Adaptive Conformal Inference (ACI) provides finite-sample coverage guarantees, enhancing the prediction reliability under non-exchangeability. This study demonstrates that these desirable properties of ACI do not require the use of Conformal Predictors (CP). We show that the guarantees hold for the broader class of confidence predictors, defined by the requirement of producing nested prediction sets, a property we argue is essential for meaningful confidence statements. We empirically investigate the performance of Non-Conformal Confidence Predictors (NCCP) against CP when used with ACI on non-exchangeable data. In online settings, the NCCP offers significant computational advantages while maintaining a comparable predictive efficiency. In batch settings, inductive NCCP (INCCP) can outperform inductive CP (ICP) by utilising the full training dataset without requiring a separate calibration set, leading to improved efficiency, particularly when the data are limited. Although these initial results highlight NCCP as a theoretically sound and practically effective alternative to CP for uncertainty quantification with ACI in non-exchangeable scenarios, further empirical studies are warranted across diverse datasets and predictors. • ACI ensures finite-sample coverage guarantees without conformal predictors. • NCCPs can match or exceed CP performance on non-exchangeable data. • Inductive NCCP avoids data splitting, improving predictive efficiency. • NCCP’s online benefit is speed; in batch settings, it’s data usage. • Nested prediction sets are vital for meaningful confidence predictions.

Abstract Artificial Intelligence (AI) methods are an integral part of modern decision support systems. The best-performing predictive models used in AI-based decision support systems lack transparency. Explainable Artificial Intelligence (XAI) aims to create AI systems that can explain their rationale to human users. Local explanations in XAI can provide information about the causes of individual predictions in terms of feature importance. However, a critical drawback of existing local explanation methods is their inability to quantify the uncertainty associated with a feature’s importance. This paper introduces an extension of a feature importance explanation method, Calibrated Explanations, previously only supporting classification, with support for standard regression and probabilistic regression, i.e., the probability that the target is below an arbitrary threshold. The extension for regression keeps all the benefits of Calibrated Explanations, such as calibration of the prediction from the underlying model with confidence intervals, uncertainty quantification of feature importance, and allows both factual and counterfactual explanations. Calibrated Explanations for regression provides fast, reliable, stable, and robust explanations. Calibrated Explanations for probabilistic regression provides an entirely new way of creating probabilistic explanations from any ordinary regression model, allowing dynamic selection of thresholds. The method is model agnostic with easily understood conditional rules. An implementation in Python is freely available on GitHub and for installation using both and , making the results in this paper easily replicable.

Automatic checkout systems are designed to predict a complete shopping receipt using an image from the checkout area. These systems require high classification accuracy across numerous classes and must operate in real-time, despite domain differences between training data and real-world conditions. Building on recent advancements, we propose a method that outperforms current solutions and can be applied in real-time in automatic checkout systems. Our method leverages the Segment Anything Model to extract high-quality masks from lab product images, which are then transformed into synthetic checkout images and adapted to the real domain using contrastive unpaired translation. We train a product recognition model with data augmentation, named SCA+Y8, and further improve it through fine-tuning with pseudo-labels from unlabeled checkout images, resulting in an improved model called SCAFT+Y8. SCAFT+Y8 achieves a great increase in state-of-the-art performance, with an average receipt classification accuracy of 97.58%, and shows strong performance in smaller models, indicating the potential for deployment on low-cost edge devices.

While local explanations for AI models can offer insights into individual predictions, such as feature importance, they are plagued by issues like instability. The unreliability of feature weights, often skewed due to poorly calibrated ML models, deepens these challenges. Moreover, the critical aspect of feature importance uncertainty remains mostly unaddressed in Explainable AI (XAI). The novel feature importance explanation method presented in this paper, called Calibrated Explanations (CE), is designed to tackle these issues head-on. Built on the foundation of Venn-Abers, CE not only calibrates the underlying model but also delivers reliable feature importance explanations with an exact definition of the feature weights. CE goes beyond conventional solutions by addressing output uncertainty. It accomplishes this by providing uncertainty quantification for both feature weights and the model’s probability estimates. Additionally, CE is model-agnostic, featuring easily comprehensible conditional rules and the ability to generate counterfactual explanations with embedded uncertainty quantification. Results from an evaluation with 25 benchmark datasets underscore the efficacy of CE, making it stand as a fast, reliable, stable, and robust solution.

