{ "paper_id": "U18-1002", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T03:12:05.034452Z" }, "title": "Text-dependent Forensic Voice Comparison: Likelihood Ratio Estimation with the Hidden Markov Model (HMM) and Gaussian Mixture Model -Universal Background Model (GMM-UBM) Approaches", "authors": [ { "first": "Satoru", "middle": [], "last": "Tsuge", "suffix": "", "affiliation": {}, "email": "tsuge@daido-it.ac.jp" }, { "first": "Shunichi", "middle": [], "last": "Ishihara", "suffix": "", "affiliation": {}, "email": "shunichi.ishihara@anu.edu.au" } ], "year": "", "venue": null, "identifiers": {}, "abstract": "Among the more typical forensic voice comparison (FVC) approaches, the acoustic-phonetic statistical approach is suitable for text-dependent FVC, but it does not fully exploit available time-varying information of speech in its modelling. The automatic approach, on the other hand, essentially deals with text-independent cases, which means temporal information is not explicitly incorporated in the modelling. Text-dependent likelihood ratio (LR)based FVC studies, in particular those that adopt the automatic approach, are few. This preliminary LR-based FVC study compares two statistical models, the Hidden Markov Model (HMM) and the Gaussian Mixture Model (GMM), for the calculation of forensic LRs using the same speech data. FVC experiments were carried out using different lengths of Japanese short words under a forensically realistic, but challenging condition: only two speech tokens for model training and LR estimation. Log-likelihood-ratio cost (Cllr) was used as the assessment metric. The study demonstrates that the HMM system constantly outperforms the GMM system in terms of average Cllr values. However, words longer than three mora are needed if the advantage of the HMM is to become evident. With a seven-mora word, for example, the HMM outperformed the GMM by a Cllr value of 0.073.", "pdf_parse": { "paper_id": "U18-1002", "_pdf_hash": "", "abstract": [ { "text": "Among the more typical forensic voice comparison (FVC) approaches, the acoustic-phonetic statistical approach is suitable for text-dependent FVC, but it does not fully exploit available time-varying information of speech in its modelling. The automatic approach, on the other hand, essentially deals with text-independent cases, which means temporal information is not explicitly incorporated in the modelling. Text-dependent likelihood ratio (LR)based FVC studies, in particular those that adopt the automatic approach, are few. This preliminary LR-based FVC study compares two statistical models, the Hidden Markov Model (HMM) and the Gaussian Mixture Model (GMM), for the calculation of forensic LRs using the same speech data. FVC experiments were carried out using different lengths of Japanese short words under a forensically realistic, but challenging condition: only two speech tokens for model training and LR estimation. Log-likelihood-ratio cost (Cllr) was used as the assessment metric. The study demonstrates that the HMM system constantly outperforms the GMM system in terms of average Cllr values. However, words longer than three mora are needed if the advantage of the HMM is to become evident. With a seven-mora word, for example, the HMM outperformed the GMM by a Cllr value of 0.073.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "After the DNA success story, the likelihood ratio (LR)-based approach became the new paradigm for evaluating and presenting forensic evidence in court. The LR approach has also been applied to speech evidence (Rose, 2006) , and it is increasing-ly accepted in forensic voice comparison (FVC) as well (Morrison, 2009) .", "cite_spans": [ { "start": 209, "end": 221, "text": "(Rose, 2006)", "ref_id": "BIBREF21" }, { "start": 300, "end": 316, "text": "(Morrison, 2009)", "ref_id": "BIBREF13" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "There are two different approaches in FVC. They are the 'acoustic-phonetic statistical approach' and the 'automatic approach' (Morrison et al., 2018) . The former usually works on comparable phonetic units that can be found in both the offender and suspect samples. In the latter, acoustic measurements are usually carried out over all portions of the available recordings, resulting in more detailed acoustic characteristics of the speakers. The common statistical models used in the automatic approach are the Gaussian mixture modeluniversal background model (GMM-UBM) (Reynolds et al., 2000) and i-vectors with probabilistic linear discrimination analysis (PLDA) (Burget et al., 2011) . Due to its nature, the automatic approach is mainly used for text-'independent' FVC, and there is a good amount of research on this (Enzinger & Morrison, 2017; Enzinger et al., 2016) . The acoustic-phonetic statistical approach is a type of text-'dependent' FVC because it tends to focus on particular linguistic units, such as phonemes, words, phrases, etc. Having said that, even if one is targeting a particular word or phrase, for example 'hello', all obtainable features are not exploited in the acoustic-phonetic statistical approach because it still tends to focus on particular segments or phonemes of the word or phrase, e.g. the formant trajectories of the diphthong and the static spectral information of the fricative (Rose, 2017) .", "cite_spans": [ { "start": 126, "end": 149, "text": "(Morrison et al., 2018)", "ref_id": "BIBREF16" }, { "start": 571, "end": 594, "text": "(Reynolds et al., 2000)", "ref_id": "BIBREF19" }, { "start": 666, "end": 687, "text": "(Burget et al., 2011)", "ref_id": null }, { "start": 822, "end": 849, "text": "(Enzinger & Morrison, 2017;", "ref_id": "BIBREF7" }, { "start": 850, "end": 872, "text": "Enzinger et al., 2016)", "ref_id": "BIBREF8" }, { "start": 1420, "end": 1432, "text": "(Rose, 2017)", "ref_id": "BIBREF23" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "One of the advantages of text-dependent FVC is the availability of the time-varying characteristics of a speaker, which is information that can be explicitly included in the modelling.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "There are a good number of LR-based textindependent FVC studies in the automatic approach (Enzinger & Morrison, 2017; Enzinger et al., 2016) . However, although there are some stud-ies in which text-independent models (e.g. GMM) were applied to text-dependent FVC scenarios (Morrison, 2011) , to the best of our knowledge, studies on LR-based text-dependent FVC in the automatic approach are scarce.", "cite_spans": [ { "start": 90, "end": 117, "text": "(Enzinger & Morrison, 2017;", "ref_id": "BIBREF7" }, { "start": 118, "end": 140, "text": "Enzinger et al., 2016)", "ref_id": "BIBREF8" }, { "start": 274, "end": 290, "text": "(Morrison, 2011)", "ref_id": "BIBREF14" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "In this study, a text-dependent LR-based FVC system with the GMM-UBM based system (GMM system) and that with the hidden Markov model (HMM system) are compared in their performance using the same data. The transitional characteristic of individual speech can be explicitly modelled in the latter system.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "Words of various length are used for testing purposes to see how word duration influences the performance of the systems. Having the forensically realistic condition of data sparsity in mind, we used only two tokens of each word for modelling and testing.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "It is naturally expected that, given a sufficient amount of data, the HMM system outperforms the GMM system. However, it is not so clear whether the above expectation is realistic when the amount of data is limited. Even if the HMM system works better, it is important to establish how the HMM and GMM systems compare with respect to the calculation of strength of LR, and also how and under what conditions the former is more advantageous than the latter.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "The LR framework has been advocated by many as the logically and legally correct framework for assessing forensic evidence and reporting the outcome in court (Aitken, 1995; Aitken & Stoney, 1991; Aitken & Taroni, 2004; Balding & Steele, 2015; Evett, 1998; Robertson & Vignaux, 1995) . A substantial amount of fundamental research on FVC has been carried out since the late 1990s (Gonzalez-Rodriguez et al., 2007; Morrison, 2009; Rose, 2006) , and it is now accepted in an increasing number of countries (Morrison et al., 2016) .", "cite_spans": [ { "start": 158, "end": 172, "text": "(Aitken, 1995;", "ref_id": "BIBREF0" }, { "start": 173, "end": 195, "text": "Aitken & Stoney, 1991;", "ref_id": "BIBREF1" }, { "start": 196, "end": 218, "text": "Aitken & Taroni, 2004;", "ref_id": "BIBREF2" }, { "start": 219, "end": 242, "text": "Balding & Steele, 2015;", "ref_id": "BIBREF3" }, { "start": 243, "end": 255, "text": "Evett, 1998;", "ref_id": "BIBREF9" }, { "start": 256, "end": 282, "text": "Robertson & Vignaux, 1995)", "ref_id": "BIBREF20" }, { "start": 379, "end": 412, "text": "(Gonzalez-Rodriguez et al., 2007;", "ref_id": "BIBREF10" }, { "start": 413, "end": 428, "text": "Morrison, 2009;", "ref_id": "BIBREF13" }, { "start": 429, "end": 440, "text": "Rose, 2006)", "ref_id": "BIBREF21" }, { "start": 503, "end": 526, "text": "(Morrison et al., 2016)", "ref_id": "BIBREF18" } ], "ref_spans": [], "eq_spans": [], "section": "Likelihood Ratios", "sec_num": "2" }, { "text": "In the LR framework, the task of the forensic expert is to estimate strength of evidence and report it to the court. LR is a measure of the quantitative strength of evidence, and is calculated using the formula in 1).