An urn model for majority voting in classification ensembles

In this work we analyze the class prediction of parallel randomized ensembles by majority voting as an urn model. For a given test instance, the ensemble can be viewed as an urn of marbles of different colors. A marble represents an individual classifier. Its color represents the class label prediction of the corresponding classifier. The sequential querying of classifiers in the ensemble can be seen as draws without replacement from the urn. An analysis of this classical urn model based on the hypergeometric distribution makes it possible to estimate the confidence on the outcome of majority voting when only a fraction of the individual predictions is known. These estimates can be used to speed up the prediction by the ensemble. Specifically, the aggregation of votes can be halted when the confidence in the final prediction is sufficiently high. If one assumes a uniform prior for the distribution of possible votes the analysis is shown to be equivalent to a previous one based on Dirichlet distributions. The advantage of the current approach is that prior knowledge on the possible vote outcomes can be readily incorporated in a Bayesian framework. We show how incorporating this type of problem-specific knowledge into the statistical analysis of majority voting leads to faster classification by the ensemble and allows us to estimate the expected average speed-up beforehandThe authors acknowledge financial support from the Comunidad de Madrid (project CASI-CAMCM S2013/ICE-2845), and from the Spanish Ministerio de Economía y Competitividad (projects TIN2013-42351-P and TIN2015-70308-REDT

Boosting Randomized Smoothing with Variance Reduced Classifiers

Randomized Smoothing (RS) is a promising method for obtaining robustness certificates by evaluating a base model under noise. In this work, we: (i) theoretically motivate why ensembles are a particularly suitable choice as base models for RS, and (ii) empirically confirm this choice, obtaining state-of-the-art results in multiple settings. The key insight of our work is that the reduced variance of ensembles over the perturbations introduced in RS leads to significantly more consistent classifications for a given input. This, in turn, leads to substantially increased certifiable radii for samples close to the decision boundary. Additionally, we introduce key optimizations which enable an up to 55-fold decrease in sample complexity of RS, thus drastically reducing its computational overhead. Experimentally, we show that ensembles of only 3 to 10 classifiers consistently improve on their strongest constituting model with respect to their average certified radius (ACR) by 5% to 21% on both CIFAR10 and ImageNet, achieving a new state-of-the-art ACR of 0.86 and 1.11, respectively. We release all code and models required to reproduce our results upon publication

An urn model for majority voting in classification ensembles

Abstract In this work we analyze the class prediction of parallel randomized ensembles by majority voting as an urn model. For a given test instance, the ensemble can be viewed as an urn of marbles of different colors. A marble represents an individual classifier. Its color represents the class label prediction of the corresponding classifier. The sequential querying of classifiers in the ensemble can be seen as draws without replacement from the urn. An analysis of this classical urn model based on the hypergeometric distribution makes it possible to estimate the confidence on the outcome of majority voting when only a fraction of the individual predictions is known. These estimates can be used to speed up the prediction by the ensemble. Specifically, the aggregation of votes can be halted when the confidence in the final prediction is sufficiently high. If one assumes a uniform prior for the distribution of possible votes the analysis is shown to be equivalent to a previous one based on Dirichlet distributions. The advantage of the current approach is that prior knowledge on the possible vote outcomes can be readily incorporated in a Bayesian framework. We show how incorporating this type of problem-specific knowledge into the statistical analysis of majority voting leads to faster classification by the ensemble and allows us to estimate the expected average speed-up beforehand

Artificial Intelligence Based Classification for Urban Surface Water Modelling

Estimations and predictions of surface water runoff can provide very useful insights, regarding flood risks in urban areas. To automatically predict the flow behaviour of the rainfall-runoff water, in real-world satellite images, it is important to precisely identify permeable and impermeable areas. This identification indicates and helps to calculate the amount of surface water, by taking into account the amount of water being absorbed in a permeable area and what remains on the impermeable area. In this research, a model of surface water has been established, to predict the behavioural flow of rainfall-runoff water. This study employs a combination of image processing, artificial intelligence and machine learning techniques, for automatic segmentation and classification of permeable and impermeable areas, in satellite images. These techniques investigate the image classification approaches for classifying three land-use categories (roofs, roads, and pervious areas), commonly found in satellite images of the earth’s surface. Three different classification scenarios are investigated, to select the best classification model. The first scenario involves pixel by pixel classification of images, using Classification Tree and Random Forest classification techniques, in 2 different settings of sequential and parallel execution of algorithms. In the second classification scenario, the image is divided into objects, by using Superpixels (SLIC) segmentation method, while three kinds of feature sets are extracted from the segmented objects. The performance of eight different supervised machine learning classifiers is probed, using 5-fold cross-validation, for multiple SLIC values, while detailed performance comparisons lead to conclusions about the classification into different classes, regarding Object-based and Pixel-based classification schemes. Pareto analysis and Knee point selection are used to select SLIC value and the suitable type of classification, among the aforementioned two. Furthermore, a new diversity and weighted sum-based ensemble classification model, called ParetoEnsemble, is proposed, in this classification scenario. The weights are applied to selected component classifiers of an ensemble, creating a strong classifier, where classification is done based on multiple votes from candidate classifiers of the ensemble, as opposed to individual classifiers, where classification is done based on a single vote, from only one classifier. Unbalanced and balanced data-based classification results are also evaluated, to determine the most suitable mode, for satellite image classifications, in this study. Convolutional Neural Networks, based on semantic segmentation, are also employed in the classification phase, as a third scenario, to evaluate the strength of deep learning model SegNet, in the classification of satellite imaging. The best results, from the three classification scenarios, are compared and the best classification method, among the three scenarios, is used in the next phase of water modelling, with the InfoWorks ICM software, to explore the potential of modelling process, regarding a partially automated surface water network. By using the parameter settings, with a specified amount of simulated rain falling, onto the imaged area, the amount of surface water flow is estimated, to get predictions about runoff situations in urban areas, since runoff, in such a situation, can be high enough to pose a dangerous flood risk. The area of Feock, in Cornwall, is used as a simulation area of study, in this research, where some promising results have been derived, regarding classification and modelling of runoff. The correlation coefficient estimation, between classification and runoff accuracy, provides useful insight, regarding the dependence of runoff performance on classification performance. The trained system was tested on some unknown area images as well, demonstrating a reasonable performance, considering the training and classification limitations and conditions. Furthermore, in these unknown area images, reasonable estimations were derived, regarding surface water runoff. An analysis of unbalanced and balanced data-based classification and runoff estimations, for multiple parameter configurations, provides aid to the selection of classification and modelling parameter values, to be used in future unknown data predictions. This research is founded on the incorporation of satellite imaging into water modelling, using selective images for analysis and assessment of results. This system can be further improved, and runoff predictions of high precision can be better achieved, by adding more high-resolution images to the classifiers training. The added variety, to the trained model, can lead to an even better classification of any unknown image, which could eventually provide better modelling and better insights into surface water modelling. Moreover, the modelling phase can be extended, in future research, to deal with real-time parameters, by calibrating the model, after the classification phase, in order to observe the impact of classification on the actual calibration