Abstract Automatic recognition of grocery products can be used to improve customer flow at checkouts and reduce labor costs and store losses. Product recognition is, however, a challenging task for machine learning-based solutions due to the large number of products and their variations in appearance. In this work, we tackle the challenge of fine-grained product recognition by first extracting a large dataset from a grocery store containing products that are only differentiable by subtle details. Then, we propose a multimodal product recognition approach that uses product images with extracted OCR text from packages to improve fine-grained recognition of grocery products. We evaluate several image and text models separately and then combine them using different multimodal models of varying complexities. The results show that image and textual information complement each other in multimodal models and enable a classifier with greater recognition performance than unimodal models, especially when the number of training samples is limited. Therefore, this approach is suitable for many different scenarios in which product recognition is used to further improve recognition performance. The dataset can be found at https://github.com/Tubbias/finegrainocr .

The retail sector is undergoing an apparent digital transformation that completely revolutionises shopping operations. To stay competitive, retailer stakeholders are forced to rethink and improve their business models to provide an attractive personalised experience to consumers. The self-service checkout process is at the heart of this transformation and should be designed to identify the products accurately and detect any possible anomalous behaviour. In this paper, we introduce a product verification system based on OCR classification and Mondrian conformal prediction . The proposed system includes three components: OCR reading, text classification and product verification. By using image data from existing grocery stores, the system can detect anomalies with high performance, even when there is partial text information on the products. This makes the system applicable for reducing shrinkage loss (caused, for example, by employee theft or shoplifting) in grocery stores by identifying fraudulent behaviours such as barcode switching and miss-scan. Additionally, OCR reading with NLP classification shows that it is in itself a powerful classifier of products.

Tools for understanding and explaining complex predictive models are critical for user acceptance and trust. One such tool is rule extraction, i.e., approximating opaque models with less powerful but interpretable models. Pedagogical (or black-box) rule extraction, where the interpretable model is induced using the original training instances, but with the predictions from the opaque model as targets, has many advantages compared to the decompositional (white-box) approach. Most importantly, pedagogical methods are agnostic to the kind of opaque model used, and any learning algorithm producing interpretable models can be employed for the learning step. The pedagogical approach has, however, one main problem, clearly limiting its utility. Specifically, while the extracted models are trained to mimic the opaque, there are absolutely no guarantees that this will transfer to novel data. This potentially low test set fidelity must be considered a severe drawback, in particular when the extracted models are used for explanation and analysis. In this paper, a novel approach, solving the problem with test set fidelity by utilizing the conformal prediction framework, is suggested for extracting interpretable regression models from opaque models. The extracted models are standard regression trees, but augmented with valid prediction intervals in the leaves. Depending on the exact setup, the use of conformal prediction guarantees that either the test set fidelity or the test set accuracy will be equal to a preset confidence level, in the long run. In the extensive empirical investigation, using 20 publicly available data sets, the validity of the extracted models is demonstrated. In addition, it is shown how normalization can be used to provide individualized prediction intervals, thus providing highly informative extracted models.

