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46 lines
1.7 KiB
Markdown
46 lines
1.7 KiB
Markdown
# Convert Arbitrary Number To Probability With Sigmoid
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A sigmoid function is a useful function in statistics and machine learning for
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converting a number in the range of positive and negative real numbers into a
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value between 0 and 1. Sigmoid functions can be a bit more diverse than this,
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but this is a good basic definition.
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Wikipedia defines another characteristic of sigmoid functions:
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> A sigmoid function is any mathematical function whose graph has a
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> characteristic S-shaped or sigmoid curve.
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This S-shape is because it is asymptotic at the ends allowing it to cover all
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real numbers in either direction.
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A common sigmoid function and the one used by [PyTorch's `Sigmoid`](https://docs.pytorch.org/docs/2.13/generated/torch.nn.Sigmoid.html)
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is this exponential form -- `σ(x) = 1 / (1 + exp(-x))`.
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Here is what this looks like plotted on a graph:
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This function can be used any time we want to convert an arbitrary number into a
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probability. Large negative numbers will approach 0. Large positive numbers will
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approach 1. Numbers near 0 will settle somewhere in the middle.
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Here are a few examples run through PyTorch's `sigmoid` function:
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```python
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print("σ(-99) => ", torch.sigmoid(torch.tensor(-99.0)))
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print("σ(99) => ", torch.sigmoid(torch.tensor(99.0)))
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print("σ(0.123) => ", torch.sigmoid(torch.tensor(0.123)))
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print("σ(-2) => ", torch.sigmoid(torch.tensor(-2.0)))
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print("σ(1) => ", torch.sigmoid(torch.tensor(1.0)))
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```
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which prints out:
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```
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σ(-99) => tensor(0.)
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σ(99) => tensor(1.)
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σ(0.123) => tensor(0.5307)
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σ(-2) => tensor(0.1192)
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σ(1) => tensor(0.7311)
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```
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