Improved customer choice predictions using ensemble methods

In this paper various ensemble learning methods from machinelearning and statistics are considered and applied to the customerchoice modeling problem. The application of ensemble learningusually improves the prediction quality of flexible models likedecision trees and thus leads to improved predictions. We giveexperimental results for two real-life marketing datasets usingdecision trees, ensemble versions of decision trees and thelogistic regression model, which is a standard approach for thisproblem. The ensemble models are found to improve upon individualdecision trees and outperform logistic regression.Next, an additive decomposition of the prediction error of amodel, the bias/variance decomposition, is considered. A modelwith a high bias lacks the flexibility to fit the data well. Ahigh variance indicates that a model is instable with respect todifferent datasets. Decision trees have a high variance componentand a low bias component in the prediction error, whereas logisticregression has a high bias component and a low variance component.It is shown that ensemble methods aim at minimizing the variancecomponent in the prediction error while leaving the bias componentunaltered. Bias/variance decompositions for all models for bothcustomer choice datasets are given to illustrate these concepts.brand choice;data mining;boosting;choice models;Bias/Variance decomposition;Bagging;CART;ensembles

Modeling brand choice using boosted and stacked neural networks

The brand choice problem in marketing has recently been addressed with methods from computational intelligence such as neural networks. Another class of methods from computational intelligence, the so-called ensemble methods such as boosting and stacking have never been applied to the brand choice problem, as far as we know. Ensemble methods generate a number of models for the same problem using any base method and combine the outcomes of these different models. It is well known that in many cases the predictive performance of ensemble methods significantly exceeds the predictive performance of the their base methods. In this report we use boosting and stacking of neural networks and apply this to a scanner dataset that is a benchmark dataset in the marketing literature. Using these methods, we find a significant improvement in predictive performance on this dataset.

Boosting the accuracy of hedonic pricing models

Hedonic pricing models attempt to model a relationship between object attributes andthe object's price. Traditional hedonic pricing models are often parametric models that sufferfrom misspecification. In this paper we create these models by means of boosted CARTmodels. The method is explained in detail and applied to various datasets. Empirically,we find substantial reduction of errors on out-of-sample data for two out of three datasetscompared with a stepwise linear regression model. We interpret the boosted models by partialdependence plots and relative importance plots. This reveals some interesting nonlinearitiesand differences in attribute importance across the model types.pricing;marketing;data mining;conjoint analysis;ensemble learning;gradient boosting;hedonic pricing

Age effects on visual perceptual decisions of ambiguous stimuli

The brain is constantly making choices while interpreting the environment. To understand how age affects visual decision-making, we investigated age-related changes in spontaneous percept switches and percept choices during intermittent presentations of ambiguous stimuli. Spontaneous switches can be triggered by different visual stimuli, such as monocular ambiguous visual stimuli or binocular rivalry images. An ambiguous visual stimulus has multiple and equally plausible interpretations, such as the bi-stable rotating sphere. In such a sphere two transparently moving dots are moving in opposite directions and due to structure-from-motion the stimulus is perceived as a 3-dimensional rotating sphere moving in one or the opposite direction. During binocular rivalry experiments, the left and the right eye receive different input simultaneously. During stimulus-presentation only one of the two presented images is perceived, and the other image is suppressed. Dominance durations (the time a percept remains dominant) are typically in the order of several seconds. In this study, 52 observers ranging from 17 to 72 years old, viewed bi-stable rotating spheres and binocular rivalry stimuli and were forced to make a choice between two percepts. Stimuli were presented continuously for 2 minutes or intermittently for 1 second, with a range of inter-stimulus intervals (0.125 - 2 seconds). The results show that dominance durations during continuous viewing are longer for older subjects for the binocular rivalry stimulus but not for the bi-stable rotating spheres. For the intermittent stimulus presentation, perceptual alternations decrease at an older age in binocular rivalry, while for the bi-stable rotating sphere there are only differences in perceptual alternations among different age groups at a short off-duration. Based on these results, we conclude that the effect of age is not a general phenomenon for ambiguous stimuli. Visual decisions are more stimulus dependent, rather than experience dependent

