On minimizing the maximum eigenvalue of a symmetric matrix
SIAM Journal on Matrix Analysis and Applications
Introduction to algorithms
Machine Learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ridge Regression Learning Algorithm in Dual Variables
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
On the influence of the kernel on the consistency of support vector machines
The Journal of Machine Learning Research
The Journal of Machine Learning Research
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Adaptive language modeling using minimum discriminant estimation
HLT '91 Proceedings of the workshop on Speech and Natural Language
Smoothing Technique and its Applications in Semidefinite Optimization
Mathematical Programming: Series A and B
Confidence-weighted linear classification
Proceedings of the 25th international conference on Machine learning
Sample Selection Bias Correction Theory
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Discriminative Learning Under Covariate Shift
The Journal of Machine Learning Research
Domain adaptation in regression
ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory
New analysis and algorithm for learning with drifting distributions
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
Hi-index | 5.23 |
We present a series of new theoretical, algorithmic, and empirical results for domain adaptation and sample bias correction in regression. We prove that the discrepancy is a distance for the squared loss when the hypothesis set is the reproducing kernel Hilbert space induced by a universal kernel such as the Gaussian kernel. We give new pointwise loss guarantees based on the discrepancy of the empirical source and target distributions for the general class of kernel-based regularization algorithms. These bounds have a simpler form than previous results and hold for a broader class of convex loss functions not necessarily differentiable, including L"q losses and the hinge loss. We also give finer bounds based on the discrepancy and a weighted feature discrepancy parameter. We extend the discrepancy minimization adaptation algorithm to the more significant case where kernels are used and show that the problem can be cast as an SDP similar to the one in the feature space. We also show that techniques from smooth optimization can be used to derive an efficient algorithm for solving such SDPs even for very high-dimensional feature spaces and large samples. We have implemented this algorithm and report the results of experiments both with artificial and real-world data sets demonstrating its benefits both for general scenario of adaptation and the more specific scenario of sample bias correction. Our results show that it can scale to large data sets of tens of thousands or more points and demonstrate its performance improvement benefits.