ABSTRACT
We introduce a new algorithm for binary classification in the selective sampling protocol. Our algorithm uses Regularized Least Squares (RLS) as base classifier, and for this reason it can be efficiently run in any RKHS. Unlike previous margin-based semi-supervised algorithms, our sampling condition hinges on a simultaneous upper bound on bias and variance of the RLS estimate under a simple linear label noise model. This fact allows us to prove performance bounds that hold for an arbitrary sequence of instances. In particular, we show that our sampling strategy approximates the margin of the Bayes optimal classifier to any desired accuracy ε by asking Õ (d/ε2) queries (in the RKHS case d is replaced by a suitable spectral quantity). While these are the standard rates in the fully supervised i.i.d. case, the best previously known result in our harder setting was Õ (d3/ε4). Preliminary experiments show that some of our algorithms also exhibit a good practical performance.
- Auer, P. (2002). Using confidence bounds for exploitation-exploration trade-offs. Journal of Machine Learning Research, 3, 397--422. Google ScholarDigital Library
- Balcan, M., Beygelzimer, A., & Langford, J. (2006). Agnostic active learning. Proc. of the 23rd International Conference on Machine Learning (pp. 65--72). Google ScholarDigital Library
- Balcan, M., Broder, A., & Zhang, T. (2007). Margin-based active learning. Proceedings of the 20th Annual Conference on Learning Theory (pp. 35--50). Google ScholarDigital Library
- Cavallanti, G., Cesa-Bianchi, N., & Gentile, C. (2007). Tracking the best hyperplane with a simple budget Perceptron. Machine Learning, 69, 143--167. Google ScholarDigital Library
- Cavallanti, G., Cesa-Bianchi, N., & Gentile, C. (2009). Linear classification and selective sampling under low noise conditions. In Advances in Neural Information Processing Systems 21 (pp. 249--256).Google Scholar
- Cesa-Bianchi, N., Gentile, C., & Zaniboni, L. (2006a). Incremental algorithms for hierarchical classification. Journal of Machine Learning Research, 7, 31--54. Google ScholarDigital Library
- Cesa-Bianchi, N., Gentile, C., & Zaniboni, L. (2006b). Worst-case analysis of selective sampling for linear classification. Journal of Machine Learning Research, 7, 1025--1230. Google ScholarDigital Library
- Cohn, R., Atlas, L., & Ladner, R. (1990). Training connectionist networks with queries and selective sampling. In Advances in Neural Information Processing Systems 2 (pp. 566--573). Google ScholarDigital Library
- Dasgupta, S., Hsu, D., & Monteleoni, C. (2008). A general agnostic active learning algorithm. In Advances in Neural Information Processing Systems 21 (pp. 353--360).Google Scholar
- Dasgupta, S., Kalai, A. T., & Monteleoni, C. (2005). Analysis of perceptron-based active learning. Proceedings of the 18th Annual Conference on Learning Theory (pp. 249--263). Google ScholarDigital Library
- Dekel, O., Shalev-Shwartz, S., & Singer, Y. (2007). The Forgetron: A kernel-based Perceptron on a budget. SIAM Journal on Computing, 37, 1342--1372. Google ScholarDigital Library
- Freund, Y., Seung, S., Shamir, E., & Tishby, N. (1997). Selective sampling using the query by committee algorithm. Machine Learning, 28, 133--168. Google ScholarDigital Library
- Li, L., Littman, M., & Walsh, T. (2008). Knows what it knows: a framework for self-aware learning. Proceedings of the 25th International Conference on Machine Learning (pp. 568--575). Google ScholarDigital Library
- Orabona, F., Keshet, J., & Caputo, B. (2008). The Projectron: a bounded kernel-based Perceptron. Proceedings of the 25th International Conference on Machine Learning (pp. 720--727). Google ScholarDigital Library
- Strehl, A., & Littman, M. (2008). Online linear regression and its application to model-based reinforcement learning. In Advances in Neural Information Processing Systems 20 (pp. 631--638).Google Scholar
- Weston, J., Bordes, A., & Bottou, L. (2005). Online (and offline) on an even tighter budget. Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics (pp. 413--420).Google Scholar
Index Terms
- Robust bounds for classification via selective sampling
Recommendations
Trading via selective classification
ICAIF '21: Proceedings of the Second ACM International Conference on AI in FinanceA binary classifier that tries to predict if the price of an asset will increase or decrease naturally gives rise to a trading strategy that follows the prediction and thus always has a position in the market. Selective classification extends a binary ...
Robust Adversarial Classification via Abstaining
2021 60th IEEE Conference on Decision and Control (CDC)In this work, we consider a binary classification problem and cast it into a binary hypothesis testing framework, where the observations can be perturbed by an adversary. To improve the adversarial robustness of a classifier, we include an abstain option, ...
Sampling lower bounds via information theory
STOC '03: Proceedings of the thirty-fifth annual ACM symposium on Theory of computingWe present a novel technique, based on the Jensen-Shannon divergence from information theory, to prove lower bounds on the query complexity of sampling algorithms that approximate functions over arbitrary domain and range. Unlike previous methods, our ...
Comments