RBF Kernel
~12 mincode completion
Implement rbf_kernel(x1, x2, gamma) that returns the RBF kernel value between two vectors.
Examples
Identical points: K = 1.0
- Input
- rbf_kernel([1, 2], [1, 2], 0.5)
- Output
- 1
Unit distance, gamma=1: K = e^-1 ≈ 0.3679
- Input
- rbf_kernel([0, 0], [1, 0], 1)
- Output
- 0.36788
Larger gamma: faster decay
- Input
- rbf_kernel([0, 0], [1, 0], 2)
- Output
- 0.13534
Hints
Hint 1
applies elementwise, so negate the whole array and exponentiate it in one go.
Hint 2
Reach for squared rather than euclidean.
Requirements
x1: First vectorx2: Second vectorgamma: Kernel width parameter (gamma > 0)Return Scalar kernel value in (0, 1].
Constraints
Allowed library: NumPy only
Time limit: 200 ms, Memory: 64 MB
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Where this shows up
~12 min
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Python
import numpy as np
def rbf_kernel(x1: np.ndarray, x2: np.ndarray, gamma: float) -> float:
"""
Compute the RBF (Gaussian) kernel between two vectors.
Args:
x1: First vector
x2: Second vector
gamma: Kernel width parameter (gamma > 0)
Returns:
Scalar kernel value in (0, 1].
"""
# YOUR CODE HERE
pass