Matrix analysis
Evaluating rational functions: infinite precision is finite cost and tractable on average
SIAM Journal on Computing
On the efficiency of Newton's method in approximating all zeros of a system of complex polynomials
Mathematics of Operations Research
Complexity theory of numerical linear algebra
Journal of Computational and Applied Mathematics - Special Issue on Emerging Paradigms in Applied Mathematical Modelling
Eigenvalues and condition numbers of random matrices
SIAM Journal on Matrix Analysis and Applications
Complexity of Bezout's theorem V: polynomial time
Selected papers of the workshop on Continuous algorithms and complexity
Complexity of Bezout's theorem IV: probability of success; extensions
SIAM Journal on Numerical Analysis
Applied numerical linear algebra
Applied numerical linear algebra
Kernel PCA and de-noising in feature spaces
Proceedings of the 1998 conference on Advances in neural information processing systems II
Machine Learning
Smoothed analysis of the perceptron algorithm for linear programming
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Probabilistic analysis of condition numbers for linear programming
Journal of Optimization Theory and Applications
Robust Preconditioners for Saddle Point Problems
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
On the influence of the kernel on the consistency of support vector machines
The Journal of Machine Learning Research
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Learning and evaluating classifiers under sample selection bias
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Tails of Condition Number Distributions
SIAM Journal on Matrix Analysis and Applications
Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices
SIAM Journal on Matrix Analysis and Applications
Beyond Hirsch Conjecture: Walks on Random Polytopes and Smoothed Complexity of the Simplex Method
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The complexity of semilinear problems in succinct representation
Computational Complexity
Estimates on the Distribution of the Condition Number of Singular Matrices
Foundations of Computational Mathematics
Smoothed analysis of integer programming
Mathematical Programming: Series A and B
Average-Case and Smoothed Competitive Analysis of the Multilevel Feedback Algorithm
Mathematics of Operations Research
Training a Support Vector Machine in the Primal
Neural Computation
The condition number of a randomly perturbed matrix
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Multi-task learning for HIV therapy screening
Proceedings of the 25th international conference on Machine learning
Covariate Shift Adaptation by Importance Weighted Cross Validation
The Journal of Machine Learning Research
Dataset Shift in Machine Learning
Dataset Shift in Machine Learning
Inlier-Based Outlier Detection via Direct Density Ratio Estimation
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Kernel conjugate gradient for fast kernel machines
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Worst-Case and Smoothed Analysis of k-Means Clustering with Bregman Divergences
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Mutual information approximation via maximum likelihood estimation of density ratio
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
A Least-squares Approach to Direct Importance Estimation
The Journal of Machine Learning Research
Discriminative Learning Under Covariate Shift
The Journal of Machine Learning Research
Estimating divergence functionals and the likelihood ratio by convex risk minimization
IEEE Transactions on Information Theory
Statistical outlier detection using direct density ratio estimation
Knowledge and Information Systems
Least-squares independent component analysis
Neural Computation
Neural Networks
A preconditioning technique for a class of PDE-constrained optimization problems
Advances in Computational Mathematics
Smoothed Analysis of Moore-Penrose Inversion
SIAM Journal on Matrix Analysis and Applications
Density Ratio Estimation in Machine Learning
Density Ratio Estimation in Machine Learning
Machine Learning in Non-Stationary Environments: Introduction to Covariate Shift Adaptation
Machine Learning in Non-Stationary Environments: Introduction to Covariate Shift Adaptation
Sequential change-point detection based on direct density-ratio estimation
Statistical Analysis and Data Mining
| Hi-index | 0.00 |
In this study, the computational properties of a kernel-based least-squares density-ratio estimator are investigated from the viewpoint of condition numbers. The condition number of the Hessian matrix of the loss function is closely related to the convergence rate of optimization and the numerical stability. We use smoothed analysis techniques and theoretically demonstrate that the kernel least-squares method has a smaller condition number than other M-estimators. This implies that the kernel least-squares method has desirable computational properties. In addition, an alternate formulation of the kernel least-squares estimator that possesses an even smaller condition number is presented. The validity of the theoretical analysis is verified through numerical experiments.