New Ways for Optimizing Gradient Descent

The new era of machine learning and artificial intelligence is the Deep learning era. It not only has immeasurable accuracy but also a huge hunger for data. Employing neural nets, functions with more exceeding complexity can be mapped on given data points.

But there are a few very precise things which make the experience with neural networks more incredible and perceiving.

Xavier Initialization

Let us assume that we have trained a huge neural network. For simplicity, the constant term is zero and the activation function is identity.

#ai #gradient-descent #machine-learning #neural-networks #deep-learning

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New Ways for Optimizing Gradient Descent
Hollie  Ratke

Hollie Ratke

1603753200

ML Optimization pt.1 - Gradient Descent with Python

So far in our journey through the Machine Learning universe, we covered several big topics. We investigated some regression algorithms, classification algorithms and algorithms that can be used for both types of problems (SVM**, **Decision Trees and Random Forest). Apart from that, we dipped our toes in unsupervised learning, saw how we can use this type of learning for clustering and learned about several clustering techniques.

We also talked about how to quantify machine learning model performance and how to improve it with regularization. In all these articles, we used Python for “from the scratch” implementations and libraries like TensorFlowPytorch and SciKit Learn. The word optimization popped out more than once in these articles, so in this and next article, we focus on optimization techniques which are an important part of the machine learning process.

In general, every machine learning algorithm is composed of three integral parts:

  1. loss function.
  2. Optimization criteria based on the loss function, like a cost function.
  3. Optimization technique – this process leverages training data to find a solution for optimization criteria (cost function).

As you were able to see in previous articles, some algorithms were created intuitively and didn’t have optimization criteria in mind. In fact, mathematical explanations of why and how these algorithms work were done later. Some of these algorithms are Decision Trees and kNN. Other algorithms, which were developed later had this thing in mind beforehand. SVMis one example.

During the training, we change the parameters of our machine learning model to try and minimize the loss function. However, the question of how do you change those parameters arises. Also, by how much should we change them during training and when. To answer all these questions we use optimizers. They put all different parts of the machine learning algorithm together. So far we mentioned Gradient Decent as an optimization technique, but we haven’t explored it in more detail. In this article, we focus on that and we cover the grandfather of all optimization techniques and its variation. Note that these techniques are not machine learning algorithms. They are solvers of minimization problems in which the function to minimize has a gradient in most points of its domain.

Dataset & Prerequisites

Data that we use in this article is the famous Boston Housing Dataset . This dataset is composed 14 features and contains information collected by the U.S Census Service concerning housing in the area of Boston Mass. It is a small dataset  with only 506 samples.

For the purpose of this article, make sure that you have installed the following _Python _libraries:

  • **NumPy **– Follow this guide if you need help with installation.
  • **SciKit Learn **– Follow this guide if you need help with installation.
  • Pandas – Follow this guide if you need help with installation.

Once installed make sure that you have imported all the necessary modules that are used in this tutorial.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import SGDRegressor

Apart from that, it would be good to be at least familiar with the basics of linear algebracalculus and probability.

Why do we use Optimizers?

Note that we also use simple Linear Regression in all examples. Due to the fact that we explore optimizationtechniques, we picked the easiest machine learning algorithm. You can see more details about Linear regression here. As a quick reminder the formula for linear regression goes like this:

where w and b are parameters of the machine learning algorithm. The entire point of the training process is to set the correct values to the w and b, so we get the desired output from the machine learning model. This means that we are trying to make the value of our error vector as small as possible, i.e. to find a global minimum of the cost function.

One way of solving this problem is to use calculus. We could compute derivatives and then use them to find places where is an extrema of the cost function. However, the cost function is not a function of one or a few variables; it is a function of all parameters of a machine learning algorithm, so these calculations will quickly grow into a monster. That is why we use these optimizers.

#ai #machine learning #python #artificaial inteligance #artificial intelligence #batch gradient descent #data science #datascience #deep learning #from scratch #gradient descent #machine learning #machine learning optimizers #ml optimization #optimizers #scikit learn #software #software craft #software craftsmanship #software development #stochastic gradient descent

August  Larson

August Larson

1625043360

Understanding Gradient Descent with Python

So far in our journey through the Machine Learning universe, we covered several big topics. We investigated some regression algorithms, classification algorithms and algorithms that can be used for both types of problems (SVM, Decision Trees and Random Forest). Apart from that, we dipped our toes in unsupervised learning, saw how we can use this type of learning for clustering and learned about several clustering techniques.

We also talked about how to quantify machine learning model performance and how to improve it with regularization. In all these articles, we used Python for “from the scratch” implementations and libraries like TensorFlowPytorch and SciKit Learn. The word optimization popped out more than once in these articles, so in this article, we focus on optimization techniques which are an important part of the machine learning process.

