Evolving Gaussian process kernels from elementary mathematical expressions for time series extrapolation

[EN]Choosing the best kernel is crucial in many Machine Learning applications. Gaussian Processes are a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian Processes literature, kernels have usually been either ad hoc designed, selected from a predefined set, or searched for in a space of compositions of kernels which have been defined a priori. In this paper, we propose a Genetic Programming algorithm that represents a kernel function as a tree of elementary mathematical expressions. By means of this representation, a wider set of kernels can be modeled, where potentially better solutions can be found, although new challenges also arise. The proposed algorithm is able to overcome these difficulties and find kernels that accurately model the characteristics of the data. This method has been tested in several real-world time series extrapolation problems, improving the state-of-the-art results while reducing the complexity of the kernels.This work has been supported by the Spanish Ministry of Science and Innovation (project PID2019-104966 GB-I00) , and the Basque Government (projects KK-2020/00049 and IT1244-19, and ELKARTEK program) . Jose A. Lozano is also supported by BERC 2018-2021 (Basque government) and BCAM Severo Ochoa accred-itation SEV-2017-0718 (Spanish Ministry of Science and Innovation)

Modeling for seasonal marked point processes: An analysis of evolving hurricane occurrences

Seasonal point processes refer to stochastic models for random events which are only observed in a given season. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity. We assume the point process is a nonhomogeneous Poisson process and propose a nonparametric mixture of beta densities to model dynamically evolving temporal Poisson process intensities. Dependence structure is built through a dependent Dirichlet process prior for the seasonally-varying mixing distributions. We extend the nonparametric model to incorporate time-varying marks, resulting in flexible inference for both the seasonal point process intensity and for the conditional mark distribution. The motivating application involves the analysis of hurricane landfalls with reported damages along the U.S. Gulf and Atlantic coasts from 1900 to 2010. We focus on studying the evolution of the intensity of the process of hurricane landfall occurrences, and the respective maximum wind speed and associated damages. Our results indicate an increase in the number of hurricane landfall occurrences and a decrease in the median maximum wind speed at the peak of the season. Introducing standardized damage as a mark, such that reported damages are comparable both in time and space, we find that there is no significant rising trend in hurricane damages over time.Comment: Published at http://dx.doi.org/10.1214/14-AOAS796 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Sentiment analysis with genetically evolved Gaussian kernels

Sentiment analysis consists of evaluating opinions or statements based on text analysis. Among the methods used to estimate the degree to which a text expresses a certain sentiment are those based on Gaussian Processes. However, traditional Gaussian Processes methods use a prede- fined kernels with hyperparameters that can be tuned but whose structure can not be adapted. In this paper, we propose the application of Genetic Programming for the evolution of Gaussian Process kernels that are more precise for sentiment analysis. We use use a very flexible representation of kernels combined with a multi-objective approach that considers si- multaneously two quality metrics and the computational time required to evaluate those kernels. Our results show that the algorithm can outper- form Gaussian Processes with traditional kernels for some of the sentiment analysis tasks considered

Evolving Gaussian Process Kernels for Translation Editing Effort Estimation

In many Natural Language Processing problems the combination of machine learning and optimization techniques is essential. One of these problems is estimating the effort required to improve, under direct human supervision, a text that has been translated using a machine translation method. Recent developments in this area have shown that Gaussian Processes can be accurate for post-editing effort prediction. However, the Gaussian Process kernel has to be chosen in advance, and this choice in- fluences the quality of the prediction. In this paper, we propose a Genetic Programming algorithm to evolve kernels for Gaussian Processes. We show that the combination of evolutionary optimization and Gaussian Processes removes the need for a-priori specification of the kernel choice, and achieves predictions that, in many cases, outperform those obtained with fixed kernels.TIN2016-78365-

Quantum correlation functions and the classical limit

We study the transition from the full quantum mechanical description of physical systems to an approximate classical stochastic one. Our main tool is the identification of the closed-time-path (CTP) generating functional of Schwinger and Keldysh with the decoherence functional of the consistent histories approach. Given a degree of coarse-graining in which interferences are negligible, we can explicitly write a generating functional for the effective stochastic process in terms of the CTP generating functional. This construction gives particularly simple results for Gaussian processes. The formalism is applied to simple quantum systems, quantum Brownian motion, quantum fields in curved spacetime. Perturbation theory is also explained. We conclude with a discussion on the problem of backreaction of quantum fields in spacetime geometry.Comment: 30 pages, latex; minor changes, added some explanations and refeence

Generalized Laguerre Unitary Ensembles and an interacting particles model with a wall

We introduce and study a new interacting particles model with a wall and two kinds of interactions - blocking and pushing - which maintain particles in a certain order. We show that it involves a random matrix model.Comment: