Feature-Based Forensic Text Comparison Using a Poisson Model for Likelihood Ratio Estimation

1 Abstract Score- and feature-based methods are the two main ones for estimating a forensic likelihood ratio (LR) quantifying the strength of evidence. In this forensic text comparison (FTC) study, a score-based method using the Cosine distance is com- pared with a feature-based method built on a Poisson model with texts collected from 2,157 authors. Distance measures (e.g. Bur- rows’s Delta, Cosine distance) are a stand- ard tool in authorship attribution studies. Thus, the implementation of a score-based method using a distance measure is natu- rally the first step for estimating LRs for textual evidence. However, textual data of- ten violates the statistical assumptions un- derlying distance-based models. Further- more, such models only assess the similar- ity, not the typicality, of the objects (i.e. documents) under comparison. A Poisson model is theoretically more appropriate than distance-based measures for author- ship attribution, but it has never been tested with linguistic text evidence within the LR framework. The log-LR cost (Cllr) was used to assess the performance of the two meth- ods. This study demonstrates that: (1) the feature-based method outperforms the score-based method by a Cllr value of ca. 0.09 under the best-performing settings and; (2) the performance of the feature- based method can be further improved by feature selection. 1 Introduction The essential part of any source-detection task is to assess the similarity or difference between the ob- jects or items under comparison. For this purpose, in stylometric studies too, various distance measures have been devised and tested, particu- larly in studies concerned with the authorship of text sources (Argamon, 2008; Burrows, 2002; Hoover, 2004a; Smith and Aldridge, 2011). Bur- rows’s Delta (Burrows, 2002) is probably the most studied distance measure in stylometric studies, and its effectiveness and robustness have been demonstrated for a variety of texts from different genres and languages (AbdulRazzaq and Mustafa, 2014; Hoover, 2004b; Rybicki and Eder, 2011; Þorgeirsson, 2018). Since Burrows (2002), several variants, including, for example, those based on Euclidian distance, Cosine similarity and Ma- halanobis distance have been proposed to better deal with the unique characteristics of linguistic texts, expecting to result in a better identification and discrimination performance (Argamon, 2008; Eder, 2015; Hoover, 2004b; Smith and Aldridge, 2011). Similarity- and distance-based measures make some assumptions about the distribution of the un- derlying data. For example, a Laplace distribution is assumed by Burrows’s Delta, which itself is based on Manhattan distance, and a normal distri- bution by the Euclidean and cosine distances. However, it is well known that stylometric features do not always conform to, for example, a normal distribution (Argamon, 2008; Jannidis et al., 2015). Moreover, a normal distribution is not theoretically appropriate for discrete count data (e.g. occur- rences of function words) Figure 1 shows the dis- tributions of the counts of three words (‘a’, ‘not’ and ‘they’), sampled from the database used in the current study. Frequently-occurring words, such as ‘a’ (Figure 1a), tend to be normally distributed. However the distribution starts skewing positively for less-frequently-occurring words, such as ‘not’ …

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