dorsal/arxiv
View SchemaLocal EGOP for Continuous Index Learning
| Authors | Alex Kokot, Anand Hemmady, Vydhourie Thiyageswaran, Marina Meila |
|---|---|
| Categories | |
| ArXiv ID | 2601.07061vv1 |
| URL | https://arxiv.org/abs/2601.07061 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
We introduce the setting of continuous index learning, in which a function of many variables varies only along a small number of directions at each point. For efficient estimation, it is beneficial for a learning algorithm to adapt, near each point $x$, to the subspace that captures the local variability of the function $f$. We pose this task as kernel adaptation along a manifold with noise, and introduce Local EGOP learning, a recursive algorithm that utilizes the Expected Gradient Outer Product (EGOP) quadratic form as both a metric and inverse-covariance of our target distribution. We prove that Local EGOP learning adapts to the regularity of the function of interest, showing that under a supervised noisy manifold hypothesis, intrinsic dimensional learning rates are achieved for arbitrarily high-dimensional noise. Empirically, we compare our algorithm to the feature learning capabilities of deep learning. Additionally, we demonstrate improved regression quality compared to two-layer neural networks in the continuous single-index setting.
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"abstract": "We introduce the setting of continuous index learning, in which a function of many variables varies only along a small number of directions at each point. For efficient estimation, it is beneficial for a learning algorithm to adapt, near each point $x$, to the subspace that captures the local variability of the function $f$. We pose this task as kernel adaptation along a manifold with noise, and introduce Local EGOP learning, a recursive algorithm that utilizes the Expected Gradient Outer Product (EGOP) quadratic form as both a metric and inverse-covariance of our target distribution. We prove that Local EGOP learning adapts to the regularity of the function of interest, showing that under a supervised noisy manifold hypothesis, intrinsic dimensional learning rates are achieved for arbitrarily high-dimensional noise. Empirically, we compare our algorithm to the feature learning capabilities of deep learning. Additionally, we demonstrate improved regression quality compared to two-layer neural networks in the continuous single-index setting.",
"arxiv_id": "2601.07061",
"authors": [
"Alex Kokot",
"Anand Hemmady",
"Vydhourie Thiyageswaran",
"Marina Meila"
],
"categories": [
"stat.ML",
"cs.LG"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Local EGOP for Continuous Index Learning",
"url": "https://arxiv.org/abs/2601.07061",
"version": "v1"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "49b4b4bc-06f1-4348-a0ad-f587b70511ea",
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"variant": "snapshot-2026-01-17",
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