t-DCF and minDCF: the tandem detection cost function explained

This page belongs to the deepfake detection hub and sits beside the equal error rate page, which covers the metric t-DCF replaced. The scores it explains appear on the voice anti-spoofing benchmark overview.

01Why did ASVspoof stop ranking by EER?

The first two ASVspoof editions, 2015 and 2017, scored countermeasures on their own with the equal error rate, the threshold at which false alarms and misses are equal. The t-DCF paper by Kinnunen and colleagues (Odyssey 2018) gives two reasons that this stopped being enough: "the CM EER is not necessarily a reliable predictor of performance when ASV and CMs are combined", and the EER operating point is "ill-suited to user authentication applications" such as telephone banking, where almost every caller is the genuine account holder and spoofing attempts are rare (arXiv 1804.09618). A countermeasure sits in front of an automatic speaker verification (ASV) system, and what matters is what the pair does together.

The authors re-scored the top ten 2015 and 2017 submissions with the new metric and found that "system rankings derived with the EER and t-DCF show differences for higher priors". A metric that changes the ranking of real submissions is a different metric, not a re-labelling.

02What does the tandem detection cost function add up?

The t-DCF is an expected cost over three kinds of trial: a target speaker, a non-target (zero-effort impostor) and a spoofing attack. The original formulation has six parameters, "false alarm and miss costs for both systems, and prior probabilities of target and spoof trials", with the non-target prior implied. It sums four cost-weighted error terms: the ASV rejecting a target, the ASV accepting a non-target, the countermeasure passing a spoof that the ASV then accepts, and the countermeasure rejecting a target.

The 2018 paper's worked example sets the target and non-target priors to 0.99 and 0.01 of the non-spoof mass, both false alarm costs to 10 and both miss costs to 1, following the NIST speaker recognition evaluations. The ASVspoof 2021 evaluation plan fixes the operational values for the LA and PA tasks: a target prior of 0.9405, a non-target prior of 0.0095, a spoof prior of 0.05, a miss cost of 1 and false alarm costs of 10 for both non-targets and spoofs, the same values used in 2019 (ASVspoof 2021 evaluation plan). The costs encode the view that letting a fraudster in is ten times worse than turning away a customer; the priors encode an authentication service where nineteen in twenty calls are genuine.

03How is the minimum t-DCF computed and normalised?

In ASVspoof the ASV system is the organisers' and is fixed, with its threshold at its own EER point, so the only thing a participant controls is the countermeasure's score for each trial. The 2021 plan writes the ASV-constrained t-DCF as C0 plus C1 times the countermeasure's miss rate plus C2 times its false alarm rate, where C0, C1 and C2 fold together the priors, the costs and the fixed ASV's error rates. C0 is the cost the ASV incurs on its own; the 2021 plan notes that this term was "discarded in 2019" and is kept in 2021.

Two steps make the number readable. The cost is divided by that of a countermeasure that accepts everything or rejects everything, whichever is cheaper, so that 1 means "the countermeasure is useless". Then the countermeasure threshold is swept to the value that gives the lowest normalised cost. That minimum over the threshold is the min t-DCF, the primary metric. It "ranges in between [ASV floor, 1]", where the floor is the normalised cost a perfect countermeasure would still inherit from the verifier's own errors. A min t-DCF uses the best threshold in hindsight, as an EER does, which is why ASVspoof 5 also reports an actual DCF at a fixed threshold.

04What do the ASVspoof 2021 figures say?

The 2021 journal paper states the metric split plainly: "whereas the tandem detection cost function (t-DCF) is used as the primary metric for LA and PA tasks, that for the DF task is the CM equal error rate (EER)", because the deepfake task has no speaker verifier in the loop (arXiv 2210.02437). Of 54 teams, the top LA submission, T23, scored a min t-DCF of 0.2176 with an EER of 1.32 percent, against baselines B03 at 0.3445 and B04 at 0.4257; the best post-challenge system reached 0.2066 with an EER of 0.82 percent. The top PA submission, T07, scored 0.6824 on the evaluation set, and the paper notes that every PA system was "substantially worse than the ASV floor of 0.12". The DF winner, also T23, scored an EER of 15.64 percent against baselines of 22.38 and 23.48, and the best post-challenge DF result was 2.85 percent.

The two LA columns show why the metric matters. An EER of 1.32 percent reads as excellent; a min t-DCF of 0.2176 says that, with a verifier behind it and one call in twenty an attack, the pair still carries about a fifth of the cost of having no countermeasure at all. The ASVspoof 2021 task by task page gives the full rank tables and the codec conditions behind them.

05What changed with minDCF in ASVspoof 5?

ASVspoof 5 split the problem into a stand-alone deepfake detection track without a verifier (Track 1) and a spoofing-robust verification track (Track 2). Track 1 adopted a plain detection cost function with a miss cost of 1, a false alarm cost of 10 and a spoof prior of 0.05, normalised by the cheaper of the two trivial detectors, and its primary metric is the minimum of that cost, minDCF; actDCF at a fixed threshold, the log-likelihood-ratio cost Cllr and EER are reported alongside (ASVspoof 5 evaluation plan). Track 2 uses the architecture-agnostic a-DCF with the same priors as the 2021 t-DCF and reports min t-DCF as a secondary figure. The ASVspoof 5 page carries the results.

The 2020 journal extension of t-DCF had already proposed "a simplified version of the t-DCF with fewer parameters" and analysed "a special case for a fixed ASV system", which is the case every ASVspoof edition since 2019 has run (arXiv 2007.05979). The Track 1 DCF is what remains when the verifier is removed entirely.

06Why do face benchmarks not use t-DCF?

Face recognition reports a true accept rate at a fixed false accept rate, and face deepfake detection reports AUC or EER; the AUC, EER and false positive rate definitions page sets those out. Those metrics describe one system alone. The t-DCF exists because voice anti-spoofing was framed from the start as a guard on a verifier, so its benchmark asks what the guard costs the verifier. A face liveness check in front of a face verifier is the same tandem, and the ISO presentation attack metrics report the two halves separately; the open-source face recognition toolkits page shows how far the verifier's own score moves with its training data, which is the C0 term a face t-DCF would have to carry. Benchmarks of generated video, covered on the AI video generators and detection page, report F1 and average precision and assume no downstream system at all. One more caveat applies to every cost metric: the costs and priors are asserted, not measured, and a different application would rank the same systems differently.