techniques. Essentially, the process of searching and identifying the best θ parameter by minimizing the loss function using the gradient descent-based optimizers is referred to as “training”. The whole procedure is well illustrated in the algorithm below [46], and can be implemented in solving the PDE in equation (3.13): The learning rate α is employed to scale the intensity of the parameter updates during the gradient descent. Choosing the learning rate, as the descent parameter α, in the network training is crucial since this factor plays a significant role in aiding the algorithm’s convergence to the true solution in the gradient descent. It equally affects the pace at which the algorithm learns and whether or not the cost function is minimized. When α implies divergence, and thus, the optimal point can be missed. Also, a fixed value of α can most likely make the local optima overshoot after some iterations, leading to divergence. Defining the learning rate as a dynamic decreasing function is preferable since it allows the algorithm to identify the needed point rapidly. Another limitation in employing the gradient descent method is obtaining the value of the initial parameters of the loss function. If the value is significantly close to the local optimum, then the slope of the loss function reduces, thereby leading to the optimal convergence. Otherwise, there will be no convergence as the solution explodes abnormally. 3.1. Solution of bitcoin option pricing PDE 3.1. Solution of bitcoin option pricing PDE While the pricing PDE has a proven smooth solution under the model dynamics, obtaining the analytical form is intractable. Numerical methods must be used to approximate the solution. Neural networks provide a flexible parametric approach based on their universal approximation theoretical results. Given sufficient network capacity, neural networks can represent a wide class of functions, including solutions to PDEs like the pricing equation. However, challenges remain in finding the optimal network parameters to recover the true solution robustly. While existence is guaranteed, the non-convex optimization of neural networks does not assure convergence to global optimality. Care must be taken in specifying the network architecture, loss function, regularization, and training methodology to promote the learning of the pricing function. Subject to these caveats, neural networks present a promising computational technique for approximating smooth pricing solutions, circumventing discretization of the domain. We note the limitations of using neural networks as function approximators. However, their generalization capabilities provide a methodology for data-driven extraction of the pricing mapping across the entire domain. This avoids the constraints of methods like grid-based techniques that rely on local consistency. Future work should explore neural network training enhancements and theoretical guarantees to ensure robust solutions.

Neural Network for Valuing Bitcoin: Neural Network Methodology

Get Ready, Future Web Developers! Let's create a simple HTML website that connects to a Postgres Database. For this example, we will be using JavaScript (Node JS, and Express JS) for its middleware functionalities. Whether you want to showcase your portfolio, run a blog, or complete a due mini project on web development, web development is a skill that's still in demand. The Learning Path Ahead We'll dive into the process of building a simple HTML website from scratch. We'll explore how to integrate a Postgres database, using JavaScript as middleware to handle API requests. To spice things up, we can also use Bootstrap5 to design the webpage! But that will be covered in a different blog. Technologies Used: HTML5
Postgres (Database)
Express JS (Backend) Prerequisites Make sure Postgres is downloaded and ready to use. Also, download Node JS for installing npm packages like Express JS, Body Parser and Postgres APIs.
Download Postgres here
Download NodeJS here Step 1: Setup Postgres Database Create a new Postgres Database either using psql, which is the CLI for running SQL commands or a graphical user interface like pgAdmin (which comes pre-installed). For this demonstration, we will be using psql for creating the database. Open psql and enter the credentials to get started. Create a database called webapp and connect to it!
(You can use any name you want for your project!) CREATE database webapp; \c webapp Start building your table in this database by CREATE TABLE command. You can use Postgres docs to guide you with the commands.
For this demonstration, we are creating a student database that stores Name, Year and Branch. (Add more attributes if you want) CREATE TABLE student 
(name varchar(20), semester int, branch varchar(20)); \d student Now, we can start uploading some dummy data to the table via INSERT command INSERT INTO student VALUES
('Abel', 4, 'CE'), 
('John', 6, 'ME'), 
('Doe', 2, 'ETC'); Once we are done, adding the dummy data, we can view the Student table with the below command SELECT * FROM student; If you followed the steps till now, you would get the below student table! Step 2: Create a simple HTML Website Below is the Boilerplate HTML code for a simple website: <!DOCTYPE html>
<html lang='en'>
<head>
  <meta charset="utf-8">
  <meta name="viewport" content="width=device-width">
  <title> Student Management System </title>
</head>
<body>
  <h1> Student Management System </h1>
</body>
</html> Let's start adding the custom div blocks as per our needs: ...
<body>
  <h1> Student Management System </h1>
  <p> Here, are the student details as below: </p>
  <div id='students_list'></div>
... students_list div block is for showing the list of students that have been registered to the database. We will be using Express JS to fetch the data from Postgres and showcase it in the block. Step 3: Connecting HTML to Postgres via Express JS Install the necessary libraries first in your Command Prompt or Terminal npm install express body-parser pg Let's start building the script.js file for connecting HTML and PostgreSQL. Firstly, we require importing the necessary libraries for handling requests and establishing a connection // Import required modules
const express = require('express');
const { Pool } = require('pg');
const path = require('path');
const bodyParser = require('body-parser'); express works as a backend service, for parsing requests from the HTML webapp
pg is a Postgres API for establishing the connection
path provides utilities for managing directory paths
body-parser is a middle-ware for extracting data from POST requests
(We will be understanding them in depth as we move along) Let's now create an express application connection and also, define the port at which the server will be listening to. // Connect and Create an Express Application
const app = express();
const port = 3000; // By default, its 3000, you can customize Establish a connection to Postgres by creating an instance of the Pool object. Add the necessary values to match your Postgres setup. // Create a Postgres Connection
const pool = new Pool({
  user: 'postgres',
  host: 'localhost',
  database: 'webapp',
  password: 'password', // Change to your password
  port: 5432, // Default Port
}); Add functionalities to register static files via express.static() middleware. It specifies the root directory from which to serve static files app.use(express.static(path.join(''))); Now, we have to parse HTML requests sent from the app. In simple words, it's a middleware used to recieve data from users, such as forms or uploads app.use(bodyParser.urlencoded({ extended: false })); (Don't add the above line if you are not planning to take input from users. We will be adding a registeration form in the next blog and that's why we require body-parser) Set up a Route handler for the root URL ('/'). So that, when a GET request is made to the root URL, the server responds by sending the "index.html" file located in the same directory // Setup Route handler
app.get('/', (req, res) => {
  res.sendFile(path.join(__dirname, '', 'index.html'));
}); Now, comes the main part! We will now be setting up a route handler for '/students' URL with the HTTP GET method. This handler retrieves student data (from query) from the Postgres Database. // Route handler for GET student data
app.get('/students', (req, res) => {
  const query = 'SELECT * FROM student;';

