An Analysis of Active Learning with Uniform Feature Noise

Aaditya Ramdas, Barnabas Poczos, Aarti Singh, Larry Wasserman
Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, PMLR 33:805-813, 2014.

Abstract

In active learning, the user sequentially chooses values for feature X and an oracle returns the corresponding label Y. In this paper, we consider the effect of feature noise in active learning, which could arise either because X itself is being measured, or it is corrupted in transmission to the oracle, or the oracle returns the label of a noisy version of the query point. In statistics, feature noise is known as“errors in variables” and has been studied extensively in non-active settings. However, the effect of feature noise in active learning has not been studied before. We consider the well-known Berkson errors-in-variables model with additive uniform noise of width σ. Our simple but revealing setting is that of one-dimensional binary classification setting where the goal is to learn a threshold (point where the probability of a + label crosses half). We deal with regression functions that are antisymmetric in a region of size σaround the threshold and also satisfy Tsybakov’s margin condition around the threshold. We prove minimax lower and upper bounds which demonstrate that when σis smaller than the minimiax active/passive noiseless error derived in Castro & Nowak (2007), then noise has no effect on the rates and one achieves the same noiseless rates. For larger σ, the \textitunflattening of the regression function on convolution with uniform noise, along with its local antisymmetry around the threshold, together yield a behaviour where noise \textitappears to be beneficial. Our key result is that active learning can buy significant improvement over a passive strategy even in the presence of feature noise.

Cite this Paper

BibTeX
@InProceedings{pmlr-v33-ramdas14, title = {{An Analysis of Active Learning with Uniform Feature Noise}}, author = {Ramdas, Aaditya and Poczos, Barnabas and Singh, Aarti and Wasserman, Larry}, booktitle = {Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics}, pages = {805--813}, year = {2014}, editor = {Kaski, Samuel and Corander, Jukka}, volume = {33}, series = {Proceedings of Machine Learning Research}, address = {Reykjavik, Iceland}, month = {22--25 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v33/ramdas14.pdf}, url = {https://proceedings.mlr.press/v33/ramdas14.html}, abstract = {In active learning, the user sequentially chooses values for feature X and an oracle returns the corresponding label Y. In this paper, we consider the effect of feature noise in active learning, which could arise either because X itself is being measured, or it is corrupted in transmission to the oracle, or the oracle returns the label of a noisy version of the query point. In statistics, feature noise is known as“errors in variables” and has been studied extensively in non-active settings. However, the effect of feature noise in active learning has not been studied before. We consider the well-known Berkson errors-in-variables model with additive uniform noise of width σ. Our simple but revealing setting is that of one-dimensional binary classification setting where the goal is to learn a threshold (point where the probability of a + label crosses half). We deal with regression functions that are antisymmetric in a region of size σaround the threshold and also satisfy Tsybakov’s margin condition around the threshold. We prove minimax lower and upper bounds which demonstrate that when σis smaller than the minimiax active/passive noiseless error derived in Castro & Nowak (2007), then noise has no effect on the rates and one achieves the same noiseless rates. For larger σ, the \textitunflattening of the regression function on convolution with uniform noise, along with its local antisymmetry around the threshold, together yield a behaviour where noise \textitappears to be beneficial. Our key result is that active learning can buy significant improvement over a passive strategy even in the presence of feature noise.} }
Endnote
%0 Conference Paper %T An Analysis of Active Learning with Uniform Feature Noise %A Aaditya Ramdas %A Barnabas Poczos %A Aarti Singh %A Larry Wasserman %B Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2014 %E Samuel Kaski %E Jukka Corander %F pmlr-v33-ramdas14 %I PMLR %P 805--813 %U https://proceedings.mlr.press/v33/ramdas14.html %V 33 %X In active learning, the user sequentially chooses values for feature X and an oracle returns the corresponding label Y. In this paper, we consider the effect of feature noise in active learning, which could arise either because X itself is being measured, or it is corrupted in transmission to the oracle, or the oracle returns the label of a noisy version of the query point. In statistics, feature noise is known as“errors in variables” and has been studied extensively in non-active settings. However, the effect of feature noise in active learning has not been studied before. We consider the well-known Berkson errors-in-variables model with additive uniform noise of width σ. Our simple but revealing setting is that of one-dimensional binary classification setting where the goal is to learn a threshold (point where the probability of a + label crosses half). We deal with regression functions that are antisymmetric in a region of size σaround the threshold and also satisfy Tsybakov’s margin condition around the threshold. We prove minimax lower and upper bounds which demonstrate that when σis smaller than the minimiax active/passive noiseless error derived in Castro & Nowak (2007), then noise has no effect on the rates and one achieves the same noiseless rates. For larger σ, the \textitunflattening of the regression function on convolution with uniform noise, along with its local antisymmetry around the threshold, together yield a behaviour where noise \textitappears to be beneficial. Our key result is that active learning can buy significant improvement over a passive strategy even in the presence of feature noise.
RIS
TY - CPAPER TI - An Analysis of Active Learning with Uniform Feature Noise AU - Aaditya Ramdas AU - Barnabas Poczos AU - Aarti Singh AU - Larry Wasserman BT - Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics DA - 2014/04/02 ED - Samuel Kaski ED - Jukka Corander ID - pmlr-v33-ramdas14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 33 SP - 805 EP - 813 L1 - http://proceedings.mlr.press/v33/ramdas14.pdf UR - https://proceedings.mlr.press/v33/ramdas14.html AB - In active learning, the user sequentially chooses values for feature X and an oracle returns the corresponding label Y. In this paper, we consider the effect of feature noise in active learning, which could arise either because X itself is being measured, or it is corrupted in transmission to the oracle, or the oracle returns the label of a noisy version of the query point. In statistics, feature noise is known as“errors in variables” and has been studied extensively in non-active settings. However, the effect of feature noise in active learning has not been studied before. We consider the well-known Berkson errors-in-variables model with additive uniform noise of width σ. Our simple but revealing setting is that of one-dimensional binary classification setting where the goal is to learn a threshold (point where the probability of a + label crosses half). We deal with regression functions that are antisymmetric in a region of size σaround the threshold and also satisfy Tsybakov’s margin condition around the threshold. We prove minimax lower and upper bounds which demonstrate that when σis smaller than the minimiax active/passive noiseless error derived in Castro & Nowak (2007), then noise has no effect on the rates and one achieves the same noiseless rates. For larger σ, the \textitunflattening of the regression function on convolution with uniform noise, along with its local antisymmetry around the threshold, together yield a behaviour where noise \textitappears to be beneficial. Our key result is that active learning can buy significant improvement over a passive strategy even in the presence of feature noise. ER -
APA
Ramdas, A., Poczos, B., Singh, A. & Wasserman, L.. (2014). An Analysis of Active Learning with Uniform Feature Noise. Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 33:805-813 Available from https://proceedings.mlr.press/v33/ramdas14.html.

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