A Novel Boolean Kernels Family for Categorical Data

Abstract

Kernel based classifiers, such as SVM, are considered state-of-the-art algorithms and are widely used on many classification tasks. However, this kind of methods are hardly interpretable and for this reason they are often considered as black-box models. In this paper, we propose a new family of Boolean kernels for categorical data where features correspond to propositional formulas applied to the input variables. The idea is to create human-readable features to ease the extraction of interpretation rules directly from the embedding space. Experiments on artificial and benchmark datasets show the effectiveness of the proposed family of kernels with respect to established ones, such as RBF, in terms of classification accuracy.

Determining the most influential human factors in maritime accidents: A data-driven approach

“…The first step is to build a predictive model (Shalev-Shwartz & Ben-David, 2014) of the accident type based on the presence or not of the different human factors. This step can be performed using different approaches, in this paper the authors will exploit two different state-of-the-art approaches: Random Forests (RF) (Breiman, 2001;Harb et al, 2009) and Multiclass (Hsu & Lin, 2002) Support Vector Machines (Shawe-Taylor & Cristianini, 2004) with Boolean Kernels (Polato et al, 2018) -MSVM-BK, since the presence or not of the different human factors can be represented with a Boolean vector. The second step is to rank (Guyon & Elisseeff, 2003;Guyon et al, 2008) the different human factors based on their ability to influence the model outputs.…”

“…The third one is the kernel parameters if present. For what concerns the type of kernels, some of them are specifically developed for the case when X = {0, 1} d and are called Boolean Kernels, reviewed and evolved here (Polato et al, 2018). Without describing them in details, since the mathematical background needed is over-complicated for the purposed of this paper, the idea is to not represent all the possible analogical functions in R d but just all the possible Boolean functions in {0, 1} d .…”

“…This allows to remove much useless function and improve the quality of the learning procedure. All these Boolean Kernels are characterised by one or more hyperparameters and in this work we will explore all the kernels and all the ranges of hyperparameters adopted in (Polato et al, 2018). Even if SVM is a very powerful tool, real world problems are frequently characterised by c > 2 classes.…”

“…Ensemble methods (Breiman, 2001) and Kernel methods (Hsu & Lin, 2002;Polato et al, 2018;Shawe-Taylor & Cristianini, 2004) represent the state-ofthe-art for dealing with Phase (I). During Phase (II), state-of-the-art feature ranking methods for Ensemble and Kernel methods (Guyon & Elisseeff, 2003;Guyon et al, 2008;Louppe, 2014;Louppe et al, 2013) will be exploited to rank the human factor and then to identify the most important maritime accidents contributing factors.…”

Distribution-Dependent Weighted Union Bound

“…DDWUB applies to finite hypotheses spaces and surely more sophisticated techniques, such as Local Vapnik–Chervonenkis [ 28 ] or the Local Rademacher Complexity [ 10 ], can be employed and can sometimes result in tighter bounds. However, insight into finite classes remains quite useful [ 20 , 29 ]. Finite class analysis can be exploited for as a pedagogical tool.…”