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Likelihood Ratios", "sec_num": "2" }, { "text": "In 1), E is the evidence, i.e. the measured properties of the voice evidence; p(E|Hp) is the proba-bility of E, given Hp, in other words the prosecution or same-speaker hypothesis; p(E|Hd) is the probability of E, given Hd, in other words the defence or different-speaker hypothesis (Robertson & Vignaux, 1995) . The LR can be considered in terms of the ratio between similarity and typicality. Similarity here means the similarity of evidence attributable to the offender and the suspect, respectively. Typicality means the typicality of that evidence against the relevant population.", "cite_spans": [ { "start": 283, "end": 310, "text": "(Robertson & Vignaux, 1995)", "ref_id": "BIBREF20" } ], "ref_spans": [], "eq_spans": [], "section": "Likelihood Ratios", "sec_num": "2" }, { "text": "The relative strength of the given evidence with respect to the competing hypotheses (Hp vs. Hd) is reflected in the magnitude of the LR. If the evidence is more likely to occur under the prosecution hypothesis than under the defence hypothesis, the LR will be higher than 1. If the evidence is more likely to occur under the defence hypothesis than under the persecution hypothesis, the LR will be lower than 1. For example, LR = 30 means that the evidence is 30 times more likely to occur on the assumption that the evidence is from the same person than on the assumption that it is not.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Likelihood Ratios", "sec_num": "2" }, { "text": "The important point is that the LR is concerned with the probability of the evidence, given the hypothesis (either Hp or Hd). The probability of the evidence can be estimated by forensic scientists. They legally must not and logically cannot estimate the probability of the hypothesis, given the evidence. This is because the forensic scientist is not legally in a position to refer to the ultimate 'guilty vs. non-guilty' question, i.e. the probability of the hypothesis, given the evidence. That is the task of the trier-of-fact. Furthermore, the forensic scientist would need to refer to the Bayesian theorem to estimate the probability of the hypothesis, given the evidence, using prior information that is only accessible to the trier-of-fact; thus the forensic scientist cannot logically estimate the probability of the hypothesis.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Likelihood Ratios", "sec_num": "2" }, { "text": "In this section, the nature of the database used for the experiments is explained first. This is followed by an illustration as to how the speaker comparisons were set up for the experiments. The acoustic features used in this study will be explained towards the end.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experimental Design", "sec_num": "3" }, { "text": "Our data were extracted from the National Research Institute of Police Science (NRIPS) data-", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Database", "sec_num": "3.1" }, { "text": "LR= p(E|H p ) p(E|H d ) 1)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Database", "sec_num": "3.1" }, { "text": "base (Makinae et al., 2007) . The database consists of recordings collected from 316 male and 323 female speakers. All utterances were read-out speech, consisting of single syllables, words, selected sentences and so on. The word-based recordings stored in the database provided the data used in this study. Participants ranged in age from 18 to 76 years. The metadata provide information on the areas of Japan (or overseas in some cases) where they have resided, as well as their height, weight, and their health conditions on the day of recording. Only male speakers who completed the recordings in two different sessions separated by 2-3 months, without any mis-recordings for the target 66 words, were selected for the current study (resulting in 310 speakers). Each word was recorded only twice in each session.", "cite_spans": [ { "start": 5, "end": 27, "text": "(Makinae et al., 2007)", "ref_id": "BIBREF12" } ], "ref_spans": [], "eq_spans": [], "section": "Database", "sec_num": "3.1" }, { "text": "The rhythmic unit of Japanese is the mora. Based on mora, the 66 words, all listed in Table 1 , consist of 25 two-, 16 three-, 22 four-, 2 five-and 1 seven-mora words.", "cite_spans": [], "ref_spans": [ { "start": 86, "end": 93, "text": "Table 1", "ref_id": null } ], "eq_spans": [], "section": "Database", "sec_num": "3.1" }, { "text": "The 310 speakers were separated into six different, mutually exclusive groups: Gr1 (59 speakers), Gr2 (60), Gr3 (60), Gr4 (60), Gr5 (60) and Gr6 (13). Five different experiments were conducted using the six groups, as shown in Table 2 .", "cite_spans": [], "ref_spans": [ { "start": 227, "end": 234, "text": "Table 2", "ref_id": "TABREF0" } ], "eq_spans": [], "section": "Database", "sec_num": "3.1" }, { "text": "The test database was used for simulating two types of offender-suspect comparisons: samespeaker (SS) and different-speaker (DS). An LR was estimated for each of the comparisons. The development database was also called upon for simulating offender-suspect comparisons, but the derived scores (pre-calibration LRs) were specifically used to obtain the weights for calibration (refer to \u00a74.4 for details on calibration). The background database was used to build the statistical model for typicality.