Marcelo Azevedo Costa

Improving generalization of MLPs with sliding mode control and the Levenberg-Marquardt algorithm

A variation of the well-known Levenberg-Marquardt for training neural networks is proposed in this work. The algorithm presented restricts the norm of the weights vector to a preestablished norm value and finds the minimum error solution for that norm value. The norm constrain controls the neural networks degree of freedom. The more the norm increases, the more flexible is the neural model. Therefore, more fitted to the training set. A range of different norm solutions is generated and the best generalization solution is selected according to the validation set error. The results show the efficiency of the algorithm in terms of generalization performance.

Training neural networks with a multi-objective sliding mode control algorithm

Abstract This paper presents a new sliding mode control algorithm that is able to guide the trajectory of a multi-layer perceptron within the plane formed by the two objective functions: training set error and norm of the weight vectors. The results show that the neural networks obtained are able to generate an approximation to the Pareto set, from which an improved generalization performance model is selected.

A fair comparison between the spatial scan and the Besag–Newell Disease clustering tests

Routine surveillance of a large geographic region for clusters of adverse health events, particularly cancers, often involves small area health data, possibly controlling for exposure information. Many different methods have been proposed to test for the presence of geographical clusters. Two of the most popular methods are the spatial scan method proposed by Kulldorff and that using a fixed number of cases within scanning circles proposed by Besag and Newell. Although the second test is very popular, it has some difficulties. While the scan test controls for the multiple testing problem, the Besag and Newell test does not. Additionally, the latter method requires the setting of several tuning parameters whose values affect the test performance and are subjectively chosen by the user. This creates a difficulty to make a fair comparison between the two methods and it explains why there have been few formal studies evaluating their relative performances. In this paper, we modify the Besag and Newell test allowing for the control of the error type I probability and compare its power with respect to that of the spatial scan test. We used data sets from a publicly available simulated benchmark. We found that the two methods have similar results, except for clusters located in sparsely populated regions, where the spatial scan method presented a better performance.

Constrained spanning tree algorithms for irregularly-shaped spatial clustering

Spatial clustering methodologies that are capable of detecting and delineating irregular clusters can provide information about the geographical spread of various diseases under surveillance. This paper proposes and compares three spatial scan statistics designed to detect clusters with irregular shapes. The proposed methods use geographical boundary information to construct a graph in which a cluster growing process is performed based on likelihood function maximization. Constraints on cluster shape are imposed through early stopping, a double connection requirement and a maximum linkage criteria. The methods are evaluated using simulated data sets with either circular or irregular clusters, and compared to the circular and elliptic scan statistics. Results show that for circular clusters, the standard circular scan statistic is optimal, as expected. The double connection, elliptic maximum linkage scan statistics also achieve good results. For irregularly-shaped clusters, the elliptic, maximum linkage and double connected scan statistics are optimal for different cluster models and by different evaluation criteria, but the circular scan statistic also performs well. If the emphasis is on statistical power for cluster detection, the simple circular scan statistic is attractive across the board choice. If the emphasis is on the accurate determination of cluster size, shape and boundaries, the double connected, maximum linkage and elliptical scan statistics are often more suitable choices. All methods perform well though, with the exception of the unrestricted dynamic minimum spanning tree scan statistic and the early stopping scan statistic, which we do not recommend.

Power of the Sequential Monte Carlo Test

Abstract Many statistical tests obtain their p-value from a Monte Carlo sample of m values of the test statistic under the null hypothesis. The number m of simulations is fixed by the researcher prior to any analysis. In contrast, the sequential Monte Carlo test does not fix the number of simulations in advance. It keeps simulating the test statistics until it decides to stop based on a certain rule. The final number of simulations is a random number N. This sequential Monte Carlo procedure can decrease substantially the execution time in order to reach a decision. This paper has two aims concerning the sequential Monte Carlo tests: to minimize N without affecting its power; and to compare its power with that of the fixed-sample Monte Carlo test. We show that the power of the sequential Monte Carlo test is constant after a certain number of simulations and therefore, that there is a bound to N. We also show that the sequential test is always preferable to a fixed-sample test. That is, for every test with a fixed sample size m there is a sequential Monte Carlo test with equal power but with smaller number of simulations.