In many predictive modeling scenarios, the production set inputs that later will be used for the actual prediction is available and could be utilized in the modeling process. In fact, many predictive models are generated with an existing production set in mind. Despite this, few approaches utilize this information in order to produce models optimized on the production set at hand. If these models need to be comprehensible, the oracle coaching framework can be applied, often resulting in interpretable models, e.g., decision trees and rule sets, with accuracies on par with opaque models like neural networks and ensembles, on the specific production set. In oracle coaching, a strong but opaque predictive model is used to label instances, including the production set, which are later learned by a weaker but interpretable model. In this paper, oracle coaching is, for the first time, used for improving the calibration of probabilistic predictors. More specifically, setups where oracle coaching are combined with the techniques Platt scaling, isotonic regression and Venn-Abers are suggested and evaluated for calibrating probability estimation trees (PETs). A key contribution is the setup designs ensuring that the oracle-coached PETs, that per definition utilize knowledge about production data, remain well-calibrated. In the experimentation, using 23 publicly available data sets, it is shown that oracle-coached models are not only more accurate, but also significantly better calibrated, compared to standard induction. Interestingly enough, this holds both for the uncalibrated PETs, and for all calibration techniques evaluated, i.e., Platt scaling, isotonic regression and Venn-Abers. As expected, all three external techniques significantly improved the calibration of the original PETs. Finally, an outright comparison between the three external calibration techniques showed that Venn-Abers significantly outperformed the alternatives in most setups.

Managing campaigns and promotions effectively is vital for the fashion retail industry. While retailers invest a lot of money in campaigns, customer retention is often very low. At innovative retailers, data-driven methods, aimed at understanding and ultimately optimizing campaigns are introduced. In this application paper, machine learning techniques are employed to analyze data about campaigns and promotions from a leading Swedish e-retailer. More specifically, predictive modeling is used to forecast the profitability and activation of campaigns using different kinds of promotions. In the empirical investigation, regression models are generated to estimate the profitability, and classification models are used to predict the overall success of the campaigns. In both cases, random forests are compared to individual tree models. As expected, the more complex ensembles are more accurate, but the usage of interpretable tree models makes it possible to analyze the underlying relationships, simply by inspecting the trees. In conclusion, the accuracy of the predictive models must be deemed high enough to make these data-driven methods attractive.

Interpretability is recognized as a key property of trustworthy predictive models. Only interpretable models make it straightforward to explain individual predictions, and allow inspection and analysis of the model itself. In real-world scenarios, these explanations and insights are often needed for a specific batch of predictions, i.e., a production set. If the input vectors for this production set are available when generating the predictive model, a methodology called oracle coaching can be used to produce highly accurate and interpretable models optimized for the specific production set. In this paper, oracle coaching is, for the first time, combined with the conformal prediction framework for predictive regression. A conformal regressor, which is built on top of a standard regression model, outputs valid prediction intervals, i.e., the error rate on novel data is bounded by a preset significance level, as long as the labeled data used for calibration is exchangeable with production data. Since validity is guaranteed for all conformal predictors, the key performance metric is the size of the prediction intervals, where tighter (more efficient) intervals are preferred. The efficiency of a conformal model depends on several factors, but more accurate underlying models will generally also lead to improved efficiency in the corresponding conformal predictor. A key contribution in this paper is the design of setups ensuring that when oracle coached regression trees, that per definition utilize knowledge about production data, are used as underlying models for conformal regressors, these remain valid. The experiments, using 20 publicly available regression data sets, demonstrate the validity of the suggested setups. Results also show that utilizing oracle-coached underlying models will generally lead to significantly more efficient conformal regressors, compared to when these are built on top of models induced using only training data.

Class labels output by standard decision trees are not very useful for making informed decisions, e.g., when comparing the expected utility of various alternatives. In contrast, probability estimation trees (PETs) output class probability distributions rather than single class labels. It is well known that estimating class probabilities in PETs by relative frequencies often lead to extreme probability estimates, and a number of approaches to provide more well-calibrated estimates have been proposed. In this study, a recent model-agnostic calibration approach, called Venn-Abers predictors is, for the first time, considered in the context of decision trees. Results from a large-scale empirical investigation are presented, comparing the novel approach to previous calibration techniques with respect to several different performance metrics, targeting both predictive performance and reliability of the estimates. All approaches are considered both with and without Laplace correction. The results show that using Venn-Abers predictors for calibration is a highly competitive approach, significantly outperforming Platt scaling, Isotonic regression and no calibration, with respect to almost all performance metrics used, independently of whether Laplace correction is applied or not. The only exception is AUC, where using non-calibrated PETs together with Laplace correction, actually is the best option, which can be explained by the fact that AUC is not affected by the absolute, but only relative, values of the probability estimates.

