3 Machine Learning questions.

Question

Hello,

I have 3 machine learning questions:

(1)

I was taught in Microsoft Azure AI Fundamentals that something like the regression algorithm tries to find f(x) = y.

I'm wanting to know is the function always represented this simply?

What are some example functions, if it is ok to ask? more complex ones welcome.

(2)

I understand ŷ is the predicted value(s).

But are predicted values actual values?  Like "real" / "truthful" values?

I hope this makes some sense..

(3)

What is a sigmoid function?

Thank you in advance,

Albert Yu

Answer 1

(1) In Azure AI Fundamentals, regression is introduced as learning a function that maps inputs to a numeric output, often written abstractly as f(x) = y. That notation is just a shorthand; the actual learned function can take many forms and can use many input variables.

Examples of regression functions:

• Simple linear regression (one feature):
  • y = w₀ + w₁x
• Multiple linear regression (many features):
  • y = w₀ + w₁x₁ + w₂x₂ + … + wₙxₙ
• Polynomial regression (non‑linear in x, but still linear in the parameters):
  • y = w₀ + w₁x + w₂x² + w₃x³
• More complex models (still “f(x) = y” in abstract form):
  • y = f(x) where f is a decision tree, a random forest, a neural network, etc. The internal form is more complex, but conceptually it is still “a function that maps inputs to a numeric prediction”.

So “f(x) = y” is a conceptual way to say “the model implements some function from inputs to outputs”; the actual formula can be simple or very complex.

(2) ŷ (y-hat) is the model’s predicted value, not the ground‑truth value.

• y: the true/actual value from the labeled dataset (for example, the real house price).
• ŷ: the value the model predicts for that same input.

Predicted values are estimates of the true values. They are “real numbers” in the mathematical sense, but they are not guaranteed to be correct; the difference between y and ŷ is the prediction error. Regression training and evaluation focus on minimizing and measuring this error (for example, via least squares or other error metrics).

(3) A sigmoid function is a smooth, S‑shaped mathematical function that maps any real number to a value between 0 and 1. A common sigmoid used in machine learning is the logistic function:

σ(z) = 1 / (1 + e^(−z))

Key properties:

• Input z can be any real number (−∞ to +∞).
• Output σ(z) is always between 0 and 1.
• The curve is S‑shaped and differentiable, which makes it useful in models like logistic regression and neural networks (for example, as an activation function or to convert a score into something interpretable as a probability).

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References:

• Train and understand regression models in machine learning
• Linear Regression component
• Microsoft Linear Regression Algorithm
• What is automated machine learning (AutoML)?
• Train and evaluate regression models
• Introduction to regression models by using R and tidymodels
• Deep learning vs. machine learning in Azure Machine Learning
• Machine Learning Algorithm Cheat Sheet for Azure Machine Learning designer