#ai #machine learning #python #artificaial inteligance #artificial intelligence #batch gradient descent #data science #datascience #deep learning #from scratch #gradient descent #machine learning optimizers #ml optimization #optimizers #scikit learn #software #software craft #software craftsmanship #software development

New Ways for Optimizing Gradient Descent

The new era of machine learning and artificial intelligence is the Deep learning era. It not only has immeasurable accuracy but also a huge hunger for data. Employing neural nets, functions with more exceeding complexity can be mapped on given data points.

But there are a few very precise things which make the experience with neural networks more incredible and perceiving.

Xavier Initialization

Let us assume that we have trained a huge neural network. For simplicity, the constant term is zero and the activation function is identity.

#ai #gradient-descent #machine-learning #neural-networks #deep-learning

Agnes  Sauer

Agnes Sauer

1597385280

New Ways for Optimizing Gradient Descent

The new era of machine learning and artificial intelligence is the Deep learning era. It not only has immeasurable accuracy but also a huge hunger for data. Employing neural nets, functions with more exceeding complexity can be mapped on given data points.

But there are a few very precise things which make the experience with neural networks more incredible and perceiving.

Xavier Initialization

Let us assume that we have trained a huge neural network. For simplicity, the constant term is zero and the activation function is identity.

For the given condition, we can have the following equations of gradient descent and expression of the target variable in terms of weights of all layer and input a[0].

For ease of understanding, let us consider all weights to be equal, i.e.

Here we have considered the last weight different as it will give the output value and in case of binary classification it may be a sigmoid function or ReLu function.

When we replace all the weights in the expression of the target variable, we obtain a new expression for y, the expression of prediction of the target variable.

Let us consider two different situations for the weights.

Image for post

#ai #gradient-descent #machine-learning #neural-networks #deep-learning #deep learning

Justen  Hintz

Justen Hintz

1663559281

To-do List App with HTML, CSS and JavaScript

Learn how to create a to-do list app with local storage using HTML, CSS and JavaScript. Build a Todo list application with HTML, CSS and JavaScript. Learn the basics to JavaScript along with some more advanced features such as LocalStorage for saving data to the browser.

HTML:

<!DOCTYPE html>
<html lang="en">
  <head>
    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
    <title>To Do List With Local Storage</title>
    <!-- Font Awesome Icons -->
    <link
      rel="stylesheet"
      href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.2.0/css/all.min.css"
    />
    <!-- Google Fonts -->
    <link
      href="https://fonts.googleapis.com/css2?family=Poppins:wght@400;500&display=swap"
      rel="stylesheet"
    />
    <!-- Stylesheet -->
    <link rel="stylesheet" href="style.css" />
  </head>
  <body>
    <div class="container">
      <div id="new-task">
        <input type="text" placeholder="Enter The Task Here..." />
        <button id="push">Add</button>
      </div>
      <div id="tasks"></div>
    </div>
    <!-- Script -->
    <script src="script.js"></script>
  </body>
</html>

CSS:

* {
  padding: 0;
  margin: 0;
  box-sizing: border-box;
}
body {
  background-color: #0b87ff;
}
.container {
  width: 90%;
  max-width: 34em;
  position: absolute;
  transform: translate(-50%, -50%);
  top: 50%;
  left: 50%;
}
#new-task {
  position: relative;
  background-color: #ffffff;
  padding: 1.8em 1.25em;
  border-radius: 0.3em;
  box-shadow: 0 1.25em 1.8em rgba(1, 24, 48, 0.15);
  display: grid;
  grid-template-columns: 9fr 3fr;
  gap: 1em;
}
#new-task input {
  font-family: "Poppins", sans-serif;
  font-size: 1em;
  border: none;
  border-bottom: 2px solid #d1d3d4;
  padding: 0.8em 0.5em;
  color: #111111;
  font-weight: 500;
}
#new-task input:focus {
  outline: none;
  border-color: #0b87ff;
}
#new-task button {
  font-family: "Poppins", sans-serif;
  font-weight: 500;
  font-size: 1em;
  background-color: #0b87ff;
  color: #ffffff;
  outline: none;
  border: none;
  border-radius: 0.3em;
  cursor: pointer;
}
#tasks {
  background-color: #ffffff;
  position: relative;
  padding: 1.8em 1.25em;
  margin-top: 3.8em;
  width: 100%;
  box-shadow: 0 1.25em 1.8em rgba(1, 24, 48, 0.15);
  border-radius: 0.6em;
}
.task {
  background-color: #ffffff;
  padding: 0.3em 0.6em;
  margin-top: 0.6em;
  display: flex;
  align-items: center;
  border-bottom: 2px solid #d1d3d4;
  cursor: pointer;
}
.task span {
  font-family: "Poppins", sans-serif;
  font-size: 0.9em;
  font-weight: 400;
}
.task button {
  color: #ffffff;
  padding: 0.8em 0;
  width: 2.8em;
  border-radius: 0.3em;
  border: none;
  outline: none;
  cursor: pointer;
}
.delete {
  background-color: #fb3b3b;
}
.edit {
  background-color: #0b87ff;
  margin-left: auto;
  margin-right: 3em;
}
.completed {
  text-decoration: line-through;
}