Modulating basal ganglia and cerebellar activity to suppress parkinsonian tremor

Despite extensive research, the detailed pathophysiology of the parkinsonian tremor is still unknown. It has been hypothesized that the generation of parkinsonian tremor is related to abnormal activity within the basal ganglia. The cerebello-thalamic-cortical loop has been suggested to indirectly contribute to the expression of parkinsonian tremor. However, the observed tremor-related hyperactivity in the cerebellar loop may have a compensatory rather than a causal role in Parkinson's disease (PD) by preventing tremor from spilling over into voluntary movement. Furthermore, observed overactivation in cerebellar loops has also been associated with a higher ability of PD patients to perform repetitive movements that are cued by auditory or visual stimuli, suggesting that rhythmic synchronization with an auditory timekeeper can be achieved in the absence of intact basal ganglia function. Deep brain stimulation (DBS) in the subthalamic nucleus (STN) is currently an accepted treatment for advanced PD that may significantly improve motor complications and reduce tremor. While DBS directly influences neuronal activity patterns in basal ganglia loops, it may be expected that modulation of the cerebellar loops have an additional effect on parkinsonian tremor if both loops are involved in tremor generation and expression.\ud The aim of this pilot study is to test whether the combination of DBS and auditory cueing has an enhanced effect on tremor reduction. Therefore, in a group of seven PD patients receiving STN-DBS, tremor occurrence in both hands and both feet was sequentially tested while performing repetitive movements cued by an auditory signal. The frequency of the auditory cues ranged from 1.6 Hz, which is within the range of frequencies that can be found during normal movements, and 4.8 Hz, which is near the average PD tremor frequency. Movements and tremor were registered by inertial sensors attached to the hands and feet. The Chi-square test was used to compare the occurrence of tremor in any of the extremities for the different cueing frequencies and DBS “on” and “off”.\ud Compared to the resting condition and the performance of self-paced hand or foot movements, the number of extremities showing tremor was significantly reduced under external cueing conditions when stimulation was “on”. With DBS “off”, only the lower cueing frequencies (1.6 and 3.2 Hz) provided a beneficial effect.\ud From the results it may be hypothesized that modulation of the pathological patterns in basal ganglia (by DBS) and cerebellar activity (by auditory cueing) provides enhanced suppression of action tremor in PD

Improved customer choice predictions using ensemble methods

In this paper various ensemble learning methods from machine learning and statistics are considered and applied to the customer choice modeling problem. The application of ensemble learning usually improves the prediction quality of flexible models like decision trees and thus leads to improved predictions. We give experimental results for two real-life marketing datasets using decision trees, ensemble versions of decision trees and the logistic regression model, which is a standard approach for this problem. The ensemble models are found to improve upon individual decision trees and outperform logistic regression. Next, an additive decomposition of the prediction error of a model, the bias/variance decomposition, is considered. A model with a high bias lacks the flexibility to fit the data well. A high variance indicates that a model is instable with respect to different datasets. Decision trees have a high variance component and a low bias component in the prediction error, whereas logistic regression has a high bias component and a low variance component. It is shown that ensemble methods aim at minimizing the variance component in the prediction error while leaving the bias component unaltered. Bias/variance decompositions for all models for both customer choice datasets are given to illustrate these concepts

Generating artificial data with monotonicity constraints

The monotonicity constraint is a common side condition imposed on modeling problems as diverse as hedonic pricing, personnel selection and credit rating. Experience tells us that it is not trivial to generate artificial data for supervised learning problems when the monotonicity constraint holds. Two algorithms are presented in this paper for such learning problems. The first one can be used to generate random monotone data sets without an underlying model, and the second can be used to generate monotone decision tree models. If needed, noise can be added to the generated data. The second algorithm makes use of the first one. Both algorithms are illustrated with an example