Vera Hofer

Drift mining in data

A novel statistical methodology for analysing population drift in classification is introduced. Drift denotes changes in the joint distribution of explanatory variables and class labels over time. It entails the deterioration of a classifiers performance and requires the optimal decision boundary to be adapted after some time. However, in the presence of verification latency a re-estimation of the classification model is impossible, since in such a situation only recent unlabelled data are available, and the true corresponding labels only become known after some lapse in time. For this reason a novel drift mining methodology is presented which aims at detecting changes over time. It allows us either to understand evolution in the data from an ex-post perspective or, ex-ante, to anticipate changes in the joint distribution. The proposed drift mining technique assumes that the class priors change by a certain factor from one time point to the next, and that the conditional distributions do not change within this time period. Thus, the conditional distributions can be estimated at a time where recent labelled data are available. In subsequent periods the unconditional distribution can be expressed as a mixture of the conditional distributions, where the mixing proportions are equal to the class priors. However, as the unconditional distributions can also be estimated from new unlabelled data, they can then be compared to the mixture representation by means of least-squares criteria. This allows for easy and fast estimation of the changes in class prior values in the presence of verification latency. The usefulness of this drift mining approach is demonstrated using a real-world dataset from the area of credit scoring. Highlights? A novel statistical methodology for analysing population drift in classification is presented. ? Drift mining that aims at modelling changes in distributions over time is introduced. ? A model on global drift that addresses a change in class prior is introduced.

Classification in Presence of Drift and Latency

Changes in underlying distributions over time are a challenging problem in supervised learning. While this problem of drift is subject to an increasing effort in research, some definitions required for proper distinction of types of drift remain ambiguous. Furthermore, the approaches discussed in literature so far require new, labelled data for incremental model updates. However, there are domains in which such data is scarce or only available with a considerable time lag, a so-called verification latency. This issues are addressed in this paper: First, the different notations used in literature are related, and an overview over types of drift is given. Second, following the change mining paradigm, explicit models of drift are introduced. These drift models can be employed when actual, labelled data is scarce or not available at all, as they allow to anticipate changes in distributions over time. Third, an exemplary drift-adaptive learning strategy that employs such a drift model is presented: Using an expectation-maximisation algorithm, a mixture of subpopulations is tracked. As a result, the classification model can be updated using solely new, unlabelled data.

Educational effects in an experiment with the management game SINTO-Market

This paper examines how the educational background influences the performance of managers’ strategies. The research is based on data collected by an experiment with the management game SINTO-Market. This management game puts the players in a competitive situation in the branded food product sector, within which the subjects take over the role of the managers who have to find out the most successful strategy. From experimental research with this management game we will draw some interesting conclusions about human behavior in complex economic decision-making situations. To investigate educational effects the management game SINTO-Market was performed with students of different educational levels 17 times. The results show some significant differences between graduates and undergraduates.

Adapting a classification rule to local and global shift when only unlabelled data are available

For evolving populations the training data and the test data need not follow the same distribution. Thus, the performance of a prediction model will deteriorate over the course of time. This requires the re-estimation of the prediction model after some time. However, in many applications e.g. credit scoring, new labelled data are not available for re-estimation due to verification latency, i.e. label delay. Thus, methods which enable a prediction model to adapt to distributional changes by using only unlabelled data are highly desirable. A shift adaptation method for binary classification is presented here. The model is based on mixture distributions. The conditional feature distributions are determined at the time where labelled data are available, and the unconditional feature distribution is determined at the time where new unlabelled data are accessible. These mixture distributions provide information on the old and the new positions of subpopulations. A transition model then describes how the subpopulations of each class have drifted to form the new unconditional feature distribution. Assuming that the conditional distributions are reorganised using a minimum of energy, a two-step estimation procedure results. First, for a given class prior distribution the transfer of probability mass is estimated such that the energy required to obtain the new unconditional distribution by a local transfer of the old conditional distributions is a minimum. Since the optimal solution of the resulting transportation problem measures the distance between the old and the new distributions, the change of the class prior distribution is found in a second step by solving the transportation problem for varying class prior distributions and selecting the value for which the objective function is a minimum. Using the solution of the transportation problem and the component parameters of the unconditional feature distribution, the new conditional feature distribution can be determined. This thus allows for a shift adaptation of the classification rule. The performance of the proposed model is investigated using a large real-world dataset on default rates in Danish companies. The results show that the shift adaptation improves classification results.

