Hard-Margin Active Linear Regression
نویسندگان
چکیده
We consider the fundamental problem of linear regression in which the designer can actively choose observations. This model naturally captures various experiment design settings in medical experiments, ad placement problems and more. Whereas previous literature addresses the soft-margin or mean-square-error variants of the problem, we consider a natural machine learning hard-margin criterion. In this setting, we show that active learning admits significantly better sample complexity bounds than the passive learning counterpart, and give efficient algorithms that attain near-optimal bounds.
منابع مشابه
SVM via Saddle Point Optimization: New Bounds and Distributed Algorithms
Support Vector Machine is one of the most classical approaches for classification and regression. Despite being studied for decades, obtaining practical algorithms for SVM is still an active research problem in machine learning. In this paper, we propose a new perspective for SVM via saddle point optimization. We provide an algorithm which achieves (1 − )-approximations with running time Õ(nd +...
متن کاملApproximate Reduction from AUC Maximization to 1-Norm Soft Margin Optimization
Finding linear classifiers that maximize AUC scores is important in ranking research. This is naturally formulated as a 1-norm hard/soft margin optimization problem over pn pairs of p positive and n negative instances. However, directly solving the optimization problems is impractical since the problem size (pn) is quadratically larger than the given sample size (p + n). In this paper, we give ...
متن کاملThe comparison of Normal Bayes and SVM classifiers in the context of face shape recognition
In this paper the face recognition system based on the shape information extracted with the Active Shape Model is presented. Three different classification approaches have been used: the Normal Bayes Classifier, the Linear Support Vector Machine (LSVM) with a hard margin and the LSVM with a soft margin. The influence of the shape extraction algorithm parameters on the classification efficiency ...
متن کاملPresentation of quasi-linear piecewise selected models simultaneously with designing of bump-less optimal robust controller for nonlinear vibration control of composite plates
The idea of using quasi-linear piecewise models has been established on the decomposition of complicated nonlinear systems, simultaneously designing with local controllers. Since the proper performance and the final system close loop stability are vital in multi-model controllers designing, the main problem in multi-model controllers is the number of the local models and their position not payi...
متن کاملComputational Complexity of Linear Large Margin Classification With Ramp Loss
Minimizing the binary classification error with a linear model leads to an NP-hard problem. In practice, surrogate loss functions are used, in particular loss functions leading to large margin classification such as the hinge loss and the ramp loss. The intuitive large margin concept is theoretically supported by generalization bounds linking the expected classification error to the empirical m...
متن کامل