Search results for "monimuuttujamenetelmät"
showing 10 items of 22 documents
On the Extension of the DIRECT Algorithm to Multiple Objectives
2020
AbstractDeterministic global optimization algorithms like Piyavskii–Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce r…
Blind recovery of sources for multivariate space-time random fields
2022
AbstractWith advances in modern worlds technology, huge datasets that show dependencies in space as well as in time occur frequently in practice. As an example, several monitoring stations at different geographical locations track hourly concentration measurements of a number of air pollutants for several years. Such a dataset contains thousands of multivariate observations, thus, proper statistical analysis needs to account for dependencies in space and time between and among the different monitored variables. To simplify the consequent multivariate spatio-temporal statistical analysis it might be of interest to detect linear transformations of the original observations that result in stra…
Asymptotic and bootstrap tests for subspace dimension
2022
Most linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss (2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo and Li (2016). The eigen-decomposition of one scatter matrix with respect to another is then often used to determine the dimension of the signal subspace and to separate signal and noise parts of the data. Three popular dimension reduction methods, namely principal component analysis (PCA), fourth order blind identification (FOBI) and sliced inverse regression (SIR) are considered in detail and the first two moments of subsets of the eigenvalues are used to test…
Flexible Data Driven Inventory Management with Interactive Multiobjective Lot Size Optimization
2021
We study data-driven decision support and formalise a path from data to decision making. We focus on lot sizing in inventory management with stochastic demand and propose an interactive multi-objective optimisation approach. We forecast demand with a Bayesian model, which is based on sales data. After identifying relevant objectives relying on the demand model, we formulate an optimisation problem to determine lot sizes for multiple future time periods. Our approach combines different interactive multi-objective optimisation methods for finding the best balance among the objectives. For that, a decision maker with substance knowledge directs the solution process with one’s preference inform…
Analyzing environmental‐trait interactions in ecological communities with fourth‐corner latent variable models
2021
In ecological community studies it is often of interest to study the effect of species related trait variables on abundances or presence-absences. Specifically, the interest may lay in the interactions between environmental and trait variables. An increasingly popular approach for studying such interactions is to use the so-called fourth-corner model, which explicitly posits a regression model where the mean response of each species is a function of interactions between covariate and trait predictors (among other terms). On the other hand, many of the fourth-corner models currently applied in the literature are too simplistic to properly account for variation in environmental and trait resp…
Blind source separation for non-stationary random fields
2022
Regional data analysis is concerned with the analysis and modeling of measurements that are spatially separated by specifically accounting for typical features of such data. Namely, measurements in close proximity tend to be more similar than the ones further separated. This might hold also true for cross-dependencies when multivariate spatial data is considered. Often, scientists are interested in linear transformations of such data which are easy to interpret and might be used as dimension reduction. Recently, for that purpose spatial blind source separation (SBSS) was introduced which assumes that the observed data are formed by a linear mixture of uncorrelated, weakly stationary random …
On the usage of joint diagonalization in multivariate statistics
2022
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also enco…
Dimension reduction for time series in a blind source separation context using r
2021
Funding Information: The work of KN was supported by the CRoNoS COST Action IC1408 and the Austrian Science Fund P31881-N32. The work of ST was supported by the CRoNoS COST Action IC1408. The work of JV was supported by Academy of Finland (grant 321883). We would like to thank the anonymous reviewers for their comments which improved the paper and package considerably. Publisher Copyright: © 2021, American Statistical Association. All rights reserved. Multivariate time series observations are increasingly common in multiple fields of science but the complex dependencies of such data often translate into intractable models with large number of parameters. An alternative is given by first red…
Test of the Latent Dimension of a Spatial Blind Source Separation Model
2024
We assume a spatial blind source separation model in which the observed multivariate spatial data is a linear mixture of latent spatially uncorrelated random fields containing a number of pure white noise components. We propose a test on the number of white noise components and obtain the asymptotic distribution of its statistic for a general domain. We also demonstrate how computations can be facilitated in the case of gridded observation locations. Based on this test, we obtain a consistent estimator of the true dimension. Simulation studies and an environmental application in the Supplemental Material demonstrate that our test is at least comparable to and often outperforms bootstrap-bas…
Birth weight, adult weight, and cardiovascular biomarkers : Evidence from the Cardiovascular Young Finns Study
2021
This study quantifies the causal effect of birth weight on cardiovascular biomarkers in adulthood using the Cardiovascular Risk in Young Finns Study (YFS). We apply a multivariable Mendelian randomization (MVMR) method that provides a novel approach to improve inference in causal analysis based on a mediation framework. The results show that birth weight is linked to triglyceride levels (β = −0.294; 95% CI [−0.591, 0.003]) but not to low-density lipoprotein (LDL) cholesterol levels (β = 0.007; 95% CI [−0.168, 0.183]). The total effect of birth weight on triglyceride levels is partly offset by a mediation pathway linking birth weight to adult BMI (β = 0.111; 95% CI [−0.013, 0.234]). The nega…