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Database", "sec_num": "3.1" }, { "text": "As mentioned earlier, there are two recordings per speaker for each word in each session. The suspect model was built using two recordings taken from one session, and an LR was estimated for each of the two recordings of the other session (offender evidence). The same process was repeated by swapping the recordings of the sessions. In this way, 4 LRs were obtained for each SS comparison, and 8 LRs for each DS comparison. Thus, the number of comparisons is 4*n (n = number of speakers) for the SS comparisons, and 8*nC2 (C=combination) for the DS comparisons. Using the five different groups (Gr1~5) separately as a test database, it was possible, altogether, to carry out 1188 SS comparisons and 69392 DS comparisons. The breakdowns of the SS and DS comparisons are given in Table 3 for the five experiments (Exp1~5).", "cite_spans": [], "ref_spans": [ { "start": 779, "end": 786, "text": "Table 3", "ref_id": "TABREF2" } ], "eq_spans": [], "section": "Database", "sec_num": "3.1" }, { "text": "The NRIPS database also contains the recordings of 50 sentences that are based on ATR phonetically balanced Japanese sentences (Kurematsu et al., 1990) . These sentences were used to build the initial statistical models (refer to \u00a74.1 and \u00a74.2 for details).", "cite_spans": [ { "start": 127, "end": 151, "text": "(Kurematsu et al., 1990)", "ref_id": "BIBREF11" } ], "ref_spans": [], "eq_spans": [], "section": "Database", "sec_num": "3.1" }, { "text": "Twelve mel-frequency cepstral coefficients (MFCCs), 12 \u0394 MFCCs and \u0394 log power (a feature vector of 25 th -order) were extracted with a 20 msec wide hamming window shirting every 10 msec.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Acoustic Features", "sec_num": "3.2" }, { "text": "In this section, the two different modelling techniques used in the current study are explained. This is followed by an exposition of the method for calculating scores with these models. The method used for converting the scores to the LRs, namely calibration, will be explained last.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Estimation of Likelihood Ratios", "sec_num": "4" }, { "text": "For this study, the suspect model, rather than being based solely on the data of the suspect speaker, was generated by adapting a speakerunspecific model (background model) by means of a maximum a posteriori (MAP) procedure. Three different numbers of Gaussians (4, 8 and 16) were tried in the models.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Estimation of Likelihood Ratios", "sec_num": "4" }, { "text": "The following is the process of building a speaker-specific word-dependent GMM for each speaker. 1) To build a speaker-unspecific wordindependent GMM using the recordings of the phonetically balanced utterances; 2) To build a speaker-unspecific word-dependent GMM for each word by training the speaker-unspecific word-independent GMM, which was generated in 1), with the relevant word recordings of the background database; 3) To build the speaker-specific word-dependent GMM (suspect model = \u03bbsus) for each word by training the speaker-unspecific wordindependent GMM, which was built in 2), with the speaker specific data in the test database, while applying a MAP adaptation.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "GMM Models", "sec_num": "4.1" }, { "text": "The speaker-unspecific word-dependent GMM, which was built in 2) for each word, was used as the background model (\u03bbbkg).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "GMM Models", "sec_num": "4.1" }, { "text": "The following is the process of building a speaker-specific word-dependent HMM for each speaker. 1) To build speaker-unspecific phonemedependent HMMs using the recordings of the phonetically balanced utterances; 2) To build an initial speaker-unspecific worddependent HMM for each word by concatenating speaker-unspecific phonemedependent HMMs, which were built in 1).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "HMM Models", "sec_num": "4.2" }, { "text": "3) To build speaker-specific word-dependent HMM (suspect model = \u03bbsus) by training the initial speaker-unspecific word-dependent HMM, which was built in 2), with the speaker specific data in the test database, while applying a MAP adaptation.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "HMM Models", "sec_num": "4.2" }, { "text": "The initial speaker-unspecific word-dependent HMM, which was built in 2), was trained with the relevant word recordings of the background database, and the resultant model was used as the speaker-unspecific word-dependent background model (\u03bbbkg).