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Application of the Cox regression model with time dependent parameters to unemployment data
Volf, Petr
2019 - English
The contribution deals with the application of statistical survival analysis with the intensity described by a generalized version of Cox regression model with time dependent parameters. A\nmethod of model components non-parametric estimation is recalled, the flexibility of result is assessed with a goodness-of-fit test based on martingale residuals. The application\nconcerns to the real data representing the job opportunities development and reduction, during a given period. The risk of leaving the company is changing in time and depends also on the age of employees and their time with company. Both these covariates are considered and their impact to the risk analyzed.
Keywords:
mathematical statistics; survival analysis; unemployment data
Fulltext is available at external website.
Application of the Cox regression model with time dependent parameters to unemployment data
The contribution deals with the application of statistical survival analysis with the intensity described by a generalized version of Cox regression model with time dependent parameters. A\nmethod of ...
A Robustified Metalearning Procedure for Regression Estimators
Kalina, Jan; Neoral, A.
2019 - English
Metalearning represents a useful methodology for selecting and recommending a suitable algorithm or method for a new dataset exploiting a database of training datasets. While metalearning is potentially beneficial for the analysis of economic data, we must be aware of its instability and sensitivity to outlying measurements (outliers) as well as measurement errors. The aim of this paper is to robustify the metalearning process. First, we prepare some useful theoretical tools exploiting the idea of implicit weighting, inspired by the least weighted squares estimator. These include a robust coefficient of determination, a robust version of mean square error, and a simple rule for outlier detection in linear regression. We perform a metalearning study for recommending the best linear regression estimator for a new dataset (not included in the training database). The prediction of the optimal estimator is learned over a set of 20 real datasets with economic motivation, while the least squares are compared with several (highly) robust estimators. We investigate the effect of variable selection on the metalearning results. If the training as well as validation data are considered after a proper robust variable selection, the metalearning performance is improved remarkably, especially if a robust prediction error is used.
Keywords:
model choice; computational statistics; robustness; variable selection
Fulltext is available at external website.
A Robustified Metalearning Procedure for Regression Estimators
Metalearning represents a useful methodology for selecting and recommending a suitable algorithm or method for a new dataset exploiting a database of training datasets. While metalearning is ...
Two Algorithms for Risk-averse Reformulation of Multi-stage Stochastic Programming Problems
Šmíd, Martin; Kozmík, Václav
2018 - English
Many real-life applications lead to risk-averse multi-stage stochastic problems, therefore effective solution of these problems is of great importance. Many tools can be used to their solution (GAMS, Coin-OR, APML or, for smaller problems, Excel), it is, however, mostly up to researcher to reformulate the problem into its deterministic equivalent. Moreover, such solutions are usually one-time, not easy to modify for different applications. We overcome these problems by providing a front-end software package, written in C++, which enables to enter problem definitions in a way close to their mathematical definition. Creating of a deterministic equivalent (and its solution) is up to the computer. In particular, our code is able to solve linear multi-stage with Multi-period Mean-CVaR or Nested Mean-CVaR criteria. In the present paper, we describe the algorithms, transforming these problems into their deterministic equivalents.
Keywords:
Multi-stage stochastic programming; deterministic equivalent; multi-period CVaR; nested CVaR; optimization algorithm
Fulltext is available at external website.
Two Algorithms for Risk-averse Reformulation of Multi-stage Stochastic Programming Problems
Many real-life applications lead to risk-averse multi-stage stochastic problems, therefore effective solution of these problems is of great importance. Many tools can be used to their solution (GAMS, ...
Problem of competing risks with covariates: Application to an unemployment study
Volf, Petr
2018 - English
The study deals with the methods of statistical analysis in the situation of competing risks in the presence of regression. First, the problem of identification of marginal and joint distributions of competing random variables is recalled. The main objective is then to demonstrate that the parameters and, in particular, the correlation of competing variables, may depend on covariates. The approach is applied to solution of a real example with unemployment data. The model uses the Gauss copula and Cox’s regression model.
Keywords:
statistical analysis; competing risks; unemployment study
Fulltext is available at external website.
Problem of competing risks with covariates: Application to an unemployment study
The study deals with the methods of statistical analysis in the situation of competing risks in the presence of regression. First, the problem of identification of marginal and joint distributions of ...
Heuristics in blind source separation
Kautský, Václav; Štěch, Jakub
2018 - English
This paper deals with application of heuristic algorithms (DEBR, MCRS) in blind source separation (BSS). BSS methods focus on a separation of the (source) signal from a linear mixture. The idea of using heuristic algorithms is introduced on the independent component extraction (ICE) model. The motivation for considering heuristics is to obtain an initial guess needed by many ICE algorithms. Moreover, the comparison of this initialization, and other algorithms accuracy is performed.\n
Keywords:
Blind Source Separation; DEBR; Independent Component Extraction
Fulltext is available at external website.
Heuristics in blind source separation
This paper deals with application of heuristic algorithms (DEBR, MCRS) in blind source separation (BSS). BSS methods focus on a separation of the (source) signal from a linear mixture. The idea of ...
Dynamic Bayesian Networks for the Classification of Sleep Stages
Vomlel, Jiří; Kratochvíl, Václav
2018 - English
Human sleep is traditionally classified into five (or six) stages. The manual classification is time consuming since it requires knowledge of an extensive set of rules from manuals and experienced experts. Therefore automatic classification methods appear useful for this task. In this paper we extend the approach based on Hidden Markov Models by relating certain features not only to the current time slice but also to the previous one. Dynamic Bayesian Networks that results from this generalization are thus capable of modeling features related to state transitions. Experiments on real data revealed that in this way we are able to increase the prediction accuracy.