Successful use of probabilistic classification requires well-calibrated probability estimates, i.e., the predicted class probabilities must correspond to the true probabilities. In addition, a probabilistic classifier must, of course, also be as accurate as possible. In this paper, Venn predictors, and its special case Venn-Abers predictors, are evaluated for probabilistic classification, using random forests as the underlying models. Venn predictors output multiple probabilities for each label, i.e., the predicted label is associated with a probability interval. Since all Venn predictors are valid in the long run, the size of the probability intervals is very important, with tighter intervals being more informative. The standard solution when calibrating a classifier is to employ an additional step, transforming the outputs from a classifier into probability estimates, using a labeled data set not employed for training of the models. For random forests, and other bagged ensembles, it is, however, possible to use the out-of-bag instances for calibration, making all training data available for both model learning and calibration. This procedure has previously been successfully applied to conformal prediction, but was here evaluated for the first time for Venn predictors. The empirical investigation, using 22 publicly available data sets, showed that all four versions of the Venn predictors were better calibrated than both the raw estimates from the random forest, and the standard techniques Platt scaling and isotonic regression. Regarding both informativeness and accuracy, the standard Venn predictor calibrated on out-of-bag instances was the best setup evaluated. Most importantly, calibrating on out-of-bag instances, instead of using a separate calibration set, resulted in tighter intervals and more accurate models on every data set, for both the Venn predictors and the Venn-Abers predictors.

A conformal predictor outputs prediction regions, for classification label sets. The key property of all conformal predictors is that they are valid, i.e., their error rate on novel data is bounded by a preset significance level. Thus, the key performance metric for evaluating conformal predictors is the size of the output prediction regions, where smaller (more informative) prediction regions are said to be more efficient. All conformal predictions rely on nonconformity functions, measuring the strangeness of an input-output pair, and the efficiency depends critically on the quality of the chosen nonconformity function. In this paper, three model-agnostic nonconformity functions, based on well-known loss functions, are evaluated with regard to how they affect efficiency. In the experimentation on 21 publicly available multi-class data sets, both single neural networks and ensembles of neural networks are used as underlying models for conformal classifiers. The results show that the choice of nonconformity function has a major impact on the efficiency, but also that different nonconformity functions should be used depending on the exact efficiency metric. For a high fraction of single-label predictions, a margin-based nonconformity function is the best option, while a nonconformity function based on the hinge loss obtained the smallest label sets on average.

Conformal prediction (CP) is a relatively new framework in which predictive models output sets of predictions with a bound on the error rate, i.e., the probability of making an erroneous prediction is guaranteed to be equal to or less than a predefined significance level. Label-conditional conforma l prediction (LCCP) is a specialization of the framework which gives a bound on the error rate for each individual class. For datasets with class imbalance, many learning algorithms have a tendency to predict the majority class more often than the expected relative frequency, i.e., they are biased in favor of the majority class. In this study, the class bias of standard and label-conditional conformal predictors is investigated. An empirical investigation on 32 publicly available datasets with varying degrees of class imbalance is presented. The experimental results show that CP is highly biased towards the majority class on imbalanced datasets, i.e., it can be expected to make a majority of its errors on the minority class. LCCP, on the other hand, is not biased towards the majority class. Instead, the errors are distributed between the classes almost in accordance with the prior class distribution.