  pool.query(query, (error, result) => {
    if (error) {
      console.error('Error occurred:', error);
      res.status(500).send('An error occurred while retrieving data from the database.');
    } else {
      const students = result.rows;
      res.json(students);
    }
  });
}); (Make sure the brackets are closed properly) Now, let's specify the line that listens to the server and when the time is due, it responds with its requests. As the below command listens, it logs a message to console. // Listening to Requests
app.listen(port, () => {
  console.log(`Server listening on port ${port}`);
}); (Good for debugging purposes) Done! script.js is finally complete. Let's make the changes in the index.html file for showcasing the necessary details. ...
  <div id='students_list'></div>
  <script>
  // Fetch data via requests
  fetch('/students')
    .then(response => response.json())
    .then(data => {
    const studentList = data.map(
      student => `<li> About ${student.name} : ${student.branch} - ${student.semester}th Sem</li>`
    ).join('');
    document.getElementById('students_list').innerHTML = `<ul>${studentList}</ul>`;
  })
    .catch(error => console.error('Error occurred:', error));
  </script>
... Run the Website Open Terminal and go to the directory where index.html and script.js is stored and run the following command: node script.js If everything works all right, it should display the content "Server listening on port 3000" Now, you need to go to http://localhost:3000/ where you can see a simple HTML website showcasing the data you had entered! Voila! That's it! Now, use your creativity and knowledge to explore these web development concepts and create more interesting websites! I will also be adding another blog on how to create a registration system and how to design it, which will be coming soon. Follow for more and stay tuned! Until then, Keep Coding! Get Ready, Future Web Developers! Let's create a simple HTML website that connects to a Postgres Database. For this example, we will be using JavaScript (Node JS, and Express JS) for its middleware functionalities. Whether you want to showcase your portfolio, run a blog, or complete a due mini project on web development, web development is a skill that's still in demand. The Learning Path Ahead We'll dive into the process of building a simple HTML website from scratch. We'll explore how to integrate a Postgres database, using JavaScript as middleware to handle API requests. To spice things up, we can also use Bootstrap5 to design the webpage! But that will be covered in a different blog. Technologies Used: HTML5 Postgres (Database) Express JS (Backend) HTML5 Postgres (Database) Express JS (Backend) Prerequisites Make sure Postgres is downloaded and ready to use. Also, download Node JS for installing npm packages like Express JS, Body Parser and Postgres APIs.
Download Postgres here Download NodeJS here here here Step 1: Setup Postgres Database Create a new Postgres Database either using psql , which is the CLI for running SQL commands or a graphical user interface like pgAdmin (which comes pre-installed). For this demonstration, we will be using psql for creating the database. psql psql Open psql and enter the credentials to get started. psql Create a database called webapp and connect to it! (You can use any name you want for your project!) webapp (You can use any name you want for your project!) CREATE database webapp; CREATE database webapp; \c webapp \c webapp Start building your table in this database by CREATE TABLE command. You can use Postgres docs to guide you with the commands.
For this demonstration, we are creating a student database that stores Name , Year and Branch . (Add more attributes if you want) CREATE TABLE student Name Year Branch (Add more attributes if you want) CREATE TABLE student 
(name varchar(20), semester int, branch varchar(20)); CREATE TABLE student 
(name varchar(20), semester int, branch varchar(20)); \d student \d student Now, we can start uploading some dummy data to the table via INSERT command INSERT INTO student VALUES
('Abel', 4, 'CE'), 
('John', 6, 'ME'), 
('Doe', 2, 'ETC'); INSERT INTO student VALUES
('Abel', 4, 'CE'), 
('John', 6, 'ME'), 
('Doe', 2, 'ETC'); Once we are done, adding the dummy data, we can view the Student table with the below command Student SELECT * FROM student; SELECT * FROM student; If you followed the steps till now, you would get the below student table! student Step 2: Create a simple HTML Website Below is the Boilerplate HTML code for a simple website: <!DOCTYPE html>
<html lang='en'>
<head>
  <meta charset="utf-8">
  <meta name="viewport" content="width=device-width">
  <title> Student Management System </title>
</head>
<body>
  <h1> Student Management System </h1>
</body>
</html> <!DOCTYPE html>
<html lang='en'>
<head>
  <meta charset="utf-8">
  <meta name="viewport" content="width=device-width">
  <title> Student Management System </title>
</head>
<body>
  <h1> Student Management System </h1>
</body>
</html> Let's start adding the custom div blocks as per our needs: ...
<body>
  <h1> Student Management System </h1>
  <p> Here, are the student details as below: </p>
  <div id='students_list'></div>
... ...
<body>
  <h1> Student Management System </h1>
  <p> Here, are the student details as below: </p>
  <div id='students_list'></div>
... students_list div block is for showing the list of students that have been registered to the database. We will be using Express JS to fetch the data from Postgres and showcase it in the block. students_list Step 3: Connecting HTML to Postgres via Express JS Install the necessary libraries first in your Command Prompt or Terminal Command Prompt npm install express body-parser pg npm install express body-parser pg Let's start building the script.js file for connecting HTML and PostgreSQL. Firstly, we require importing the necessary libraries for handling requests and establishing a connection script.js // Import required modules
const express = require('express');
const { Pool } = require('pg');
const path = require('path');
const bodyParser = require('body-parser'); // Import required modules
const express = require('express');
const { Pool } = require('pg');
const path = require('path');
const bodyParser = require('body-parser'); express works as a backend service, for parsing requests from the HTML webapp pg is a Postgres API for establishing the connection path provides utilities for managing directory paths body-parser is a middle-ware for extracting data from POST requests (We will be understanding them in depth as we move along) express pg path body-parser (We will be understanding them in depth as we move along) Let's now create an express application connection and also, define the port at which the server will be listening to. // Connect and Create an Express Application
const app = express();
const port = 3000; // By default, its 3000, you can customize // Connect and Create an Express Application
const app = express();
const port = 3000; // By default, its 3000, you can customize Establish a connection to Postgres by creating an instance of the Pool object. Add the necessary values to match your Postgres setup. Pool // Create a Postgres Connection
const pool = new Pool({
  user: 'postgres',
  host: 'localhost',
  database: 'webapp',
  password: 'password', // Change to your password
  port: 5432, // Default Port
}); // Create a Postgres Connection
const pool = new Pool({
  user: 'postgres',
  host: 'localhost',
  database: 'webapp',
  password: 'password', // Change to your password
  port: 5432, // Default Port
}); Add functionalities to register static files via express.static() middleware. It specifies the root directory from which to serve static files express.static() app.use(express.static(path.join(''))); app.use(express.static(path.join(''))); Now, we have to parse HTML requests sent from the app. In simple words, it's a middleware used to recieve data from users, such as forms or uploads app.use(bodyParser.urlencoded({ extended: false })); app.use(bodyParser.urlencoded({ extended: false })); (Don't add the above line if you are not planning to take input from users. We will be adding a registeration form in the next blog and that's why we require body-parser) (Don't add the above line if you are not planning to take input from users. We will be adding a registeration form in the next blog and that's why we require body-parser) Set up a Route handler for the root URL ('/'). So that, when a GET request is made to the root URL, the server responds by sending the "index.html" file located in the same directory // Setup Route handler
app.get('/', (req, res) => {
  res.sendFile(path.join(__dirname, '', 'index.html'));
}); // Setup Route handler
app.get('/', (req, res) => {
  res.sendFile(path.join(__dirname, '', 'index.html'));
}); Now, comes the main part! We will now be setting up a route handler for '/students' URL with the HTTP GET method. This handler retrieves student data (from query) from the Postgres Database. // Route handler for GET student data
app.get('/students', (req, res) => {
  const query = 'SELECT * FROM student;';