Keywords:
Dynamic Bayesian Network; Sleep Analysis
Fulltext is available at external website.
Dynamic Bayesian Networks for the Classification of Sleep Stages
Human sleep is traditionally classified into five (or six) stages. The manual classification is time consuming since it requires knowledge of an extensive set of rules from manuals and experienced ...
Comparison of Shenoy’s Expectation Operator with Probabilistic Transforms and Perez’ Barycenter
Jiroušek, R.; Kratochvíl, Václav
2018 - English
Shenoy’s paper published in this Proceedings of WUPES 2018 introduces an operator that gives instructions how to compute an expected value in the Dempster-Shafer theory of evidence. Up to now, there was no direct way to get the expected value of a utility function in D-S theory. If eeded, one had to find a probability mass function corresponding to the considered belief function, and then - using this probability mass function - to compute the classical probabilistic expectation. In this paper, we take four different approaches to defining probabilistic representatives of a belief function and compare which one yields to the best approximations of Shenoy’s expected values of various utility functions. The achieved results support our conjecture that there does not exist a probabilistic representative of a belief function that would yield the same expectations as the Shenoy’s new operator.
Keywords:
expected utility; Dempster-Shafer theory; Shenoy's operator
Fulltext is available at external website.
Comparison of Shenoy’s Expectation Operator with Probabilistic Transforms and Perez’ Barycenter
Shenoy’s paper published in this Proceedings of WUPES 2018 introduces an operator that gives instructions how to compute an expected value in the Dempster-Shafer theory of evidence. Up to now, there ...
Employing Bayesian Networks for Subjective Well-being Prediction
Švorc, Jan; Vomlel, Jiří
2018 - English
This contribution aims at using Bayesian networks for modelling the relations between the individual subjective well-being (SWB) and the individual material situation. The material situation is approximated by subjective measures (perceived economic strain, subjective evaluation of the income relative to most people in the country and to own past) and objective measures (household’s income, material deprivation, financial problems and housing defects). The suggested Bayesian network represents the relations among SWB and the variables approximating the material situation. The structure is established based on the expertise gained from literature, whereas the parameters are learnt based on empirical data from 3rd edition of European Quality of Life Study for the Czech Republic, Hungary, Poland and Slovakia conducted in 2011. Prediction accuracy of SWB is tested and compared with two benchmark models whose structures are learnt using Gobnilp software and a greedy algorithm built in Hugin software. SWB prediction accuracy of the expert model is 66,83%, which is significantly different from no information rate of 55,16%. It is slightly lower than the two machine learnt benchmark models.
Keywords:
Subjective well-being; Bayesian networks
Fulltext is available at external website.
Employing Bayesian Networks for Subjective Well-being Prediction
This contribution aims at using Bayesian networks for modelling the relations between the individual subjective well-being (SWB) and the individual material situation. The material situation is ...
Representations of Bayesian Networks by Low-Rank Models
Tichavský, Petr; Vomlel, Jiří
2018 - English
Conditional probability tables (CPTs) of discrete valued random variables may achieve high dimensions and Bayesian networks defined as the product of these CPTs may become intractable by conventional methods of BN inference because of their dimensionality. In many cases, however, these probability tables constitute tensors of relatively low rank. Such tensors can be written in the so-called Kruskal form as a sum of rank-one components. Such representation would be equivalent to adding one artificial parent to all random variables and deleting all edges between the variables. The most difficult task is to find such a representation given a set of marginals or CPTs of the random variables under consideration. In the former case, it is a problem of joint canonical polyadic (CP) decomposition of a set of tensors. The latter fitting problem can be solved in a similar manner. We apply a recently proposed alternating direction method of multipliers (ADMM), which assures that the model has a probabilistic interpretation, i.e., that all elements of all factor matrices are nonnegative. We perform experiments with several well-known Bayesian networks.\n\n
Keywords:
canonical polyadic tensor decomposition; conditional probability tables; marginal probability tables
Fulltext is available at external website.
Representations of Bayesian Networks by Low-Rank Models
Conditional probability tables (CPTs) of discrete valued random variables may achieve high dimensions and Bayesian networks defined as the product of these CPTs may become intractable by conventional ...
Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains
Sladký, Karel
2018 - English
In this note we consider continuous-time Markov decision processes with finite state and actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential utility function with a given risk sensitivitycoefficient (so-called risk-sensitive models). If the risk sensitivity coefficient equals zero (risk-neutral case) we arrive at a standard Markov decision process. Then we can easily obtain necessary and sufficient mean reward optimality conditions and the variability can be evaluated by the mean variance of total expected rewards. For the risk-sensitive case, i.e. if the risk-sensitivity coefficient is non-zero, for a given value of the risk-sensitivity coefficient we establish necessary and sufficient optimality conditions for maximal (or minimal) growth rate of expectation of the exponential utility function, along with mean value of the corresponding certainty equivalent. Recall that in this case along with the total reward also its higher moments are taken into account.
Keywords:
continuous-time Markov decision chains; exponential utility functions; certainty equivalent; mean-variance optimality; connections between risk-sensitive and risk-neutral optimality
Fulltext is available at external website.
Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains
In this note we consider continuous-time Markov decision processes with finite state and actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential ...
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