Related papers: Fixed Point Strategies in Data Science

Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in…

An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…

Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the…

Fixed-point iterations are at the heart of numerical computing and are often a computational bottleneck in real-time applications that typically need a fast solution of moderate accuracy. We present neural fixed-point acceleration which…

Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the…

Fixed points represent equilibrium states, stability, and solutions to a range of problems. It has been an active field of research. In this paper, we provide an overview of the main branches of fixed point theory. We discuss the key…

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…

In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science,…

We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…

With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering…

Over the last few years, neural networks have started penetrating safety critical systems to take decisions in robots, rockets, autonomous driving car, etc. A problem is that these critical systems often have limited computing resources.…

In this work, we address unconstrained finite-sum optimization problems, with particular focus on instances originating in large scale deep learning scenarios. Our main interest lies in the exploration of the relationship between recent…

Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…

Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…

This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…

Statistical matching methods are widely used in the social and health sciences to estimate causal effects using observational data. Often the objective is to find comparable groups with similar covariate distributions in a dataset, with the…

This paper considers the fixed point problem for a nonexpansive mapping on a real Hilbert space and proposes novel line search fixed point algorithms to accelerate the search. The termination conditions for the line search are based on the…

Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies…