2 research outputs found
VecHGrad for Solving Accurately Complex Tensor Decomposition
Tensor decomposition, a collection of factorization techniques for
multidimensional arrays, are among the most general and powerful tools for
scientific analysis. However, because of their increasing size, today's data
sets require more complex tensor decomposition involving factorization with
multiple matrices and diagonal tensors such as DEDICOM or PARATUCK2.
Traditional tensor resolution algorithms such as Stochastic Gradient Descent
(SGD), Non-linear Conjugate Gradient descent (NCG) or Alternating Least Square
(ALS), cannot be easily applied to complex tensor decomposition or often lead
to poor accuracy at convergence. We propose a new resolution algorithm, called
VecHGrad, for accurate and efficient stochastic resolution over all existing
tensor decomposition, specifically designed for complex decomposition. VecHGrad
relies on gradient, Hessian-vector product and adaptive line search to ensure
the convergence during optimization. Our experiments on five real-world data
sets with the state-of-the-art deep learning gradient optimization models show
that VecHGrad is capable of converging considerably faster because of its
superior theoretical convergence rate per step. Therefore, VecHGrad targets as
well deep learning optimizer algorithms. The experiments are performed for
various tensor decomposition including CP, DEDICOM and PARATUCK2. Although it
involves a slightly more complex update rule, VecHGrad's runtime is similar in
practice to that of gradient methods such as SGD, Adam or RMSProp
From Persistent Homology to Reinforcement Learning with Applications for Retail Banking
The retail banking services are one of the pillars of the modern economic
growth. However, the evolution of the client's habits in modern societies and
the recent European regulations promoting more competition mean the retail
banks will encounter serious challenges for the next few years, endangering
their activities. They now face an impossible compromise: maximizing the
satisfaction of their hyper-connected clients while avoiding any risk of
default and being regulatory compliant. Therefore, advanced and novel research
concepts are a serious game-changer to gain a competitive advantage. In this
context, we investigate in this thesis different concepts bridging the gap
between persistent homology, neural networks, recommender engines and
reinforcement learning with the aim of improving the quality of the retail
banking services. Our contribution is threefold. First, we highlight how to
overcome insufficient financial data by generating artificial data using
generative models and persistent homology. Then, we present how to perform
accurate financial recommendations in multi-dimensions. Finally, we underline a
reinforcement learning model-free approach to determine the optimal policy of
money management based on the aggregated financial transactions of the clients.
Our experimental data sets, extracted from well-known institutions where the
privacy and the confidentiality of the clients were not put at risk, support
our contributions. In this work, we provide the motivations of our retail
banking research project, describe the theory employed to improve the financial
services quality and evaluate quantitatively and qualitatively our
methodologies for each of the proposed research scenarios.Comment: PhD thesis, Univ Luxembourg (2019