In conformal prediction, predictive models output sets of predictions with a bound on the error rate. In classification, this translates to that the probability of excluding the correct class is lower than a predefined significance level, in the long run. Since the error rate is guaranteed, the most important criterion for conformal predictors is efficiency. Efficient conformal predictors minimize the number of elements in the output prediction sets, thus producing more informative predictions. This paper presents one of the first comprehensive studies where evolutionary algorithms are used to build conformal predictors. More specifically, decision trees evolved using genetic programming are evaluated as conformal predictors. In the experiments, the evolved trees are compared to decision trees induced using standard machine learning techniques on 33 publicly available benchmark data sets, with regard to predictive performance and efficiency. The results show that the evolved trees are generally more accurate, and the corresponding conformal predictors more efficient, than their induced counterparts. One important result is that the probability estimates of decision trees when used as conformal predictors should be smoothed, here using the Laplace correction. Finally, using the more discriminating Brier score instead of accuracy as the optimization criterion produced the most efficient conformal predictions.

Conformal prediction is a relatively new framework in which the predictive models output sets of predictions with a bound on the error rate, i.e., in a classification context, the probability of excluding the correct class label is lower than a predefined significance level. An investigation of the use of decision trees within the conformal prediction framework is presented, with the overall purpose to determine the effect of different algorithmic choices, including split criterion, pruning scheme and way to calculate the probability estimates. Since the error rate is bounded by the framework, the most important property of conformal predictors is efficiency, which concerns minimizing the number of elements in the output prediction sets. Results from one of the largest empirical investigations to date within the conformal prediction framework are presented, showing that in order to optimize efficiency, the decision trees should be induced using no pruning and with smoothed probability estimates. The choice of split criterion to use for the actual induction of the trees did not turn out to have any major impact on the efficiency. Finally, the experimentation also showed that when using decision trees, standard inductive conformal prediction was as efficient as the recently suggested method cross-conformal prediction. This is an encouraging results since cross-conformal prediction uses several decision trees, thus sacrificing the interpretability of a single decision tree.

In this paper, we introduce and evaluate a novel method, called random brains, for producing neural network ensembles. The suggested method, which is heavily inspired by the random forest technique, produces diversity implicitly by using bootstrap training and randomized architectures. More specifically, for each base classifier multilayer perceptron, a number of randomly selected links between the input layer and the hidden layer are removed prior to training, thus resulting in potentially weaker but more diverse base classifiers. The experimental results on 20 UCI data sets show that random brains obtained significantly higher accuracy and AUC, compared to standard bagging of similar neural networks not utilizing randomized architectures. The analysis shows that the main reason for the increased ensemble performance is the ability to produce effective diversity, as indicated by the increase in the difficulty diversity measure.

Conformal prediction is a new framework producing region predictions with a guaranteed error rate. Inductive conformal prediction (ICP) was designed to significantly reduce the computational cost associated with the original transductive online approach. The drawback of inductive conformal prediction is that it is not possible to use all data for training, since it sets aside some data as a separate calibration set. Recently, cross-conformal prediction (CCP) and bootstrap conformal prediction (BCP) were proposed to overcome that drawback of inductive conformal prediction. Unfortunately, CCP and BCP both need to build several models for the calibration, making them less attractive. In this study, focusing on bagged neural network ensembles as conformal predictors, ICP, CCP and BCP are compared to the very straightforward and cost-effective method of using the out-of-bag estimates for the necessary calibration. Experiments on 34 publicly available data sets conclusively show that the use of out-of-bag estimates produced the most efficient conformal predictors, making it the obvious preferred choice for ensembles in the conformal prediction framework.

Combining several ANNs into ensembles normally results in a very accurate and robust predictive models. Many ANN ensemble techniques are, however, quite complicated and often explicitly optimize some diversity metric. Unfortunately, the lack of solid validation of the explicit algorithms, at least for classification, makes the use of diversity measures as part of an optimization function questionable. The merits of implicit methods, most notably bagging, are on the other hand experimentally established and well-known. This paper evaluates a number of straightforward techniques for introducing implicit diversity in ANN ensembles, including a novel technique producing diversity by using ANNs with different and slightly randomized link structures. The experimental results, comparing altogether 54 setups and two different ensemble sizes on 30 UCI data sets, show that all methods succeeded in producing implicit diversity, but that the effect on ensemble accuracy varied. Still, most setups evaluated did result in more accurate ensembles, compared to the baseline setup, especially for the larger ensemble size. As a matter of fact, several setups even obtained significantly higher ensemble accuracy than bagging. The analysis also identified that diversity was, relatively speaking, more important for the larger ensembles. Looking specifically at the methods used to increase the implicit diversity, setups using the technique that utilizes the randomized link structures generally produced the most accurate ensembles.