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "HMM Models", "sec_num": "4.2" }, { "text": "The score of each comparison can be estimated using the equation given in 2), in which s = score, xt = an observation sequence of vectors of acoustic features constituting the offender data of which there are a total of T, \u03bbsus = suspect model and \u03bbbkg = background model. A score is estimated as the mean of the relative values of the two probability density functions for the feature vectors extracted from the offender data, and was calculated for each of the SS and DS comparisons.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Score Calculations", "sec_num": "4.3" }, { "text": "EQUATION", "cite_spans": [], "ref_spans": [], "eq_spans": [ { "start": 0, "end": 8, "text": "EQUATION", "ref_id": "EQREF", "raw_str": "= 1 \u2211 log( ( | )) =1 \u2212 log ( ( | )", "eq_num": ") 2)" } ], "section": "Score Calculations", "sec_num": "4.3" }, { "text": "The outcomes of the GMM and HMM systems are not LRs, but are known as scores. The value of a score provides information about the degree of the similarity between the two speech samples, i.e. the offender and suspect samples, having taken into account their typicality with respect to the relevant population; it is not directly interpretable as an LR (Morrison, 2013, p. 2) . Thus, the scores need to be converted to LRs by means of a calibration process. As we will see in \u00a76, calibration is an essential part of LR-based FVC.", "cite_spans": [ { "start": 352, "end": 374, "text": "(Morrison, 2013, p. 2)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Scores to Likelihood Ratios", "sec_num": "4.4" }, { "text": "Logistic-regression calibration (Br\u00fcmmer & du Preez, 2006 ) is a commonly used method that converts scores to interpretable LRs by applying linear shifting and scaling in the log odds space. A logistic-regression line (e.g. y = ax + b; x = score; y = log10LR) whose weights (i.e. a and b in y = ax + b) are estimated from the SS and DS scores of the development database is used to monotonically shift (by the amount of b) and scale (by the amount of a) the scores of the testing database to the log10LRs.", "cite_spans": [ { "start": 32, "end": 57, "text": "(Br\u00fcmmer & du Preez, 2006", "ref_id": "BIBREF4" } ], "ref_spans": [], "eq_spans": [], "section": "Scores to Likelihood Ratios", "sec_num": "4.4" }, { "text": "A common way of assessing the performance of a classification system is with reference to its correct-or incorrect-classification rate: for instance, how many of the SS comparisons were correctly assessed as coming from the same speakers, and how many of the DS comparisons were correctly assessed as coming from different speakers. In the context of LR-based FVC, an LR can be used as a classification function with LR = 1 as unity. However, correct-or incorrectclassification rate is a binary decision (same speaker or different speakers), which refers to the ultimate issue of 'guilty vs. non-guilty'. As explained in \u00a72, it is not the task of the forensic expert, but of the trier-of-fact, to make such a decision. Thus, any metrics based on binary decision are not coherent with the LR framework.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Assessment Metrics", "sec_num": "5" }, { "text": "As emphasised in \u00a72, the task of the forensic expert is to estimate the strength of evidence as accurately as possible, and the strength of evidence, which can be quantified by means of a LR, is not binary in nature, but continuous. For example, both LR = 10 and LR = 20 support the correct hypothesis for the SS comparisons, but the latter supports the hypothesis more strongly than the former. The relative strength of the LR needs to be taken into account in the assessment.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Assessment Metrics", "sec_num": "5" }, { "text": "Hence, in this study, the log-likelihood-ratio cost (Cllr), which is a gradient metric based on LR, was used as the metric for assessing the performance of the LR-based FVC system. The calculation of Cllr is given in 3) (Br\u00fcmmer & du Preez, 2006) .", "cite_spans": [ { "start": 220, "end": 246, "text": "(Br\u00fcmmer & du Preez, 2006)", "ref_id": "BIBREF4" } ], "ref_spans": [], "eq_spans": [], "section": "Assessment Metrics", "sec_num": "5" }, { "text": "C llr = 1 2 ( 1 N H p \u2211 log 2 (1+ 1 LR i ) N H p i forH p =true + 1 N H d \u2211 log 2 (1+LR j ) N H d j forH d =true )", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Assessment Metrics", "sec_num": "5" }, { "text": "3)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Assessment Metrics", "sec_num": "5" }, { "text": "In 3), NHp and NHd are the number of SS and DS comparisons, and LRi and LRj are the linear LRs derived from the SS and DS comparisons, respectively. Under a perfect system, all SS comparisons should produce LRs greater than 1, since origins are identical; as, in the case of DS comparisons, origins are different, DS comparisons should produce LRs less than 1. Cllr takes into account the magnitude of derived LR values, and assigns them appropriate penalties. In Cllr, LRs that support the counter-factual hypotheses or, in other words, contrary-to-fact LRs (LR < 1 for SS comparisons and LR > 1 for DS comparisons) are heavily penalised and the magnitude of the penalty is proportional to how much the LRs deviate from unity. Optimum performance is achieved when Cllr = 0 and decreases as Cllr approaches and exceeds 1. Thus, the lower the Cllr value, the better the performance.