Search

We consider the problem of finding the transition rates of a continuous-time homogeneous Markov chain under the empirical condition that the state changes at most once during a time interval of unit length. It is proven that this conditional embedding approach results in a unique intensity matrix for a transition matrix with non-zero diagonal entries. Hence, the presented conditional embedding approach has the merit to avoid the identification phase as well as regularization for the embedding problem. The resulting intensity matrix is compared to the approximation for the Markov generator found by Jarrow.

In previous research the importance of both Markov and semi-Markov models in manpower planning is highlighted. Maintainability and attainability of personnel structures for different types of personnel strategies (i.e. under control by promotion and control by recruitment) is extensively investigated for various types of Markov models (homogeneous as well as non-homogeneous). Semi-Markov models are extensions of Markov models that account for length of stay in the states. Less attention is paid to the study of maintainability and attainability for semi-Markov models. Although, some interesting maintainability results were obtained for non-homogeneous semi-Markov models. The current paper focuses on discrete-time homogeneous semi-Markov models, and explores concepts of maintainable and attainable personnel structures in this setting. Various types of personnel strategies are presented for which the set of maintainable and attainable structures is examined. The obtained insights can easily be converted to various application domains.

The embedding problem of Markov chains is a long standing problem where a given stochastic matrix is examined as the 1-step transition matrix of some continuous-time homogeneous Markov chain (CTHMC). This problem boils down to characterizing the empirical transition matrix P as the exponential of some matrix Q with all non-negative off-diagonal entries and zero row-sums, called an intensity matrix. If such a Q exists, P is said to be embeddable. It turns out that the embedding problem is a formidable one in a number of respects. First, P may not be embeddable. In that case, a regularization algorithm can be used to find an intensity matrix Q for which ||P - exp(Q)|| is minimized. Next, no embeddability criteria in terms of the matrix elements, which are easily verifiable in practice, seem at hand when the number of states exceeds 3. Lastly, for an embeddable P, there may not be a unique solution to the equation exp(Q) = P in the set of intensity matrices. The identification aspect of the embedding problem deals with the selection of the suitable intensity matrix reflecting the nature of the system under study. We propose the conditional embedding approach where the empirical 1-step transition matrix P corresponds with the conditional 1-step transition matrix of the CTHMC given the event that at most one jump has occurred during a time interval of unit length. For a Markov model the unit time interval can be defined in such a way that the empirical 1-step transition matrix meets this condition. Moreover, this condition is inherent in some applications. For example, in credit rating migration models the credit ratings are typically based on slowly varying characteristics, such that they do not tend to change more than once within the baseline time interval (e.g. a quarter). We found that, regardless the number of states, exactly one intensity matrix solves this conditional embedding problem when Pii > 0 for all i. Our approach results in an easy embeddability criterium and does not require identification neither regularization.

Many real-world classification problems are cost-sensitive in nature, such that the misclassification costs vary between data instances. Cost-sensitive learning adapts classification algorithms to account for differences in misclassification costs. Stacking is an ensemble method that uses predictions from several classifiers as the training data for another classifier, which in turn makes the final classification decision. While a large body of empirical work exists where stacking is applied in various domains, very few of these works take the misclassification costs into account. In fact, there is no consensus in the literature as to what cost-sensitive stacking is. In this paper we perform extensive experiments with the aim of establishing what the appropriate setup for a cost-sensitive stacking ensemble is. Our experiments, conducted on twelve datasets from a number of application domains, using real, instance-dependent misclassification costs, show that for best performance, both levels of stacking require cost-sensitive classification decision.

Many real-world classification problems are cost-sensitive in nature, such that the misclassification costs vary between data instances. Cost-sensitive learning adapts classification algorithms to account for differences in misclassification costs. Stacking is an ensemble method that uses predictions from several classifiers as the training data for another classifier, which in turn makes the final classification decision. While a large body of empirical work exists where stacking is applied in various domains, very few of these works take the misclassification costs into account. In fact, there is no consensus in the literature as to what cost-sensitive stacking is. In this paper we perform extensive experiments with the aim of establishing what the appropriate setup for a cost-sensitive stacking ensemble is. Our experiments, conducted on twelve datasets from a number of application domains, using real, instance-dependent misclassification costs, show that for best performance, both levels of stacking require cost-sensitive classification decision.

In previous research the importance of both Markov and semi-Markov models in manpower planning is highlighted. Maintainability of population structures for different types of personnel strategies (i.e. under control by promotion and control by recruitment) were extensively investigated for various types of Markov models (homogeneous as well as non-homogeneous). Semi-Markov models are extensions of Markov models that account for duration of stay in the states. Less attention is paid to the study of maintainability for semi-Markov models. Although, some interesting maintainability results were obtained for non-homogeneous semi-Markov models. The current paper focuses on discrete-time homogeneous semi-Markov models, and explores the concept of maintainable population structures in this setting. In particular, a new concept of maintainability is introduced, the so-called State Reunion maintainability. It is shown that this concept of maintainability is closely related to maintainability for non-homogeneous Markov chains.

Uplift modeling is the subfield of causal inference that focuses on the ranking of individuals by their treatment effects. Uplift models are typically evaluated using Qini curves or Qini scores. While intuitive, the theoretical grounding for Qini in the literature is limited, and the mathematical connection to the well-understood Receiver Operating Characteristic ROC is unclear. In this paper, we first introduce the ROCini, an uplift evaluation metric similar in intuition to Qini but derived from the well understood ROC. Using Ordinal Dominance Graph theory, the ROCini is extended to the pROCini, a mathematically better behaved metric that facilitates theoretical analysis. Exploiting the theoretical properties of pROCini, confidence bounds are derived. Finally, the empirical performance of ROCini and pROCini is validated in a simulation study.

Markov chains are commonly used to model transitions in a system partitioned into categories. In manpower planning models these categories are, for example, job levels or grades in the firm under study. Building a Markov model starts with selecting its states that are assumed to be homogeneous; i.e. the system units in a same state have similar transition probabilities. For systems where the transitions among the categories depend on the duration of stay in the outgoing categories, previous work considered Markov models where the states are subdivisions of the categories into duration of stay intervals, and the more complex semi-Markov models. The present work investigates alternative Markov models for systems where the categories have transition probabilities depending on the duration of stay by selecting the states in different ways: state selection by duration intervals and state selection by duration values. The resulting Markov models are compared based on the likelihood of a set of panel data given the model. For a system with two categories, we prove that the model with states defined by duration values has a better maximum likelihood fit than the base model having the initial categories as states, while this is not the case for the model with states defined by duration intervals under conditions that seem realistic in practice. Although the duration-interval approach is considered in previous studies, the likelihood-comparison is less in favor of this model.

This article studies the relationships of different strategic human resource alignment mechanisms and firms productivity, by using data on 610 Belgian medium-sized and large enterprises. The results show that efforts to achieve a fit between strategic objectives and human resource practices are associated with higher productivity, regardless the alignment mode. Furthermore, it is found that organizational capacities to adapt to changing circumstances and employee remuneration are important components in understanding the link between strategic human resource fit mechanisms and firm productivity.