While ensemble classifiers often reach high levels of predictive performance, the resulting models are opaque and hence do not allow direct interpretation. When employing methods that do generate transparent models, predictive performance typically h

Random forest is an often used ensemble technique, renowned for its high predictive performance. Random forests models are, however, due to their sheer complexity inherently opaque, making human interpretation and analysis impossible. This paper presents a method of approximating the random forest with just one decision tree. The approach uses oracle coaching, a recently suggested technique where a weaker but transparent model is generated using combinations of regular training data and test data initially labeled by a strong classifier, called the oracle. In this study, the random forest plays the part of the oracle, while the transparent models are decision trees generated by either the standard tree inducer J48, or by evolving genetic programs. Evaluation on 30 data sets from the UCI repository shows that oracle coaching significantly improves both accuracy and area under ROC curve, compared to using training data only. As a matter of fact, resulting single tree models are as accurate as the random forest, on the specific test instances. Most importantly, this is not achieved by inducing or evolving huge trees having perfect fidelity; a large majority of all trees are instead rather compact and clearly comprehensible. The experiments also show that the evolution outperformed J48, with regard to accuracy, but that this came at the expense of slightly larger trees.

Most predictive modeling techniques utilize all available data to build global models. This is despite the wellknown fact that for many problems, the targeted relationship varies greatly over the input space, thus suggesting that localized models may improve predictive performance. In this paper, we suggest and evaluate a technique inducing one predictive model for each test instance, using only neighboring instances. In the experimentation, several different variations of the suggested algorithm producing localized decision trees and neural network models are evaluated on 30 UCI data sets. The main result is that the suggested approach generally yields better predictive performance than global models built using all available training data. As a matter of fact, all techniques producing J48 trees obtained significantly higher accuracy and AUC, compared to the global J48 model. For RBF network models, with their inherent ability to use localized information, the suggested approach was only successful with regard to accuracy, while global RBF models had a better ranking ability, as seen by their generally higher AUCs.

This paper presents a novel hybrid method combining genetic programming and decision tree learning. The method starts by estimating a benchmark level of reasonable accuracy, based on decision tree performance on bootstrap samples of the training set. Next, a normal GP evolution is started with the aim of producing an accurate GP. At even intervals, the best GP in the population is evaluated against the accuracy benchmark. If the GP has higher accuracy than the benchmark, the evolution continues normally until the maximum number of generations is reached. If the accuracy is lower than the benchmark, two things happen. First, the fitness function is modified to allow larger GPs, able to represent more complex models. Secondly, a decision tree with increased size and trained on a bootstrap of the training data is injected into the population. The experiments show that the hybrid solution of injecting decision trees into a GP population gives synergetic effects producing results that are better than using either technique separately. The results, from 18 UCI data sets, show that the proposed method clearly outperforms normal GP, and is significantly better than the standard decision tree algorithm.

It is well-known that ensemble performance relies heavily on sufficient diversity among the base classifiers. With this in mind, the strategy used to balance diversity and base classifier accuracy must be considered a key component of any ensemble algorithm. This study evaluates the predictive performance of neural network ensembles, specifically comparing straightforward techniques to more sophisticated. In particular, the sophisticated methods GASEN and NegBagg are compared to more straightforward methods, where each ensemble member is trained independently of the others. In the experimentation, using 31 publicly available data sets, the straightforward methods clearly outperformed the sophisticated methods, thus questioning the use of the more complex algorithms.

