Row 66317

Row ID: 66317 | Dataset Entry | Axioma AXP Content Repository

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As far as I understand, what's claimed in the section is that the variance that's left \*after accounting for posterior variance\* is underestimated by FITC. Apparently it has a degree of freedom in estimating the variance that the other method doesn't have (namely the heteroscedastic noise term), which it uses instead:

>By placing the inducing inputs near training data that happen to lie near the mean, the heteroscedastic noise term is locally shrunk, resulting in a reduced complexity penalty. Data points both far from the mean and far from inducing inputs do not incur a data fit penalty, as the heteroscedastic noise term has increased around these points. This mechanism removes the need for the homoscedastic noise to explain deviations from the mean, such that σ2 n can be turned down to reduce the complexity penalty further.

FieldValue
text As far as I understand, what's claimed in the section is that the variance that's left \*after accounting for posterior variance\* is underestimated by FITC. Apparently it has a degree of freedom in estimating the variance that the other method doesn't have (namely the heteroscedastic noise term), which it uses instead: >By placing the inducing inputs near training data that happen to lie near the mean, the heteroscedastic noise term is locally shrunk, resulting in a reduced complexity penalty.…
label r/machinelearning
dataType comment
communityName r/MachineLearning
datetime 2024-05-23
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url_encoded Z0FBQUFBQm5Lak90S3BLYnhJQjczczN5Z0VnOG5qcm4zZTktOEdqdGpmQWd0U1JoeDNYbE9pZEdjTlFvU3kwQ0lRUnVWUTJoeFZLYUJYcXZldWxIUGhSaWk5Vll5S29DNmhrdGxVMVJTd2t1RlBzSXhPN3RWSWVOS3FCMkdwbGU4S1ZPWmUxcG1QcDdIUTliUmJUTG9nSFRfZTZOWmo0aWxpZ1Z1YjlkMGxsWnhhejN3SjhaLURfR3dSQWpnWC01QnhiejJjWGl3VTRqMGpQSGU1a3JjSzdtM2FPZ1BhYy13OUFOdXdYd0J5aU9sYWNTd2JEWDFfUT0=

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{
  "text": "As far as I understand, what's claimed in the section is that the variance that's left \\*after accounting for posterior variance\\* is underestimated by FITC. Apparently it has a degree of freedom in estimating the variance that the other method doesn't have (namely the heteroscedastic noise term), which it uses instead:\n\n>By placing the inducing inputs near training data that happen to lie near the mean, the heteroscedastic noise term is locally shrunk, resulting in a reduced complexity penalty. Data points both far from the mean and far from inducing inputs do not incur a data fit penalty, as the heteroscedastic noise term has increased around these points. This mechanism removes the need for the homoscedastic noise to explain deviations from the mean, such that σ2 n can be turned down to reduce the complexity penalty further.",
  "label": "r/machinelearning",
  "dataType": "comment",
  "communityName": "r/MachineLearning",
  "datetime": "2024-05-23",
  "username_encoded": "Z0FBQUFBQm5Lak1jd1ZCOVh3aU04QlgtajFpQzZxaGtfdXZXaWdnX21McGU3bHZsSS1rM2Q4NlpWNUpreGpURkxNS2tmUF9oMjdZYVNWWW9BUjJTWlZlVFdIUURwNHVaMFE9PQ==",
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}
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