Deep Learning 08 :Mean Square Error (MSE)

 

🎯 What It Is

Mean Squared Error (MSE) is a way to measure how wrong a model’s predictions are.
It tells you how far off your predictions are from the actual (true) values.

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🧮 Formula:

$$\text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y_i})^2$$

Where:

• $y_i$ = actual (true) value

• $\hat{y_i}$ = predicted value

• $n$ = number of samples

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⚙️ Step-by-Step:

1. Find the error for each prediction: $(y_i - \hat{y_i})$

2. Square the error → makes all values positive and punishes big errors more

3. Average them → gives the mean squared error

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📊 Example:

Actual (y)	Predicted (ŷ)	Error	Squared Error
4	5	-1	1
2	3	-1	1
6	5	1	1
3	2	1	1

$$\text{MSE} = \frac{1+1+1+1}{4} = 1$$

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💡 Why It’s Used

• It gives a single number that shows overall prediction quality.

• Smaller MSE → better model

• Commonly used in regression tasks and training neural networks (as a loss function).

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🔥 Intuition:

MSE measures the average squared distance between your predictions and the truth.
The closer to 0, the better your model fits the data.

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Would you like me to explain how MSE is used to train neural networks (via gradient descent)?

Eample : You’re trying to guess someone’s height 🎯

If they say they’re 160 cm, and you guess 170 cm, you’re 10 cm off.

Now let’s see how Mean Squared Error (MSE) works — explained like you’re 10 👇

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🍎 Step-by-Step:

1. You make several guesses.
   Example:

   True height	Your guess	Error
   160	170	+10
   150	145	-5
   180	190	+10

2. You take the difference (error) for each guess.

3. You square each error (so negative numbers don’t cancel out):
   $10^2 = 100$, $(-5)^2 = 25$, $10^2 = 100$

4. You average them all:

   $$(100 + 25 + 100) / 3 = 75$$

That’s your Mean Squared Error = 75

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🧠 What It Means:

• If MSE = big number → your guesses are way off ❌

• If MSE = small number → your guesses are close ✅

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💬 In short:

MSE tells you how wrong your guesses are —
it’s like checking how far your dart hits are from the bullseye 🎯,
but you square the distance so big misses hurt extra!