Improve the following code:def estimate_variance(xs: np.ndarray, ys: np.ndarray, affine: np.ndarray, translation: np.ndarray, responsibility: np.ndarray) -> float: """ Estimate the variance of GMM. For simplification, we assume all the Gaussian distributions share the same variance, and each feature dimension is independent, so the variance can be represented as a scalar. :param xs: a set of points with size (N, D), N is the number of samples, D is the dimension of points :param ys: a set of points with size (M, D), M is the number of samples, D is the dimension of points :param affine: an affine matrix with size (D, D) :param translation: a translation vector with size (1, D) :param responsibility: the responsibility matrix with size (N, M) :return: the variance of each Gaussian distribution, a float """ # TODO: change the code below and compute the variance of each Gaussian return
时间: 2024-01-25 07:04:30 浏览: 38
One possible improvement could be to use vectorized operations instead of loops to improve performance. Here's an updated implementation:
```python
def estimate_variance(xs: np.ndarray, ys: np.ndarray, affine: np.ndarray,
translation: np.ndarray, responsibility: np.ndarray) -> float:
"""
Estimate the variance of GMM.
For simplification, we assume all the Gaussian distributions share the same variance,
and each feature dimension is independent, so the variance can be represented as a scalar.
:param xs: a set of points with size (N, D), N is the number of samples, D is the dimension of points
:param ys: a set of points with size (M, D), M is the number of samples, D is the dimension of points
:param affine: an affine matrix with size (D, D)
:param translation: a translation vector with size (1, D)
:param responsibility: the responsibility matrix with size (N, M)
:return: the variance of each Gaussian distribution, a float
"""
# Transform xs and ys using affine and translation
xs_transformed = xs @ affine.T + translation
ys_transformed = ys @ affine.T + translation
# Compute the difference between xs and ys for each pair of samples
diff = xs_transformed[:, None, :] - ys_transformed[None, :, :]
# Compute the squared Euclidean distance for each pair of samples
dist_sq = np.sum(diff**2, axis=2)
# Compute the weighted sum of squared distances using the responsibility matrix
weighted_dist_sq = np.sum(responsibility * dist_sq)
# Compute the total weight of responsibility matrix
total_weight = np.sum(responsibility)
# Compute the variance as the weighted average of squared distances
variance = weighted_dist_sq / (total_weight * xs.shape[1])
return variance
```
This implementation uses matrix multiplication and broadcasting to perform the affine transformation and compute the pairwise distances between samples, which should be more efficient than using loops. It also computes the variance directly from the weighted sum of squared distances, without needing to compute the sum of squared differences and then dividing by the number of dimensions.
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