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Foundations of Artificial Intelligence & Machine Learning

Licence
OPEN CC-BY-4.0
Authors
Nidhi Sharma, Honey Singh, Ajay Sharma, Deepak Dagar
Published
2026-07-28 · Zenodo
Language
eng
Length
37166 words
Type
narrative text
Open ↗ Download Open original ↗
Functions in Machine Learning

Machine Learning models are built using mathematical functions that connect inputs and outputs. For example:

  • input data enters the model

  • mathematical operations process the information

  • outputs are generated as predictions A simple function may represent:

  • house price prediction

  • examination score estimation

  • sales forecasting Machine Learning algorithms continuously adjust these functions during training to improve prediction accuracy. Error Functions An important concept in Machine Learning is the error function, also called the loss function. The loss function measures how far predictions differ from actual outcomes. For example:

  • if the model predicts 90

  • but the actual value is 70 the loss function calculates the prediction error.

The objective of the machine learning model is to reduce this error as much as possible. Optimization in Machine Learning Optimization refers to the process of improving model performance by minimizing errors. Most machine learning algorithms involve large numbers of parameters known as weights and biases. These parameters influence prediction outcomes. Optimization algorithms use calculus to determine:

  • which direction reduces error

  • how much adjustment is required

  • how quickly learning should occur Without optimization, machine learning systems would not improve over time. Gradient Descent Gradient Descent is one of the most important optimization algorithms used in Machine Learning and Deep Learning. It is used to minimize the loss function by gradually adjusting model parameters. The basic idea behind Gradient Descent is simple:

  • calculate the error

  • determine the slope of the error function

  • move parameters in the direction that reduces error This process repeats many times until the model reaches optimal performance.

In practical machine learning systems, Gradient Descent helps models learn from data by improving weights step by step. Modern neural networks may perform millions of gradient calculations during training. Learning Rate The learning rate controls how large each optimization step should be during training. If the learning rate is:

  • too high, the model may become unstable
  • too low, training may become very slow Selecting an appropriate learning rate is important for efficient model training. Machine Learning engineers often experiment with learning rates to achieve better convergence and performance. Partial Derivatives Machine Learning models often involve multiple variables and parameters. In such situations, partial derivatives are used. Partial derivatives measure how one variable changes while keeping other variables constant. Deep learning systems contain thousands or even millions of parameters. Partial derivatives help calculate how each parameter contributes to prediction errors. This process is essential for neural network training.