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Assessment Metrics", "sec_num": "5" }, { "text": "The Cllr measures the overall performance of a system in terms of validity based on a cost function in which there are two main components of loss: discrimination loss (Cllr min ) and calibration loss (Cllr cal ) (Br\u00fcmmer & du Preez, 2006) . The former is obtained after the application of the socalled pooled-adjacent-violators (PAV) transformation -an optimal non-parametric calibration procedure. The latter is obtained by subtracting the former from the Cllr. In this study, besides Cllr, Cllr min and Cllr cal are also referred to.", "cite_spans": [ { "start": 213, "end": 239, "text": "(Br\u00fcmmer & du Preez, 2006)", "ref_id": "BIBREF4" } ], "ref_spans": [], "eq_spans": [], "section": "Assessment Metrics", "sec_num": "5" }, { "text": "The magnitude of the derived LRs is visually presented using Tippett plots. Details on how to read a Tippett plot are explained in \u00a76, when the plots are presented.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Assessment Metrics", "sec_num": "5" }, { "text": "The average Cllr, Cllr min and Cllr cal values were calculated according to the mora numbers; they are plotted in Figure 1 as a function of word duration, separately for the HMM and GMM systems. The numerical values of Figure 1 are given in Table 4 .", "cite_spans": [], "ref_spans": [ { "start": 114, "end": 122, "text": "Figure 1", "ref_id": "FIGREF0" }, { "start": 219, "end": 227, "text": "Figure 1", "ref_id": "FIGREF0" }, { "start": 241, "end": 248, "text": "Table 4", "ref_id": "TABREF4" } ], "eq_spans": [], "section": "Experimental Results and Discussions", "sec_num": "6" }, { "text": "Although this was expected, it can be seen from Figure 1a and Table 4 that the overall performance (Cllr) of both systems improves as the words become longer in terms of mora, and also that the HMM system constantly outperforms the GMM system as far as average Cllr values are concerned. The performance gap between the two systems becomes wider as the number of mora increases, with the performance of the two systems being similar with words of two and three moras. For 12 out of the 25 two-mora words and 6 out of the 16 three-mora words, the GMM system performed better than the HMM system in terms of Cllr. In other words, the evidence suggests that the HMM may not be clearly advantageous for short words, e.g. two-or three-mora words. For the sake of reference, for only 6 out of the 22 four-mora words, the GMM system outperformed the HMM system. For the five-and seven-mora words, the HMM system constantly outperformed the GMM system.", "cite_spans": [], "ref_spans": [ { "start": 48, "end": 57, "text": "Figure 1a", "ref_id": "FIGREF0" }, { "start": 62, "end": 69, "text": "Table 4", "ref_id": "TABREF4" } ], "eq_spans": [], "section": "Experimental Results and Discussions", "sec_num": "6" }, { "text": "The discriminability of the systems (Cllr min ) ( Figure 1b ) also exhibits the same trend as the overall performance in that discriminability improves with more moras, the HMM system constantly performed better than the GMM system, and the performance of the former improves at a faster rate than that of the latter. As a result, there is a larger gap in discriminability between the two systems with the seven-mora word (0.052 = 0.099-0.047) than there is with the two-mora words (0.009 = 0.270-0.261).", "cite_spans": [], "ref_spans": [ { "start": 50, "end": 59, "text": "Figure 1b", "ref_id": "FIGREF0" } ], "eq_spans": [], "section": "Experimental Results and Discussions", "sec_num": "6" }, { "text": "The calibration loss of both systems (Cllr cal ) (Figure 1c ) is very similar for two-, three-, fourand five-mora words, which are essentially the same for the two systems (2: 0.038 and 0.040; 3: 0.032 and 0.037; 4: 0.029 and 0.030; 5: 0.028 and 0.028). The calibration loss improves (albeit at a very small rate) as a function of word duration, except in the case of the GMM system with the seven-mora word.", "cite_spans": [], "ref_spans": [ { "start": 49, "end": 59, "text": "(Figure 1c", "ref_id": "FIGREF0" } ], "eq_spans": [], "section": "Experimental Results and Discussions", "sec_num": "6" }, { "text": "As has been described by means of