  pool.query(query, (error, result) => {
    if (error) {
      console.error('Error occurred:', error);
      res.status(500).send('An error occurred while retrieving data from the database.');
    } else {
      const students = result.rows;
      res.json(students);
    }
  });
}); // Route handler for GET student data
app.get('/students', (req, res) => {
  const query = 'SELECT * FROM student;';

  pool.query(query, (error, result) => {
    if (error) {
      console.error('Error occurred:', error);
      res.status(500).send('An error occurred while retrieving data from the database.');
    } else {
      const students = result.rows;
      res.json(students);
    }
  });
}); (Make sure the brackets are closed properly) (Make sure the brackets are closed properly) Now, let's specify the line that listens to the server and when the time is due, it responds with its requests. As the below command listens, it logs a message to console. // Listening to Requests
app.listen(port, () => {
  console.log(`Server listening on port ${port}`);
}); // Listening to Requests
app.listen(port, () => {
  console.log(`Server listening on port ${port}`);
}); (Good for debugging purposes) (Good for debugging purposes) Done! script.js is finally complete. Let's make the changes in the index.html file for showcasing the necessary details. script.js index.html ...
  <div id='students_list'></div>
  <script>
  // Fetch data via requests
  fetch('/students')
    .then(response => response.json())
    .then(data => {
    const studentList = data.map(
      student => `<li> About ${student.name} : ${student.branch} - ${student.semester}th Sem</li>`
    ).join('');
    document.getElementById('students_list').innerHTML = `<ul>${studentList}</ul>`;
  })
    .catch(error => console.error('Error occurred:', error));
  </script>
... ...
  <div id='students_list'></div>
  <script>
  // Fetch data via requests
  fetch('/students')
    .then(response => response.json())
    .then(data => {
    const studentList = data.map(
      student => `<li> About ${student.name} : ${student.branch} - ${student.semester}th Sem</li>`
    ).join('');
    document.getElementById('students_list').innerHTML = `<ul>${studentList}</ul>`;
  })
    .catch(error => console.error('Error occurred:', error));
  </script>
... Run the Website Open Terminal and go to the directory where index.html and script.js is stored and run the following command: index.html script.js node script.js node script.js If everything works all right, it should display the content "Server listening on port 3000" Now, you need to go to http://localhost:3000/ where you can see a simple HTML website showcasing the data you had entered! http://localhost:3000/ Voila! That's it! Voila! That's it! Now, use your creativity and knowledge to explore these web development concepts and create more interesting websites! I will also be adding another blog on how to create a registration system and how to design it, which will be coming soon. Follow for more and stay tuned! Until then, Keep Coding!

Build a Simple HTML Website with Postgres Database Connectivity

Postgres ডাটাবেস সংযোগ সহ একটি সাধারণ HTML ওয়েবসাইট তৈরি করুন

Erstellen Sie eine einfache HTML-Website mit Postgres-Datenbankkonnektivität

Cree un sitio web HTML simple con conectividad de base de datos Postgres

Créez un site Web HTML simple avec la connectivité de la base de données Postgres

