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## Likelihood-ratio calibration using priorweighted proper scoring rules. arXiv preprint arXiv:1307.7981 (2013)

Citations: | 6 - 0 self |

### Citations

506 |
Veri£cation of forecasts expressed in terms of probabilities’
- Brier
- 1950
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Citation Context ...og(1− q) (13) The parametrization α = β = 1, τ = 0 gives (up to scaling), the objectiveCllr, proposed in [2] for the evaluation of goodness of recognizers with likelihood-ratio output. The Brier rule =-=[10]-=-, with α = β = 2: C∗2,2(q, tar) = 3(1− q)2 C∗2,2(q, non) = 3q 2 (14) An asymmetric rule, with α = 2, β = 1: C∗2,1(q, tar) = 2(1− q) C∗2,1(q, non) = −2 log(1− q)− 2q (15) 4.3. Calibration recipe We ass... |

370 | Strictly proper scoring rules, prediction, and estimation
- Gneiting, Raftery
- 2007
(Show Context)
Citation Context ...ession that ignores scores below a suitable threshold can benefit applications with low false-alarm rate requirements. In this work we limit ourselves to cost functions which are proper scoring rules =-=[5]-=-. We expand on our previous work [6], to demonstrate theoretically and experimentally that we can tailor proper scoring rules to target the low false-alarm region. 2. Proper scoring rules Given a data... |

118 | Transforming classifier scores into accurate multiclass probability estimates
- Zadrozny, Elkan
- 2002
(Show Context)
Citation Context ...y doing worse at lower threshold values. 6.1. The PAV reference The ideal reference along the vertical axis of figure 3 is achieved via an optimization algorithm known as pool adjacent violators (PAV)=-=[14, 8]-=-. This algorithm finds the optimal log-likelihoodratio value for every trial non-parametrically, subject only to the constraint that when sorted along the real line, the order of the -10 -8 -6 -4 -2 0... |

79 | Application-Independent Evaluation of Speaker Detection
- Brummer, J
- 2006
(Show Context)
Citation Context ...take as the baseline discriminative model priorweighted logistic regression [1], which has become a standard recipe for calibration in speaker recognition, with implementations available in the FoCal =-=[2]-=- and BOSARIS [3] toolkits. Logistic regression is the minimization of the expected value of a special cost function, known as the logarithmic proper scoring rule. We are interested here in generalizin... |

68 |
Numerical Optimization (2nd edition).
- Nocedal, Wright
- 2006
(Show Context)
Citation Context ... are differentiable, one can obtain the gradient w.r.t. A,B by backpropagation and then use any of a variety of well-known unconstrained numerical optimization algorithms. For this work, we used BFGS =-=[11]-=-. 5. Experiments We performed calibration experiments on scores from a single speaker recognizer (an i-vector PLDA system), which was part of the ABC submission [12] to the NIST SRE’12 speaker recogni... |

49 | Loss functions for binary class probability estimation and classification: Structure and applications.
- Buja, Stuetzle, et al.
- 2005
(Show Context)
Citation Context ...ent applications [8]. 2.2. Canonical form Although applications may be defined via a large variety of cost functions, all of this variety can be conveniently represented in a surprisingly simple form =-=[8, 5, 9]-=-. All binary proper scoring 1We assume there is a rule—the details of which are unimportant here—to choose among multiple minimizers. ar X iv :1 30 7. 79 81 v1s[ sta t.M L]s3 0 J uls20 13 rules can be... |

23 |
Discriminatively Trained Probabilistic Linear Discriminant Analysis for Speaker Verification”, accepted to ICASSP
- Burget, Plchot, et al.
- 2011
(Show Context)
Citation Context ...erally applied, not just for calibration. These objectives could be used for fusion of multiple recognizers, or indeed for more general discriminative training of speaker recognizers in the manner of =-=[15]-=-. However for more complex recognizers, the risk of overtraining is greater—and this risk may be compounded by more narrowly focussed objectives, such as the Brier rule. In contrast, the wider focus o... |

16 |
Measuring, refining and calibrating speaker and language information extracted from speech
- Brummer
- 2010
(Show Context)
Citation Context ...ation of proper scoring rules is still a proper scoring rule, in the sense that it can be derived via (1) from a suitably constructed cost function that represents a mixture of different applications =-=[8]-=-. 2.2. Canonical form Although applications may be defined via a large variety of cost functions, all of this variety can be conveniently represented in a surprisingly simple form [8, 5, 9]. All binar... |

14 |
et al., “Fusion of heterogeneous speaker recognition systems in the STBU submission for the NIST speaker recognition evaluation 2006
- Brümmer
(Show Context)
Citation Context ...ent. This posterior can be used in a straight-forward, standard way to make minimum-expected-cost Bayes decisions. We shall take as the baseline discriminative model priorweighted logistic regression =-=[1]-=-, which has become a standard recipe for calibration in speaker recognition, with implementations available in the FoCal [2] and BOSARIS [3] toolkits. Logistic regression is the minimization of the ex... |

9 | The BOSARIS Toolkit: Theory, Algorithms and Code for Surviving the New DCF
- Brummer, Villiers
- 2011
(Show Context)
Citation Context ...line discriminative model priorweighted logistic regression [1], which has become a standard recipe for calibration in speaker recognition, with implementations available in the FoCal [2] and BOSARIS =-=[3]-=- toolkits. Logistic regression is the minimization of the expected value of a special cost function, known as the logarithmic proper scoring rule. We are interested here in generalizing this recipe by... |

1 |
The Role of Score Calibration
- Doddington
- 2012
(Show Context)
Citation Context ...expected value of a special cost function, known as the logarithmic proper scoring rule. We are interested here in generalizing this recipe by modifying the cost function. Our motivation derives from =-=[4]-=-, where it was demonstrated that a modified logistic regression that ignores scores below a suitable threshold can benefit applications with low false-alarm rate requirements. In this work we limit ou... |

1 |
The Role of Proper Scoring Rules in Training and Evaluating Probabilistic Speaker and Language
- Brümmer
- 2012
(Show Context)
Citation Context ...uitable threshold can benefit applications with low false-alarm rate requirements. In this work we limit ourselves to cost functions which are proper scoring rules [5]. We expand on our previous work =-=[6]-=-, to demonstrate theoretically and experimentally that we can tailor proper scoring rules to target the low false-alarm region. 2. Proper scoring rules Given a database of supervised trials, the sum o... |