Impact of Geometric and Petrographic Characteristics on the Variability of LA Test Values for Railway Ballast

The Los Angeles test is one of the few mechanical test methods that provides information on the quality of railway ballast. However, the Los Angeles value is subject to large variability. Since important economic decisions depend on this value, the reasons for its variability are investigated. An extensive series of tests using four types of rock as well as an in-depth analysis of particle geometry and petrography are carried out. The impact of particle characteristics on the test results is investigated. The deviation of the petrographic composition within a given sample turns out to have a considerable impact on the Los Angeles test results, whereas the influence of the respective deviation of particle geometry is relatively small. The latter effect only comes into play in connection with petrographically homogeneous rock types. The distribution of the geometric features is similar in almost all of the rock types investigated. Due to the large deviation in particle shape and angularity, the sample mass of 10 kg (as provided in the standards EN 1097-2 and EN 13450) is not found to be representative. The necessary number of test repetitions in order to exclude the effect of deviation of particle geometry is estimated. The one result parameter according to the standard, the Los Angeles value, does not allow for discriminating between the amount of abrasion and the fragmentation occurring during the test. An additional result parameter for the estimation of the fragmentation rate is therefore proposed.

A bivariate Sarmanov regression model for count data with generalised Poisson marginals

We present a bivariate regression model for count data that allows for positive as well as negative correlation of the response variables. The covariance structure is based on the Sarmanov distribution and consists of a product of generalised Poisson marginals and a factor that depends on particular functions of the response variables. The closed form of the probability function is derived by means of the moment-generating function. The model is applied to a large real dataset on health care demand. Its performance is compared with alternative models presented in the literature. We find that our model is significantly better than or at least equivalent to the benchmark models. It gives insights into influences on the variance of the response variables.

On stabilizing volatile product returns

As input flows of secondary raw materials show high volatility and tend to behave in a chaotic way, the identification of the main drivers of the dynamic behavior of returns plays a crucial role. Based on a stylized production-recycling system consisting of a set of nonlinear difference equations, we explicitly derive parameter constellations where the system will or will not converge to its equilibrium. Using a constant elasticity of substitution production function, the model is then extended to enable coverage of real world situations. Using waste paper as a reference raw material, we empirically estimate the parameters of the system. By using these regression results, we are able to show that the equilibrium solution is a Lyapunov unstable saddle point. This implies that the system is sensitive on initial conditions that will hence impede the predictability of product returns. Small variations of production input proportions could however stabilize the whole system.

A hierarchical tree layout algorithm with an application to corporate management in a change process

This work presents a hierarchical tree layout algorithm based on iterative rearrangement of subtrees. Using a greedy heuristic, all subtrees of a common parent are rearranged into a forest such that gaps between them are minimized. This heuristic is used to build a rearranged tree from bottom-up, starting with forests of the single leafs, and ending with the complete tree. Different cost measures for arrangement operations are discussed, which are based on the shape of a subtree. This shape can be characterized by the subtrees leftmost and rightmost vertices, which determine how gapless this subtree can be combined with another one. The layout algorithm is used to display an organisational hierarchy. Such a hierarchical layout aids leadership when organisational structures are complex. In particular, it can be used to monitor the performance of organisational units undergoing change, e.g. restructuring. This improves the effectiveness of leadership instruments.

Positioning of new brands in an experiment

This paper deals with an experimental investigation of positioning new brands. For this purpose, a management game was carried out with students. The brands introduced in the cause of the game were analysed in respect to their positions in a two-dimensional feature space. We try to find out which of the two strategies, niche policy and imitation, is more frequently used in complex decision situations and if there is a difference in profits. Furthermore, we want to find out, whether differences of prices and advertising exist in our experiment depending on the positioning strategy used.

Determination of tolerance limits for the reliability of semiconductor devices using longitudinal data.

Design and production of semiconductor devices for the automotive industry are characterized by high reliability requirements, such that the proper functioning of these devices is ensured over the whole specified lifetime. Therefore, manufacturers let their products undergo extensive testing procedures that simulate the tough requirements their products have to withstand. Such tests typically are highly accelerated, to test the behavior of the products over the whole lifetime. In case of drift of electrical parameters, manufacturers then need to find appropriate tolerance limits for their final electrical product tests, such that the proper functioning of their devices over the whole specified lifetime is ensured. In this study, we present a statistical model for the determination of tolerance limits that minimize yield loss. The model considers longitudinal measurements of continuous features, based on censored data from stress tests. The tolerance limits are derived from multivariate distributions where the dependence structure is described by different copulas. Based on extensive numerical testing, we are able to provide insights into the properties of our model for different drift behaviors of the devices.