Postgres डेटाबेस कनेक्टिविटी के साथ एक सरल HTML वेबसाइट बनाएं

Postgres データベース接続を備えたシンプルな HTML ウェブサイトを構築する

Postgres 데이터베이스 연결을 사용하여 간단한 HTML 웹사이트 구축

Crie um site HTML simples com conectividade de banco de dados Postgres

Создайте простой HTML-сайт с возможностью подключения к базе данных Postgres

Postgres Veritabanı Bağlantısı ile Basit Bir HTML Web Sitesi Oluşturun

Xây dựng một trang web HTML đơn giản với kết nối cơ sở dữ liệu Postgres

使用 Postgres 数据库连接构建一个简单的 HTML 网站

Population Stability Index (PSI) is a statistical measure commonly used in credit risk modeling and other fields to assess the stability of a population across different time periods or segments. It's particularly valuable in scenarios where changes in the population distribution could impact the effectiveness of a model. It is a fundamental assumption that the population on which a statistical model is applied to is similar to the population on which the model is developed at. The model performance relies on the closeness between the model development sample and the production data. Therefore, there is an intrinsic need to compare the two samples (development vs production) and assess whether a model needs to be recalibrated. The population change may occur for several reasons – change in the business strategies and policies or changes in external factors such as the political, economic and social environment. The model performance is impacted because of a change in the joint distribution p(y, X), where y is the model outcome and X is the design matrix that comprises the observations of the model features. Therefore, the entire model fit, i.e., the estimates of the model coefficients and the inherent functions get impacted. If this happens, then a decision must be made towards the recalibration or redevelopment of the model.  Before we dive deep into the PSI mathematical expression, we start with some key concepts on Entropy and KL divergence. Entropy and KL Divergence Entropy is a measure of uncertainty or randomness in a set of data. In machine learning, particularly in decision trees and information theory, entropy is used to quantify the impurity or disorder in a dataset. For instance, the splits of a decision tree for a classification problem are created to minimize the entropy. Entropy is used to determine the best attribute to split the data at each node of the decision tree. In the above definition of entropy, the negative sign ensures that Entropy is positive (because log of the probability will be negative as the probability will be < 1). Higher (lower) the value of P(X = X_i) lower (higher) is the entropy or randomness or uncertainty about X. Thus, ‘skewed’ distributions have lower entropy but ‘balanced’ distributions have higher entropy. The objective of splitting a variable at a node for a binary classification problem is to create more skewed distribution such that we can discriminate between an outcome value y = 1 and outcome value y = 0. Therefore, we move from a high entropy stage before splitting the variable to a lower entropy stage after splitting the variable.
If Entropy H(X) is high, then the uncertainty before knowing X is high. So after knowing X we have gained more information.
If Entropy H(X) is low, then the uncertainty before knowing X is low. So after knowing X we have gained less information.
We try to minimize entropy whilst building binary regression models. For example, we ‘bin’ or ‘discretize’ a model factor such the distribution of binary outcome becomes as skewed as possible across the different bins. Kullback-Liebler Divergence (KL Divergence) has been referred in several places in the literature (Lin, 2017), (Wu & Olson, 2010), (Li et al., 2008), etc. It measures the difference between two probability distributions p(x) and q(x). It quantifies how one probability distribution diverges from another. The distribution p(x) is considered the ‘true’ or ‘base’ distribution, and the distribution q(x) is considered the ‘untrue’ or ‘target’ distribution, so that KL Divergence represents some sort of loss due to using the ‘wrong’ distribution. KL divergence is non-negative and is zero if and only if p(x) and q(x) are identical, i.e., the same distribution. KL divergence measures the dissimilarity of the two probability distributions p(x) and q(x). If both the distributions are identical, KL Divergence is 0. We have a single random variable “X” and we have two different probability distributions for that variable. One is assumed to be the ‘true’ distribution and the other is the approximation of the ‘true’ distribution. So, we try “approximating” one distribution with the other and calculate the difference in the information about the event as a measure of the “divergence”. Note that the notation ‘P||Q’ implies P is approximated as Q.
Notice how the mathematical expressions for the individual terms of KL divergence are similar to that of Entropy or information which we introduced earlier. The second term inside the brackets is the information in p(x) about x. The first term inside the brackets is the information in an approximation distribution of p(x) as q(x) about x. That is if we approximate the target distribution p(x) by q(x); then the difference in the information between them is the relative entropy or KL Divergence index. The better our approximation the closer p(x) and q(x) and hence the KL divergence will be 0.