Javascript:

//Initial References
const newTaskInput = document.querySelector("#new-task input");
const tasksDiv = document.querySelector("#tasks");
let deleteTasks, editTasks, tasks;
let updateNote = "";
let count;

//Function on window load
window.onload = () => {
  updateNote = "";
  count = Object.keys(localStorage).length;
  displayTasks();
};

//Function to Display The Tasks
const displayTasks = () => {
  if (Object.keys(localStorage).length > 0) {
    tasksDiv.style.display = "inline-block";
  } else {
    tasksDiv.style.display = "none";
  }

  //Clear the tasks
  tasksDiv.innerHTML = "";

  //Fetch All The Keys in local storage
  let tasks = Object.keys(localStorage);
  tasks = tasks.sort();

  for (let key of tasks) {
    let classValue = "";

    //Get all values
    let value = localStorage.getItem(key);
    let taskInnerDiv = document.createElement("div");
    taskInnerDiv.classList.add("task");
    taskInnerDiv.setAttribute("id", key);
    taskInnerDiv.innerHTML = `<span id="taskname">${key.split("_")[1]}</span>`;
    //localstorage would store boolean as string so we parse it to boolean back
    let editButton = document.createElement("button");
    editButton.classList.add("edit");
    editButton.innerHTML = `<i class="fa-solid fa-pen-to-square"></i>`;
    if (!JSON.parse(value)) {
      editButton.style.visibility = "visible";
    } else {
      editButton.style.visibility = "hidden";
      taskInnerDiv.classList.add("completed");
    }
    taskInnerDiv.appendChild(editButton);
    taskInnerDiv.innerHTML += `<button class="delete"><i class="fa-solid fa-trash"></i></button>`;
    tasksDiv.appendChild(taskInnerDiv);
  }

  //tasks completed
  tasks = document.querySelectorAll(".task");
  tasks.forEach((element, index) => {
    element.onclick = () => {
      //local storage update
      if (element.classList.contains("completed")) {
        updateStorage(element.id.split("_")[0], element.innerText, false);
      } else {
        updateStorage(element.id.split("_")[0], element.innerText, true);
      }
    };
  });

  //Edit Tasks
  editTasks = document.getElementsByClassName("edit");
  Array.from(editTasks).forEach((element, index) => {
    element.addEventListener("click", (e) => {
      //Stop propogation to outer elements (if removed when we click delete eventually rhw click will move to parent)
      e.stopPropagation();
      //disable other edit buttons when one task is being edited
      disableButtons(true);
      //update input value and remove div
      let parent = element.parentElement;
      newTaskInput.value = parent.querySelector("#taskname").innerText;
      //set updateNote to the task that is being edited
      updateNote = parent.id;
      //remove task
      parent.remove();
    });
  });

  //Delete Tasks
  deleteTasks = document.getElementsByClassName("delete");
  Array.from(deleteTasks).forEach((element, index) => {
    element.addEventListener("click", (e) => {
      e.stopPropagation();
      //Delete from local storage and remove div
      let parent = element.parentElement;
      removeTask(parent.id);
      parent.remove();
      count -= 1;
    });
  });
};

//Disable Edit Button
const disableButtons = (bool) => {
  let editButtons = document.getElementsByClassName("edit");
  Array.from(editButtons).forEach((element) => {
    element.disabled = bool;
  });
};

//Remove Task from local storage
const removeTask = (taskValue) => {
  localStorage.removeItem(taskValue);
  displayTasks();
};

//Add tasks to local storage
const updateStorage = (index, taskValue, completed) => {
  localStorage.setItem(`${index}_${taskValue}`, completed);
  displayTasks();
};

//Function To Add New Task
document.querySelector("#push").addEventListener("click", () => {
  //Enable the edit button
  disableButtons(false);
  if (newTaskInput.value.length == 0) {
    alert("Please Enter A Task");
  } else {
    //Store locally and display from local storage
    if (updateNote == "") {
      //new task
      updateStorage(count, newTaskInput.value, false);
    } else {
      //update task
      let existingCount = updateNote.split("_")[0];
      removeTask(updateNote);
      updateStorage(existingCount, newTaskInput.value, false);
      updateNote = "";
    }
    count += 1;
    newTaskInput.value = "";
  }
});

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#html #css #javascript