Non-linear Optimization Methods for Learning Regular Distributions

Iterative methods for solving non linear Fokker-Planck equation

Non-linear conjugate gradient methods for vector optimization∗

In this work, we propose non-linear conjugate gradient methods for finding critical points of vector-valued functions with respect to the partial order induced by a closed, convex, and pointed cone with non-empty interior. No convexity assumption is made on the objectives. The concepts of Wolfe and Zoutendjik conditions are extended for the vectorvalued optimization. In particular, we show that...

Non-Gaussian Methods for Learning Linear Structural Equation Models

Special thanks to Aapo Hyvärinen, Patrik O. Hoyer and Takashi Washio. 2 Abstract • Linear structural equation models (linear SEMs) can be used to model data generating processes of variables. • We review a new approach to learn or estimate linear structural equation models. • The new estimation approach utilizes non-Gaussianity of data for model identification and uniquely estimates much wider...

Generalization Error Estimation for Non-linear Learning Methods

Estimating the generalization error is one of the key ingredients of supervised learning since a good generalization error estimator can be used for model selection. An unbiased generalization error estimator called the subspace information criterion (SIC) is shown to be useful for model selection, but its range of application is limited to linear learning methods. In this paper, we extend SIC ...

Comparative Study of Particle Swarm Optimization and Genetic Algorithm Applied for Noisy Non-Linear Optimization Problems

Optimization of noisy non-linear problems plays a key role in engineering and design problems. These optimization problems can't be solved effectively by using conventional optimization methods. However, metaheuristic algorithms such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) seem very efficient to approach in these problems and became very popular. The efficiency of these ...