Figure 1 and Table 4 , it is clearly advantageous to include temporal information in modelling in Japanese, even under the challenging condition of data sparsity. However, the difference in performance may not be evident with short, e.g. two-and threemora, words. Put differently, if a forensic speech expert is working on a comparable word or phrase of relatively good length, the decision to either include transitional information in the modelling or not is likely to substantially impact on the outcome. For example, the HMM system outperformed the GMM system by the Cllr values of 0.073 (= 0.136 -0.063) with the seven-mora word.", "cite_spans": [], "ref_spans": [ { "start": 34, "end": 42, "text": "Figure 1", "ref_id": "FIGREF0" }, { "start": 47, "end": 54, "text": "Table 4", "ref_id": "TABREF4" } ], "eq_spans": [], "section": "Experimental Results and Discussions", "sec_num": "6" }, { "text": "Three different numbers of Gaussians -4, 8 and 16 -were used in the study. Table 5 shows which mixture number of Gaussians performed best for words of different mora duration according to the different systems. For example, out of the 25 two-mora words, the GMM system with a mixture number of 8 (M = 8) returned the best result for 11 words, and the HMM system with a mixture number of 4 (M = 4) yielded the lowest Cllr value for 13 words.", "cite_spans": [], "ref_spans": [ { "start": 75, "end": 82, "text": "Table 5", "ref_id": "TABREF5" } ], "eq_spans": [], "section": "Experimental Results and Discussions", "sec_num": "6" }, { "text": "According to Table 5 , there is a clear difference between the two systems with respect to the best performing mixture number of Gaussians, in that the GMM tends to require a higher mixture number for optimal performance (overall, 76% of words worked best with a mixture number of 16), while the HMM generally does not require a higher mixture number (overall, 62% of words performed best with a mixture number of 4). To investigate whether there are any differences in the nature and magnitude of the derived LRs, a Tippett plot was generated for each word in each experiment, and this was done separately for the GMM and HMM systems. Figure 2 has Tippett plots of the five-mora word 'daijyoobu' with 16 Gaussians: Panel a) = GMM and Panel b) = HMM. The plots are fairly typical and illustrate the differences between the two systems.", "cite_spans": [], "ref_spans": [ { "start": 13, "end": 20, "text": "Table 5", "ref_id": "TABREF5" }, { "start": 636, "end": 644, "text": "Figure 2", "ref_id": null } ], "eq_spans": [], "section": "Experimental Results and Discussions", "sec_num": "6" }, { "text": "Tippet plots show the cumulative proportion of the LRs of the DS comparisons (DSLRs), which are plotted rising from the right, as well as of the LRs of the SS comparisons (SSLRs), plotted rising from the left. The solid curves are for LRs and the dotted curves are for scores (pre-calibration LRs). For all Tippett plots, the cumulative proportion of trails is plotted on the y-axis against the log10 LRs on the x-axis.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experimental Results and Discussions", "sec_num": "6" }, { "text": "As can be seen in Figure 2 , the derived scores (pre-calibration LRs), which are given in dotted curves, are uncalibrated in different ways for the GMM and HMM systems: the former (Figure 2a ) is uncalibrated to the left and the latter (Figure 2b) is uncalibrated to the right. This indicates that calibration is essential in both systems. In fact, calibrating system output is recommended as standard practice (Morrison, 2018) .", "cite_spans": [ { "start": 411, "end": 427, "text": "(Morrison, 2018)", "ref_id": "BIBREF16" } ], "ref_spans": [ { "start": 18, "end": 26, "text": "Figure 2", "ref_id": null }, { "start": 180, "end": 190, "text": "(Figure 2a", "ref_id": null }, { "start": 236, "end": 247, "text": "(Figure 2b)", "ref_id": null } ], "eq_spans": [], "section": "Experimental Results and Discussions", "sec_num": "6" }, { "text": "The dotted curves are more widely apart in Figure 2a (GMM) than in Figure 2b (HMM) . This means that the magnitude of the derived scores is ", "cite_spans": [], "ref_spans": [ { "start": 43, "end": 52, "text": "Figure 2a", "ref_id": null }, { "start": 67, "end": 82, "text": "Figure 2b (HMM)", "ref_id": null } ], "eq_spans": [], "section": "Experimental Results and Discussions", "sec_num": "6" }, { "text": "ze.ro 'zero' ku.ru.ma 'car' ko.o.so.ku 'highway' hya.ku 'hundred' ka.ne 'money';= go.ze.n 'AM' re.e 'zero' de.n.wa 'telephone' ya.ku.so.ku 'promise' sa.n.bya.ku 'three hundred' da.i.jyo.o.bu 'fine' wa.ta.shi 'I' i.chi 'one' ke.e.sa.tsu 'police' o.n.na 'woman' ro.p.pya.ku 'six hundred' ki.no.o 'yesterday' ko.do.mo 'child' sa.n 'three' do.ku 'poison' o.ku.sa.n 'wife' ha.p.pya.ku 'eight hundred' kyo.o 'today' ke.e.ta.i 'mobile phone' yo.n 'four' re.n.ra.ku 'contact' re.su.to.ra.n 'restaurant' se.n 'thousand' a.shi.ta 'tomorrow' ka.ji 