When performing predictive data mining, the use of ensembles is known to increase prediction accuracy, compared to single models. To obtain this higher accuracy, ensembles should be built from base classifiers that are both accurate and diverse. The question of how to balance these two properties in order to maximize ensemble accuracy is, however, far from solved and many different techniques for obtaining ensemble diversity exist. One such technique is bagging, where implicit diversity is introduced by training base classifiers on different subsets of available data instances, thus resulting in less accurate, but diverse base classifiers. In this paper, genetic programming is used as an alternative method to obtain implicit diversity in ensembles by evolving accurate, but different base classifiers in the form of decision trees, thus exploiting the inherent inconsistency of genetic programming. The experiments show that the GP approach outperforms standard bagging of decision trees, obtaining significantly higher ensemble accuracy over 25 UCI datasets. This superior performance stems from base classifiers having both higher average accuracy and more diversity. Implicitly introducing diversity using GP thus works very well, since evolved base classifiers tend to be highly accurate and diverse.

Both theory and a wealth of empirical studies have established that ensembles are more accurate than single predictive models. Unfortunately, the problem of how to maximize ensemble accuracy is, especially for classification, far from solved. In essence, the key problem is to find a suitable criterion, typically based on training or selection set performance, highly correlated with ensemble accuracy on novel data. Several studies have, however, shown that it is difficult to come up with a single measure, such as ensemble or base classifier selection set accuracy, or some measure based on diversity, that is a good general predictor for ensemble test accuracy. This paper presents a novel technique that for each learning task searches for the most effective combination of given atomic measures, by means of a genetic algorithm. Ensembles built from either neural networks or random forests were empirically evaluated on 30 UCI datasets. The experimental results show that when using the generated combined optimization criteria to rank candidate ensembles, a higher test set accuracy for the top ranked ensemble was achieved, compared to using ensemble accuracy on selection data alone. Furthermore, when creating ensembles from a pool of neural networks, the use of the generated combined criteria was shown to generally outperform the use of estimated ensemble accuracy as the single optimization criterion.

Genetic programming (GP), is a very general and efficient technique, often capable of outperforming more specialized techniques on a variety of tasks. In this paper, we suggest a straightforward novel algorithm for post-processing of GP classification trees. The algorithm iteratively, one node at a time, searches for possible modifications that would result in higher accuracy. More specifically, the algorithm for each split evaluates every possible constant value and chooses the best. With this design, the post-processing algorithm can only increase training accuracy, never decrease it. In this study, we apply the suggested algorithm to GP trees, extracted from neural network ensembles. Experimentation, using 22 UCI datasets, shows that the post-processing results in higher test set accuracies on a large majority of datasets. As a matter of fact, for two setups of three evaluated, the increase in accuracy is statistically significant.

The test set accuracy for ensembles of classifiers selected based on single measures of accuracy and diversity as well as combinations of such measures is investigated. It is found that by combining measures, a higher test set accuracy may be obtained than by using any single accuracy or diversity measure. It is further investigated whether a multi-criteria search for an ensemble that maximizes both accuracy and diversity leads to more accurate ensembles than by optimizing a single criterion. The results indicate that it might be more beneficial to search for ensembles that are both accurate and diverse. Furthermore, the results show that diversity measures could compete with accuracy measures as selection criterion.

The main purpose of this study was to determine whether it is possible to somehow use results on training or validation data to estimate ensemble performance on novel data. With the specific setup evaluated; i.e. using ensembles built from a pool of independently trained neural networks and targeting diversity only implicitly, the answer is a resounding no. Experimentation, using 13 UCI datasets, shows that there is in general nothing to gain in performance on novel data by choosing an ensemble based on any of the training measures evaluated here. This is despite the fact that the measures evaluated include all the most frequently used; i.e. ensemble training and validation accuracy, base classifier training and validation accuracy, ensemble training and validation AUC and two diversity measures. The main reason is that all ensembles tend to have quite similar performance, unless we deliberately lower the accuracy of the base classifiers. The key consequence is, of course, that a data miner can do no better than picking an ensemble at random. In addition, the results indicate that it is futile to look for an algorithm aimed at optimizing ensemble performance by somehow selecting a subset of available base classifiers.