Even though KL Divergence measures divergence of q(x) from p(x), it is technically not a distance measure because the definition is not symmetric. Thus KL(P||Q) != KL(Q||P) Population Stability Index – Now that we have covered the mathematical expressions of Entropy and KL Divergence Index, we will see how they would help us in understanding the expression of Population Stability Index. Notice that we have added another term q(x) inside the brackets of KL divergence expression to get the mathematical expression for PSI. But the formulae look so similar that we can think of expressing PSI as a function of KL Divergence. Here is how we can do that. That is the PSI metric is actually the sum of the relative entropies of q(x) over p(x) and p(x) over q(x). In other words we are adding the information ‘gain’ by expressing p(x) using an approximation q(x) and vice-versa. The reason we do this is because we don’t know the ‘ground truth’. We assume that one of them is a ‘true’ distribution and the other is an ‘approximation’; and as we know that the KL divergence is not symmetric, we compute it from p(x) to q(x) and vice-versa and add them to get a final metric which can be judged to ascertain the difference between p(x) and q(x). The PSI calculation typically begins by dividing the data into bins or segments based on key variables used in the model.
PSI values close to zero indicate stability between the initial and new populations.
Higher PSI values suggest significant shifts in the population distribution, which may require further investigation or model recalibration. So how high should PSI be to make that judgement? The following table summarizes the PSI values which are ‘industry wide rules of thumb’. Interestingly, PSI is very similar to ‘Information Value’ used to measure the strength of the modelling variables in developing credit risk models. We will explore that soon in a different article. Population Stability Index (PSI) is a statistical measure commonly used in credit risk modeling and other fields to assess the stability of a population across different time periods or segments. It's particularly valuable in scenarios where changes in the population distribution could impact the effectiveness of a model. It is a fundamental assumption that the population on which a statistical model is applied to is similar to the population on which the model is developed at. The model performance relies on the closeness between the model development sample and the production data. Therefore, there is an intrinsic need to compare the two samples (development vs production) and assess whether a model needs to be recalibrated. The population change may occur for several reasons – change in the business strategies and policies or changes in external factors such as the political, economic and social environment. The model performance is impacted because of a change in the joint distribution p(y, X ), where y is the model outcome and X is the design matrix that comprises the observations of the model features. Therefore, the entire model fit, i.e., the estimates of the model coefficients and the inherent functions get impacted. If this happens, then a decision must be made towards the recalibration or redevelopment of the model.  Before we dive deep into the PSI mathematical expression, we start with some key concepts on Entropy and KL divergence. X Entropy and KL Divergence Entropy and KL Divergence Entropy and KL Divergence Entropy is a measure of uncertainty or randomness in a set of data. In machine learning, particularly in decision trees and information theory, entropy is used to quantify the impurity or disorder in a dataset. For instance, the splits of a decision tree for a classification problem are created to minimize the entropy. Entropy is used to determine the best attribute to split the data at each node of the decision tree. In the above definition of entropy, the negative sign ensures that Entropy is positive (because log of the probability will be negative as the probability will be < 1). Higher (lower) the value of P(X = X_i) lower (higher) is the entropy or randomness or uncertainty about X. Thus, ‘skewed’ distributions have lower entropy but ‘balanced’ distributions have higher entropy. The objective of splitting a variable at a node for a binary classification problem is to create more skewed distribution such that we can discriminate between an outcome value y = 1 and outcome value y = 0. Therefore, we move from a high entropy stage before splitting the variable to a lower entropy stage after splitting the variable. If Entropy H(X) is high, then the uncertainty before knowing X is high. So after knowing X we have gained more information. If Entropy H(X) is low, then the uncertainty before knowing X is low. So after knowing X we have gained less information. We try to minimize entropy whilst building binary regression models. For example, we ‘bin’ or ‘discretize’ a model factor such the distribution of binary outcome becomes as skewed as possible across the different bins. Higher (lower) the value of P(X = X_i) lower (higher) is the entropy or randomness or uncertainty about X. Thus, ‘skewed’ distributions have lower entropy but ‘balanced’ distributions have higher entropy. The objective of splitting a variable at a node for a binary classification problem is to create more skewed distribution such that we can discriminate between an outcome value y = 1 and outcome value y = 0. Therefore, we move from a high entropy stage before splitting the variable to a lower entropy stage after splitting the variable. If Entropy H(X) is high, then the uncertainty before knowing X is high. So after knowing X we have gained more information. If Entropy H(X) is low, then the uncertainty before knowing X is low. So after knowing X we