I'm trying to understand how does the KernelDensity class in scikit-learn work. Consider the following two cases which build a kernel from two different arrays (a). I'm wondering why the result of scoring on the array b in both cases is the same? Shouldn't a kernel from 10 same points be different from that from 2 points? The one from the 10 points should indicate more density. So, why the final scoring result is the same in both cases?

*) case A:

a = np.array([[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]])

kde = KernelDensity(bandwidth=0.1)

kde.fit(a)

b = np.array([[1]])

log_dens = kde.score_samples(b)

print('Probability is: {}'.format(np.exp(log_dens)))

Probability is: [3.9894228]

*) case B:

a = np.array([[1],[1]])

kde = KernelDensity(bandwidth=0.1)

kde.fit(a)

b = np.array([[1]])

log_dens = kde.score_samples(b)

print('Probability is: {}'.format(np.exp(log_dens)))

Probability is: [3.9894228]

I'm trying to understand how does the KernelDensity class in scikit-learn work. Consider the following two cases which build a kernel from two different arrays (a). I'm wondering why the result of scoring on the array b in both cases is the same? Shouldn't a kernel from 10 same points be different from that from 2 points? The one from the 10 points should indicate more density. So, why the final scoring result is the same in both cases?

case A:

a = np.array([[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]])

kde = KernelDensity(bandwidth=0.1)

kde.fit(a)

b = np.array([[1]])

log_dens = kde.score_samples(b)

print('Probability is: {}'.format(np.exp(log_dens)))

Probability is: [3.9894228]

case B:

a = np.array([[1],[1]])

kde = KernelDensity(bandwidth=0.1)

kde.fit(a)

b = np.array([[1]])

log_dens = kde.score_samples(b)

print('Probability is: {}'.format(np.exp(log_dens)))

Probability is: [3.9894228]

I'm trying to understand how does the KernelDensity class in scikit-learn work. Consider the following two cases which build a kernel from two different arrays (a). I'm wondering why the result of scoring on the array b in both cases is the same? Shouldn't a kernel from 10 same points be different from that from 2 points? The one from the 10 points should indicate more density. So, why the final scoring result is the same in both cases?

*) case A:

a = np.array([[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]])

kde = KernelDensity(bandwidth=0.1)

kde.fit(a)

b = np.array([[1]])

log_dens = kde.score_samples(b)

print('Probability is: {}'.format(np.exp(log_dens)))

Probability is: [3.9894228]

*) case B:

a = np.array([[1],[1]])

kde = KernelDensity(bandwidth=0.1)

kde.fit(a)

b = np.array([[1]])

log_dens = kde.score_samples(b)

print('Probability is: {}'.format(np.exp(log_dens)))

Probability is: [3.9894228]

I'm trying to understand how does the KernelDensity class in scikit-learn work. Consider the following two cases which build a kernel from two different arrays (a). I'm wondering why the result of scoring on the array b in both cases is the same? Shouldn't a kernel from 10 same points be different from that from 2 points? The one from the 10 points should indicate more density. So, why the final scoring result is the same in both cases?

*) case A:

a = np.array([[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]])

kde = KernelDensity(bandwidth=0.1)

kde.fit(a)

b = np.array([[1]])

log_dens = kde.score_samples(b)

print('Probability is: {}'.format(np.exp(log_dens)))

Probability is: [3.9894228]

*) case B:

a = np.array([[1],[1]])

kde = KernelDensity(bandwidth=0.1)

kde.fit(a)

b = np.array([[1]])

log_dens = kde.score_samples(b)

print('Probability is: {}'.format(np.exp(log_dens)))

Probability is: [3.9894228]