'fire' ro.ku 'six' ba.ku.da.n 'bomb' po.su.to 'post' i.s.se.n 'one thousand' ge.n.ki.n 'cash' ko.n.bi.ni 'store' na.na 'seven' gi.n.ko.o 'bank' sa.a.bi.su.e.ri.a 'road house' go.go 'afternoon' a.no.o 'well (filler)' ta.ku.shi.i 'taxi' shi.chi", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null } ], "back_matter": [ { "text": "The authors thank the reviewers for their valuable comments. ", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Acknowledgments", "sec_num": null }, { "text": "greater with the GMM system than with the HMM system. However, after calibration (solid curves), it can be seen that the magnitude of the DSLRs is very similar between the two systems while the SSLRs are far stronger for the HMM system than for the GMM system. That is, the calibration causes different effects in the two systems; it brings about more conservative LRs for the GMM system, but enhanced LRs for the HMM system.Although calibration usually results in a better performance, its impact on the magnitude of LRs seems to be different depending on various factors, including the types of features and modelling techniques. Many FVC studies, in particular those based on the acoustic-phonetic statistical approach, report that calibration results in more con-servative LRs than scores (Rose, 2013) , while it contributes to stronger LRs for the automatic approach (Morrison, 2018) . However, it is not clear at this stage what the observed differences between the two systems with respect to the relationship between the scores and LRs entail. This warrants further investigation.Apart from the similar degree of magnitude of the DSLRs (including both consistent-with-fact and contrary-to-fact LRs) that were obtained for the GMM and HMM systems, Figure 2 shows that the magnitude of the consistent-with-fact SSLRs is far greater for the HMM system ( Figure 2b) , and also that all of the SS comparisons were accurately classified as being from the same speakers for the HMM system. As a result, the HMM system is assessed to be better in Cllr than the GMM system (GMM: Cllr = 0.182 and HMM: Cllr = 0.156).", "cite_spans": [ { "start": 793, "end": 805, "text": "(Rose, 2013)", "ref_id": "BIBREF22" }, { "start": 872, "end": 888, "text": "(Morrison, 2018)", "ref_id": "BIBREF16" } ], "ref_spans": [ { "start": 1255, "end": 1263, "text": "Figure 2", "ref_id": null }, { "start": 1359, "end": 1370, "text": "Figure 2b)", "ref_id": null } ], "eq_spans": [], "section": "annex", "sec_num": null }, { "text": "This is a preliminary study investigating the usefulness of speaker-individuating information manifested in the time-varying aspect of speech in a text-dependent FVC system, in particular in the automatic FVC approach. In this study, performance of the GMM and HMM systems was compared using the same data under a forensically realistic, but challenging condition, which is sparsity of data. Even with short durations of two-, three-, four-, five-and seven-mora words, the HMM system constantly outperformed the GMM system in terms of average Cllr values. However, the benefits of the transitional information become evident when the HMM system is built with words longer than two-or three mora. With a seven-mora word, for example, the HMM system performed better than the GMM system by a Cllr value of 0.073.This study also demonstrates that the outcomes (scores) of the GMM and HMM systems are not well-calibrated; thus calibration is an essential part of the FVC if they are to be used as models in the system.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7" } ], "bib_entries": { "BIBREF0": { "ref_id": "b0", "title": "Statistics and the Evaluation of Evidence for Forensic Scientists", "authors": [ { "first": "C", "middle": [ "G G" ], "last": "Aitken", "suffix": "" } ], "year": 1995, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Aitken, C. G. G. (1995). Statistics and the Evaluation of Evidence for Forensic Scientists. 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Note that the Y-axis scale in Panel c is different from that in Panels a and b.", "uris": null }, "TABREF0": { "type_str": "table", "html": null, "num": null, "content": "", "text": "Usage of Gr1~6 for experiments (Exp). Test, Dev and Back refer to test, development and background databases." }, "TABREF2": { "type_str": "table", "html": null, "num": null, "content": "
", "text": "Numbers of SS and DS comparisons for each word." }, "TABREF4": { "type_str": "table", "html": null, "num": null, "content": "
: Numerical information of Figure 1.
G = GMM and H = HMM.
MoraSystemM = 4M = 8M = 16
2 (25)G H0 1311 514 7
3 (16)G H0 132 314 0
4 (22)G H0 141 421 3
5 (2)G H0 12 10 1
7 (1)G H0 00 01 1
TotalG H0 (0%) 41 (62%) 13 (20%) 12 (18%) 16 (24%) 50 (76%)
", "text": "" }, "TABREF5": { "type_str": "table", "html": null, "num": null, "content": "", "text": "Best-performing Gaussian numbers (M) for words with different mora numbers. G = GMM and H = HMM." } } } }