have gained less information. We try to minimize entropy whilst building binary regression models. For example, we ‘bin’ or ‘discretize’ a model factor such the distribution of binary outcome becomes as skewed as possible across the different bins. Kullback-Liebler Divergence (KL Divergence) has been referred in several places in the literature (Lin, 2017), (Wu & Olson, 2010), (Li et al., 2008), etc. It measures the difference between two probability distributions p(x) and q(x). It quantifies how one probability distribution diverges from another. The distribution p(x) is considered the ‘true’ or ‘base’ distribution, and the distribution q(x) is considered the ‘untrue’ or ‘target’ distribution, so that KL Divergence represents some sort of loss due to using the ‘wrong’ distribution. KL divergence is non-negative and is zero if and only if p(x) and q(x) are identical, i.e., the same distribution. KL divergence measures the dissimilarity of the two probability distributions p(x) and q(x). If both the distributions are identical, KL Divergence is 0. We have a single random variable “X” and we have two different probability distributions for that variable. One is assumed to be the ‘true’ distribution and the other is the approximation of the ‘true’ distribution. So, we try “approximating” one distribution with the other and calculate the difference in the information about the event as a measure of the “divergence”. Note that the notation ‘P||Q’ implies P is approximated as Q. Notice how the mathematical expressions for the individual terms of KL divergence are similar to that of Entropy or information which we introduced earlier. The second term inside the brackets is the information in p(x) about x. The first term inside the brackets is the information in an approximation distribution of p(x) as q(x) about x. That is if we approximate the target distribution p(x) by q(x); then the difference in the information between them is the relative entropy or KL Divergence index. The better our approximation the closer p(x) and q(x) and hence the KL divergence will be 0. Even though KL Divergence measures divergence of q(x) from p(x), it is technically not a distance measure because the definition is not symmetric. Thus KL(P||Q) != KL(Q||P) We have a single random variable “X” and we have two different probability distributions for that variable. One is assumed to be the ‘true’ distribution and the other is the approximation of the ‘true’ distribution. So, we try “approximating” one distribution with the other and calculate the difference in the information about the event as a measure of the “divergence”. Note that the notation ‘P||Q’ implies P is approximated as Q. Notice how the mathematical expressions for the individual terms of KL divergence are similar to that of Entropy or information which we introduced earlier. The second term inside the brackets is the information in p(x) about x. The first term inside the brackets is the information in an approximation distribution of p(x) as q(x) about x. That is if we approximate the target distribution p(x) by q(x); then the difference in the information between them is the relative entropy or KL Divergence index. The better our approximation the closer p(x) and q(x) and hence the KL divergence will be 0. Even though KL Divergence measures divergence of q(x) from p(x), it is technically not a distance measure because the definition is not symmetric. Thus KL(P||Q) != KL(Q||P) Population Stability Index – Population Stability Index Population Stability Index Now that we have covered the mathematical expressions of Entropy and KL Divergence Index, we will see how they would help us in understanding the expression of Population Stability Index. Notice that we have added another term q(x) inside the brackets of KL divergence expression to get the mathematical expression for PSI. But the formulae look so similar that we can think of expressing PSI as a function of KL Divergence. Here is how we can do that. That is the PSI metric is actually the sum of the relative entropies of q(x) over p(x) and p(x) over q(x). In other words we are adding the information ‘gain’ by expressing p(x) using an approximation q(x) and vice-versa. The reason we do this is because we don’t know the ‘ground truth’. We assume that one of them is a ‘true’ distribution and the other is an ‘approximation’; and as we know that the KL divergence is not symmetric, we compute it from p(x) to q(x) and vice-versa and add them to get a final metric which can be judged to ascertain the difference between p(x) and q(x). The PSI calculation typically begins by dividing the data into bins or segments based on key variables used in the model. PSI values close to zero indicate stability between the initial and new populations. Higher PSI values suggest significant shifts in the population distribution, which may require further investigation or model recalibration. The PSI calculation typically begins by dividing the data into bins or segments based on key variables used in the model. PSI values close to zero indicate stability between the initial and new populations. Higher PSI values suggest significant shifts in the population distribution, which may require further investigation or model recalibration. So how high should PSI be to make that judgement? The following table summarizes the PSI values which are ‘industry wide rules of thumb’. Interestingly, PSI is very similar to ‘Information Value’ used to measure the strength of the modelling variables in developing credit risk models. We will explore that soon in a different article.