Limits of Brazil’s Forest Code as a means to end illegal deforestation

Significance Brazil’s new Forest Code has the potential to halt illegal deforestation in the country’s native forests and savannas through implementation of a federal land registry—along with powerful tools that facilitate enforcement and give landowners a pathway to restoring or compensating their “forest deficits.” This study suggests that these tools fall short of their promise. Although landowners in eastern Amazonia have been motivated to join state land registries, many continue to deforest and few have restored their illegally cleared areas. Results indicate that the economic benefits of full compliance with the Forest Code remain scant. To end deforestation, Brazil must realign its financial and policy incentives to encourage this outcome. The fate of the country’s forests hangs in the balance. The 2012 Brazilian Forest Code governs the fate of forests and savannas on Brazil’s 394 Mha of privately owned lands. The government claims that a new national land registry (SICAR), introduced under the revised law, could end illegal deforestation by greatly reducing the cost of monitoring, enforcement, and compliance. This study evaluates that potential, using data from state-level land registries (CAR) in Pará and Mato Grosso that were precursors of SICAR. Using geospatial analyses and stakeholder interviews, we quantify the impact of CAR on deforestation and forest restoration, investigating how landowners adjust their behaviors over time. Our results indicate rapid adoption of CAR, with registered properties covering a total of 57 Mha by 2013. This suggests that the financial incentives to join CAR currently exceed the costs. Registered properties initially showed lower deforestation rates than unregistered ones, but these differences varied by property size and diminished over time. Moreover, only 6% of registered producers reported taking steps to restore illegally cleared areas on their properties. Our results suggest that, from the landowners perspective, full compliance with the Forest Code offers few economic benefits. Achieving zero illegal deforestation in this context would require the private sector to include full compliance as a market criterion, while state and federal governments develop SICAR as a de facto enforcement mechanism. These results are relevant to other tropical countries and underscore the importance of developing a policy mix that creates lasting incentives for sustainable land-use practices.

A critical look at prospective surveillance using a scan statistic

The scan statistic is a very popular surveillance technique for purely spatial, purely temporal, and spatial-temporal disease data. It was extended to the prospective surveillance case, and it has been applied quite extensively in this situation. When the usual signal rules, as those implemented in SaTScan(TM) (Boston, MA, USA) software, are used, we show that the scan statistic method is not appropriate for the prospective case. The reason is that it does not adjust properly for the sequential and repeated tests carried out during the surveillance. We demonstrate that the nominal significance level α is not meaningful and there is no relationship between α and the recurrence interval or the average run length (ARL). In some cases, the ARL may be equal to ∞, which makes the method ineffective. This lack of control of the type-I error probability and of the ARL leads us to strongly oppose the use of the scan statistic with the usual signal rules in the prospective context.

Applications of Spatial Scan Statistics: A Review

In 1965, Joseph Naus published his now classical paper on spatial scan statistics, entitled ‘Clustering of random points in two dimensions’. This paper set in motion an important statistical theory of spatial scan statistics and an avalanche of spatial scan statistics applications in a wide variety of fields, including archaeology, astronomy, brain imaging, criminology, demography, early detection of disease outbreaks, ecology, epidemiology, forestry, geology, history, psychology and veterinary medicine. In this chapter, we survey this wide variety of applications.

Maximum linkage space-time permutation scan statistics for disease outbreak detection

BackgroundIn disease surveillance, the prospective space-time permutation scan statistic is commonly used for the early detection of disease outbreaks. The scanning window that defines potential clusters of diseases is cylindrical in shape, which does not allow incorporating into the cluster shape potential factors that can contribute to the spread of the disease, such as information about roads, landscape, among others. Furthermore, the cylinder scanning window assumes that the spatial extent of the cluster does not change in time. Alternatively, a dynamic space-time cluster may indicate the potential spread of the disease through time. For instance, the cluster may decrease over time indicating that the spread of the disease is vanishing.MethodsThis paper proposes two irregularly shaped space-time permutation scan statistics. The cluster geometry is dynamically created using a graph structure. The graph can be created to include nearest-neighbor structures, geographical adjacency information or any relevant prior information regarding the contagious behavior of the event under surveillance.ResultsThe new methods are illustrated using influenza cases in three New England states, and compared with the cylindrical version. A simulation study is provided to investigate some properties of the proposed arbitrary cluster detection techniques.ConclusionWe have successfully developed two new space-time permutation scan statistics methods with irregular shapes and improved computational performance. The results demonstrate the potential of these methods to quickly detect disease outbreaks with irregular geometries. Future work aims at performing intensive simulation studies to evaluate the proposed methods using different scenarios, number of cases, and graph structures.

Optimal selection of the spatial scan parameters for cluster detection: a simulation study.

Circular and elliptic spatial scan statistics requires the user to choose a maximum cluster size. A common value for this parameter is 50% of the underlying population. In addition to the detected primary cluster, the user may be interested in the analysis of significant secondary clusters. It can also be argued that if the true cluster is irregular, then choosing a small value for the maximum cluster size and evaluating significant secondary clusters may improve cluster detection and avoid the use of irregular cluster methods. This work explores the performance of the circular, elliptic and double scan statistics for different values of the maximum cluster size and different options for the analysis of secondary clusters. Empirical results show that for hot-spot clusters, the analysis of secondary clusters which are statistically significant do not improve the detection of the true unknown cluster, on average. There is evidence that a variable maximum cluster size improves performance. That is, the double scan statistic applies an early-stopping procedure which improves positive predictive values.