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better notation
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conjectures
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Your diagnosis about this being orange's heavier tails is correct. The model seems to be behaving properly under the circumstances.

If you simply disagree with the classification of $x < -5$ instances as blue, then flip them to orange.

However, there are several reasons this might be disadvised. First would be if your application is density estimation or prediction. I.e. things which involve a factor like $g(x)=\sum_c g(y | x, c) f(c | x)$$g(y|x)=\sum_c g(y | x, c) f(c | x)$. In which case just let the model do its thing.

The second is that such classifications could reflect a true data generating process. For instance, if the data were log returns on stocks, but there was a missing variable representing how many time steps had elapsed. You'd probably expect returns over longer periods to dominate in both tails. Then, if you classified this data, it would be reasonable for GMM to show a blue cluster (mapping to short timespans) and an orange cluster (mapping to long time spans). This is a matter of domain intuition.

Your diagnosis about this being orange's heavier tails is correct. The model seems to be behaving properly under the circumstances.

If you simply disagree with the classification of $x < -5$ instances as blue, then flip them to orange.

However, there are several reasons this might be disadvised. First would be if your application is density estimation or prediction. I.e. things which involve a factor like $g(x)=\sum_c g(y | x, c) f(c | x)$. In which case just let the model do its thing.

The second is that such classifications could reflect a true data generating process. For instance, if the data were log returns on stocks, but there was a missing variable representing how many time steps had elapsed. You'd probably expect returns over longer periods to dominate in both tails. Then, if you classified this data, it would be reasonable for GMM to show a blue cluster (mapping to short timespans) and an orange cluster (mapping to long time spans). This is a matter of domain intuition.

Your diagnosis about this being orange's heavier tails is correct. The model seems to be behaving properly under the circumstances.

If you simply disagree with the classification of $x < -5$ instances as blue, then flip them to orange.

However, there are several reasons this might be disadvised. First would be if your application is density estimation or prediction. I.e. things which involve a factor like $g(y|x)=\sum_c g(y | x, c) f(c | x)$. In which case just let the model do its thing.

The second is that such classifications could reflect a true data generating process. For instance, if the data were log returns on stocks, but there was a missing variable representing how many time steps had elapsed. You'd probably expect returns over longer periods to dominate in both tails. Then, if you classified this data, it would be reasonable for GMM to show a blue cluster (mapping to short timespans) and an orange cluster (mapping to long time spans). This is a matter of domain intuition.

Source Link
conjectures
  • 4.3k
  • 25
  • 38

Your diagnosis about this being orange's heavier tails is correct. The model seems to be behaving properly under the circumstances.

If you simply disagree with the classification of $x < -5$ instances as blue, then flip them to orange.

However, there are several reasons this might be disadvised. First would be if your application is density estimation or prediction. I.e. things which involve a factor like $g(x)=\sum_c g(y | x, c) f(c | x)$. In which case just let the model do its thing.

The second is that such classifications could reflect a true data generating process. For instance, if the data were log returns on stocks, but there was a missing variable representing how many time steps had elapsed. You'd probably expect returns over longer periods to dominate in both tails. Then, if you classified this data, it would be reasonable for GMM to show a blue cluster (mapping to short timespans) and an orange cluster (mapping to long time spans). This is a matter of domain intuition.