Population Stability Index in Machine learning models

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Jihoon Chung;
(2)  Zhenyu (James) Kong. Table of Links Abstract & Introduction
Review of Related Work
Proposed Research Methodology
Numerical Case Studies
Real-World Simulation Case Studies
Conclusion
References V. REAL-WORLD SIMULATION CASE STUDIES An assembly operation from an actual auto-body assembly process is used as a real-world case study. Fig. 5 describes a car’s floor pan, which is the assembled product from this process. The assembled product consists of four parts, including the right bracket, left bracket, right floor pan, and left floor pan. Fig. 6 shows the process assembly procedure consisting of three stations. During the assembly process, the parts are held by fixtures, which are the KCCs in this process [7]. KPCs are measured from four points, namely, M1, M2, M3, and M4, respectively, as shown in Fig. 5. Every part has a designated location for measuring the KPCs. For instance, part 1 has M1, part 2 has M2, part 3 has M3, and part 4 has M4. These measurements can be taken at each station once the relevant part has been assembled in the preceding stations. For example, M3 on part 3 cannot be measured in station 1 because part 3 has not yet been assembled at station 1 [7]. In the designated location, KPCs are measured in three directions (X, Y, and Z). In this assembly process, there exists a total of 33 KCCs, which are dimensional errors of fixture locators [8]. The fault pattern matrix Φ is established based on the literature [7], [11], [47] and provided in Appendix F. Since the number of measurements (12) is less than that of KCCs (33), it causes an underdetermined system in the fault quality linear model. Therefore, sparse estimation is required to identify process faults. In this assembly process, two lists of correlated KCCs exist; the rest are assumed to be independent [8]. The first list comprises six KCCs, including KCC8, KCC9, KCC10, KCC11, KCC12, and KCC13. The second list is composed of KCC31, KCC32, and KCC33. The correlation structures of the two groups are described (for simplification, the lower triangular terms are removed) as follows [8]: To provide nonstationary process faults along the KPCs samples collected over time, two groups are provided. In the first group, the first correlated list is provided as process faults. For the process faults of the second group, all the correlated lists and one independent KCCs are included. Therefore, the case study represents the situation when the process faults evolve over time since the variation of certain KCCs will be propagated to other KCCs if the process faults are not mitigated immediately during the process. 50 KPCs samples are generated from each group. The variances of process faults, non-process faults, and noise of KPCs are determined to be the same value as in Section IV. In addition, performance evaluation measures and benchmark methods used in Section IV are still utilized in Section V. Table III shows the performance comparison in AUC and NMSE by varying the correlation coefficients. For convenience, the correlation coefficients k1 and k2 are equal and are selected from {0.1, 0.3, 0.6, 0.9, 0.95} in the case studies. Specifically, the AUC of the proposed method is close to 1.0 at every correlations levels, representing the perfect classification between the process faults and non-process faults in terms of estimated variance. The effectiveness of the proposed method is significant in NMSE when a high correlation exists. Specifically, the NMSE of the proposed method is less than 10% of that of all the benchmark methods when the correlation coefficient is 0.9 and 0.95. To demonstrate the generalizability of the proposed method, the correlated KCCs are randomly selected in further case studies. Assuming there exist two correlated lists with the size of three, respectively. Therefore, six KCCs are randomly selected from 33 KCCs for two correlated lists in each trial. As in the previous study, one correlated list is provided as process faults in the first group, while two correlated lists and two independent KCCs are used as process faults in the remaining second group. Fig. 7 shows the performances of all the methods in AUC and NMSE results in ten different spatial correlations (i.e., k1 = k2). From Fig. 7 (a), it is prominent that the proposed method successfully differentiates between process faults and non-process faults. Specifically, the AUC of the proposed method is nearly 1.0, while those of most benchmark methods are below 0.9 in the highly correlated case studies. In addition, Fig. 7 (b) represents that the proposed method provides valuable information to the practitioners to determine when to stop the operations to maintain the process when a high correlation exists between KCCs. All the benchmark methods illustrate similar trends compared to Section IV since the methods cannot consider both the spatial correlation of KCCs and the nonstationary process faults. This paper is available on arxiv under CC 4.0 license. Authors: (1) Jihoon Chung; (2)  Zhenyu (James) Kong. This paper is available on arxiv under CC 4.0 license. Authors: (1) Jihoon Chung; (2)  Zhenyu (James) Kong. Table