Probabilistic Outputs for Support vector Machines and Comparisons to Regularized Likelihood Methods

By J. Platt. 1999

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In Statistical Learning Theory

Citations in the corpus

CNN-Generated Images Are Surprisingly Easy to Spot… for Now (2019, methodology): “regression (the method is also known as Platt scaling [19]).”
Describing Textures in the Wild (2013, methodology): “4; after Platt’s calibration [28] on an held-out test set, the classiﬁer score c q (cid:48) ( (cid:96) i ) ∈ R is transformed in a probability p ( q (cid:48) | (cid:96) i ) = σ ( c q (cid:48) ( (cid:96) )) where σ ( z ) = 1 / (1 + e − z ) is the sigmoid function.”
Calibrate Before Use: Improving Few-Shot Performance of Language Models (2021, methodology): “4 A common technique for adjusting output probabilities is to apply an affine transformation (Platt, 1999; Guo et al., 2017): q̂ = softmax(Wp̂+ b), (1) where a weight matrix W and a bias vector b are applied to the original probabilities p̂ to get the new probabilities”
Evasion Attacks against Machine Learning at Test Time (2013, background): “susceptible to failure due to the nature of a discriminant function. Besides its shape, for many classiers, g(x) is equivalent to a posterior estimate p(yc= 1jx); e.g., for neural networks, and SVMs [23]. The discriminant function does not incorporate the evidence we have about the data distribution”
Security Evaluation of Support Vector Machines in Adversarial Environments (2014, methodology): “x); e.g., for neural networks, since they directly output a posterior estimate, and for SVMs, since their posterior can be estimated as a sigmoidal function of the distance of x to the SVM hyperplane [55]. Generally, this is a non-linear optimization, which one may optimize with many well-known tech”
Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning (2018, methodology): “Known as Platt scaling [38], the approach is equivalent to fitting a logistic regression to the classifier’s class scores:”
On Fairness and Calibration (2017, neutral): “It is not straightforward to encode the calibration constraint if the probabilities are assumed to be continuous, and post-processing calibration methods [31, 35] would break equal-cost constraints by modifying classifier scores.”
Algorithmic Decision Making and the Cost of Fairness (2017, methodology): “Therefore, to estimate p Y | X we re-train a risk assessment model that predicts two-year violent recidivism using L 1 -regularized logistic regression followed by Platt scaling [33]. model is based on all available features for each defendant, excluding race.”
Learning Optimized Risk Scores (2016, methodology): “Consider, for example, using Platt scaling (Platt et al., 1999) to improve the calibration of the PLR Rd and PLR RsRd risk scores in Figure 14.”
Estimating treatment effect heterogeneity in randomized program evaluation (2013, background): “lity estimates [Lin (2002), Lee, Lin and Wahba (2004)], we follow work that transforms the values Wc i(t) to approximate the underlying probability [Franc, Zien and Scho¨lkopf (2011), Sollich (2002), Platt (1999), Menon et al. (2012)]. Specifically, let cW∗ i (t) denote the predicted value cWi(t) tr”
Ensemble of exemplar-SVMs for object detection and beyond (2011, background): “A common strategy to reconcile the outputs of multiple classifiers is to perform calibration by fitting a probability distribution to a held-out set of negative and positive samples [16].”
Verified Uncertainty Calibration (2019, methodology): “Scaling methods, for example Platt scaling [12], output a function g =”
Calibrating Deep Convolutional Gaussian Processes (2018, methodology): “Popular calibration techniques include Platt scaling [24] and isotonic regression [30].”
How to Explain Individual Classification Decisions (2009, background): “For other classiﬁcation methods such as Support Vector Machines which do not provide a probability function as its output in Section 3 we give an example for an estimation method starting from Deﬁnition 1.”
Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift (2019, methodology): “Another popular non-Bayesian approach involves re-calibration of probabilities on a held-out validation set through temperature scaling (Platt, 1999), which was shown by Guo et al. (2017) to lead to well-calibrated predictions on the i.i.d. test set.”
Posterior calibration and exploratory analysis for natural language processing models (2015, methodology): “…recalibration methods, which readjust a non-calibrated model’s predictions to be calibrated; recalibration methods have been developed for binary (Platt, 1999; Niculescu-Mizil and Caruana, 2005) and multiclass (Zadrozny and Elkan, 2002) classiﬁcation settings, but we are unaware of methods…”