Nagging Predictors

Abstract

We define the nagging predictor, which, instead of using bootstrapping to produce a series of i.i.d. predictors, exploits the randomness of neural network calibrations to provide a more stable and accurate predictor than is available from a single neural network run. Convergence results for the family of Tweedie’s compound Poisson models, which are usually used for general insurance pricing, are provided. In the context of a French motor third-party liability insurance example, the nagging predictor achieves stability at portfolio level after about 20 runs. At an insurance policy level, we show that for some policies up to 400 neural network runs are required to achieve stability. Since working with 400 neural networks is impractical, we calibrate two meta models to the nagging predictor, one unweighted, and one using the coefficient of variation of the nagging predictor as a weight, finding that these latter meta networks can approximate the nagging predictor well, only with a small loss of accuracy.

Feature Selection and Ensemble-Based Intrusion Detection System: An Efficient and Comprehensive Approach

“…Lastly, KODE achieved the best performance on the NSL-KDD dataset with a detection rate of 96.64% and a performance accuracy of 99.73%. However, it achieved the highest false alarm rates compared to [31]. Finally, unlike the selected studies and many other approaches.…”

“…Firstly, reference [31] is believed to have first proposed the concept of bagging. The authors intelligently used random draw with replacement to create several samples of the training dataset and train various models, and averaged their score with the ensemble technique of voting.…”

Interpreting Deep Learning Models with Marginal Attribution by Conditioning on Quantiles

“…Network regression models lack a certain degree of robustness as gradient descent network fitting explores different (local) minima of the objective function; note that, in general, neural network fitting is not a convex minimization problem. This issue of non-uniqueness of good predictive models has been widely discussed in the literature, and ensembling may be one solution to mitigate this problem, we refer to [Dietterich 2000a, Dietterich 2000b], [Zhou et al 2002], [Zhou 2012] and [Richman and Wüthrich 2020]. The top row shows the empirical distributions of the canonical parameters (θ(x i )) 1≤i≤n for 4 different networks; we observe that there are some differences in these empirical densities.…”

Interpreting Deep Learning Models with Marginal Attribution by Conditioning on Quantiles

“…Network regression models lack a certain degree of robustness as gradient descent network fitting explores different (local) minima of the objective function; note that, in general, neural network fitting is not a convex minimization problem. This issue of non-uniqueness of good predictive models has been widely discussed in the literature, and ensembling may be one solution to mitigate this problem, we refer to [Dietterich 2000a, Dietterich 2000b, [Zhou et al 2002], [Zhou 2012] and [Richman and Wüthrich 2020]. The top row shows the empirical distributions of the canonical parameters (θ(x i )) 1≤i≤n for 4 different networks; we observe that there are some differences in these empirical densities.…”