Related papers: A note on the multiplicative gamma process
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
In order to better model high-dimensional sequential data, we propose a collaborative multi-output Gaussian process dynamical system (CGPDS), which is a novel variant of GPDSs. The proposed model assumes that the output on each dimension is…
Mutation is one of the most important stages of the genetic algorithm because of its impact on the exploration of global optima, and to overcome premature convergence. There are many types of mutation, and the problem lies in selection of…
We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…
This paper illuminates the derivation, the applicability, and the efficiency of the Multiplicative Runge-Kutta Method, derived in the frame- work of geometric multiplicative calculus. The removal of the restrictions of geometric…
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…
Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain…
An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior,…
In this paper, we propose algorithms that exploit negative curvature for solving noisy nonlinear nonconvex unconstrained optimization problems. We consider both deterministic and stochastic inexact settings, and develop two-step algorithms…
We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…
We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of…
High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…
Augmented Lagrangian method (also called as method of multipliers) is an important and powerful optimization method for lots of smooth or nonsmooth variational problems in modern signal processing, imaging, optimal control and so on.…
Variable selection in high-dimensional scenarios is of great interested in statistics. One application involves identifying differentially expressed genes in genomic analysis. Existing methods for addressing this problem have some limits or…
We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The…
Variance partitioning methods, which are built upon multivariate statistics, have been widely applied in different taxa and habitats in community ecology. Here, I performed a literature review on the development and application of the…
This paper is about models for a vector of probabilities whose elements must have a multiplicative structure and sum to 1 at the same time; in certain applications, as basket analysis, these models may be seen as a constrained version of…