of Links Abstract & Introduction Review of Related Work Proposed Research Methodology Numerical Case Studies Real-World Simulation Case Studies Conclusion References Abstract & Introduction Abstract & Introduction Review of Related Work Review of Related Work Proposed Research Methodology Proposed Research Methodology Numerical Case Studies Numerical Case Studies Real-World Simulation Case Studies Real-World Simulation Case Studies Conclusion Conclusion References References V. REAL-WORLD SIMULATION CASE STUDIES An assembly operation from an actual auto-body assembly process is used as a real-world case study. Fig. 5 describes a car’s floor pan, which is the assembled product from this process. The assembled product consists of four parts, including the right bracket, left bracket, right floor pan, and left floor pan. Fig. 6 shows the process assembly procedure consisting of three stations. During the assembly process, the parts are held by fixtures, which are the KCCs in this process [7]. KPCs are measured from four points, namely, M1, M2, M3, and M4, respectively, as shown in Fig. 5. Every part has a designated location for measuring the KPCs. For instance, part 1 has M1, part 2 has M2, part 3 has M3, and part 4 has M4. These measurements can be taken at each station once the relevant part has been assembled in the preceding stations. For example, M3 on part 3 cannot be measured in station 1 because part 3 has not yet been assembled at station 1 [7]. In the designated location, KPCs are measured in three directions (X, Y, and Z). In this assembly process, there exists a total of 33 KCCs, which are dimensional errors of fixture locators [8]. The fault pattern matrix Φ is established based on the literature [7], [11], [47] and provided in Appendix F. Since the number of measurements (12) is less than that of KCCs (33), it causes an underdetermined system in the fault quality linear model. Therefore, sparse estimation is required to identify process faults. In this assembly process, two lists of correlated KCCs exist; the rest are assumed to be independent [8]. The first list comprises six KCCs, including KCC8, KCC9, KCC10, KCC11, KCC12, and KCC13. The second list is composed of KCC31, KCC32, and KCC33. The correlation structures of the two groups are described (for simplification, the lower triangular terms are removed) as follows [8]: To provide nonstationary process faults along the KPCs samples collected over time, two groups are provided. In the first group, the first correlated list is provided as process faults. For the process faults of the second group, all the correlated lists and one independent KCCs are included. Therefore, the case study represents the situation when the process faults evolve over time since the variation of certain KCCs will be propagated to other KCCs if the process faults are not mitigated immediately during the process. 50 KPCs samples are generated from each group. The variances of process faults, non-process faults, and noise of KPCs are determined to be the same value as in Section IV. In addition, performance evaluation measures and benchmark methods used in Section IV are still utilized in Section V. Table III shows the performance comparison in AUC and NMSE by varying the correlation coefficients. For convenience, the correlation coefficients k1 and k2 are equal and are selected from {0.1, 0.3, 0.6, 0.9, 0.95} in the case studies. Specifically, the AUC of the proposed method is close to 1.0 at every correlations levels, representing the perfect classification between the process faults and non-process faults in terms of estimated variance. The effectiveness of the proposed method is significant in NMSE when a high correlation exists. Specifically, the NMSE of the proposed method is less than 10% of that of all the benchmark methods when the correlation coefficient is 0.9 and 0.95. To demonstrate the generalizability of the proposed method, the correlated KCCs are randomly selected in further case studies. Assuming there exist two correlated lists with the size of three, respectively. Therefore, six KCCs are randomly selected from 33 KCCs for two correlated lists in each trial. As in the previous study, one correlated list is provided as process faults in the first group, while two correlated lists and two independent KCCs are used as process faults in the remaining second group. Fig. 7 shows the performances of all the methods in AUC and NMSE results in ten different spatial correlations (i.e., k1 = k2). From Fig. 7 (a), it is prominent that the proposed method successfully differentiates between process faults and non-process faults. Specifically, the AUC of the proposed method is nearly 1.0, while those of most benchmark methods are below 0.9 in the highly correlated case studies. In addition, Fig. 7 (b) represents that the proposed method provides valuable information to the practitioners to determine when to stop the operations to maintain the process when a high correlation exists between KCCs. All the benchmark methods illustrate similar trends compared to Section IV since the methods cannot consider both the spatial correlation of KCCs and the nonstationary process faults.

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