Most predictive modeling in information fusion is performed using ensembles. When designing ensembles, the prevailing opinion is that base classifier diversity is vital for how well the ensemble will generalize to new observations. Unfortunately, the key term diversity is not uniquely defined, leading to several diversity measures and many methods for diversity creation. In addition, no specific diversity measure has shown to have high correlation with generalization accuracy. The purpose of this paper is to empirically evaluate ten different diversity measures, using neural network ensembles and 8 publicly available data sets. The main result is that all diversity measures evaluated show low or very low correlation with test set accuracy. In addition, it is obvious that the most diverse ensembles often obtain very poor accuracy. Based on these results, it appears to be quite a challenge to explicitly utilize diversity when optimizing ensembles.

When designing ensembles, it is almost an axiom that the base classifiers must be diverse in order for the ensemble to generalize well. Unfortunately, there is no clear definition of the key term diversity, leading to several diversity measures and many, more or less ad hoc, methods for diversity creation in ensembles. In addition, no specific diversity measure has shown to have a high correlation with test set accuracy. The purpose of this paper is to empirically evaluate ten different diversity measures, using neural network ensembles and 11 publicly available data sets. The main result is that all diversity measures evaluated, in this study too, show low or very low correlation with test set accuracy. Having said that, two measures; double fault and difficulty show slightly higher correlations compared to the other measures. The study furthermore shows that the correlation between accuracy measured on training or validation data and test set accuracy also is rather low. These results challenge ensemble design techniques where diversity is explicitly maximized or where ensemble accuracy on a hold-out set is used for optimization.

In this paper a mapping between retail concepts and the JDL model is proposed. More specifically, the benefits of using solutions to military problems as inspiration to retail specific problems are discussed. The somewhat surprising conclusion is that there are several similarities between the military and retail domains, and that these similarities potentially could be exploited. A few examples of retail problems that could benefit from theories and techniques commonly used in the information fusion community are given. All examples are taken from recently started or planned projects within the information fusion research program at the University of Skovde, Sweden

When performing predictive modeling, the key criterion is always accuracy. With this in mind, complex techniques like neural networks or ensembles are normally used, resulting in opaque models impossible to interpret. When models need to be comprehensible, accuracy is often sacrificed by using simpler techniques directly producing transparent models; a tradeoff termed the accuracy vs. comprehensibility tradeoff. In order to reduce this tradeoff, the opaque model can be transformed into another, interpretable, model; an activity termed rule extraction. In this paper, it is argued that rule extraction algorithms should gain from using oracle data; i.e. test set instances, together with corresponding predictions from the opaque model. The experiments, using 17 publicly available data sets, clearly show that rules extracted using only oracle data were significantly more accurate than both rules extracted by the same algorithm, using training data, and standard decision tree algorithms. In addition, the same rules were also significantly more compact; thus providing better comprehensibility. The overall implication is that rules extracted in this fashion explain the predictions made on novel data better than rules extracted in the standard way; i.e. using training data only

In this paper we present and evaluate a novel algorithm for ensemble creation. The main idea of the algorithm is to first independently train a fixed number of neural networks (here ten) and then use genetic programming to combine these networks into an ensemble. The use of genetic programming makes it possible to not only consider ensembles of different sizes, but also to use ensembles as intermediate building blocks. The final result is therefore more correctly described as an ensemble of neural network ensembles. The experiments show that the proposed method, when evaluated on 22 publicly available data sets, obtains very high accuracy, clearly outperforming the other methods evaluated. In this study several micro techniques are used, and we believe that they all contribute to the increased performance. One such micro technique, aimed at reducing overtraining, is the training method, called tombola training, used during genetic evolution. When using tombola training, training data is regularly resampled into new parts, called training groups. Each ensemble is then evaluated on every training group and the actual fitness is determined solely from the result on the hardest part.