Density Ratio Estimation in Machine Learning

By Masashi Sugiyama, Taiji Suzuki, Takafumi Kanamori. 2012

696 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Probabilistic & Bayesian Methods

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Citations in the corpus

Meta-Learning Probabilistic Inference for Prediction (2018, methodology): “…theory then uses Bayes’ theorem to show that the optimal softmax classiﬁer can be expressed in terms of the conditional densities (Mohamed, 2018; Sugiyama et al., 2012): (cid:80) (cid:80) This implies that the optimal classiﬁer will construct estimators for the conditional density for each…”
Supervised Dimensionality Reduction via Distance Correlation Maximization (2016, methodology): “This is done under orthonormal constraints over B , and the optimal solution is found by approximating p zy ( z,y ) p z ( z ) p y ( y ) using method of density ratio estimation [Sugiyama et al., 2012, Vapnik et al., 2015], and also an analytical closed form solution for the minima is obtained.”
Isolating Sources of Disentanglement in VAEs (2018, methodology): “The main difference is they estimate the total correlation using the density ratio trick [35] which requires an auxiliary discriminator network and an inner optimization loop.”
Batch Stationary Distribution Estimation (2020, background): “To begin to develop a practical variational approach, ﬁrst note that (6) operates directly on the density ratio, which implies the density ratio estimation techniques of Nguyen et al. (2008) and Sugiyama et al. (2012) can be applied.”
DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections (2019, methodology): “error), various direct ratio estimators have been proposed [37], including the moment matching approach [13], probabilistic classification approach [3, 5, 33], and ratio matching approach [17, 27, 38] The proposed DualDICE algorithm, as a direct approach for density ratio estimation, bears some simi”
Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation (2018, background): “Finally, there is a comprehensive literature of two-sample density ratio estimation [e.g., 27, 35], which estimates the density ratio of two distributions from pairs of their samples.”
Learning in Implicit Generative Models (2016, methodology): “There are four general approaches to consider (Sugiyama et al., 2012a): 1) class-probability estimation, 2) divergence minimisation, 3) ratio matching, and 4) moment matching.”
VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning (2017, methodology): “In principle, any method for density ratio estimation could be used here, for example, see [9, 21].”
Variational Approaches for Auto-Encoding Generative Adversarial Networks (2017, methodology): “While using class probability estimation is amongst the most popular, the density ratio can also be computed in several other ways including by f -divergence minimization and density-ratio matching [27, 34].”
Distribution Matching in Variational Inference (2018, methodology): “The density ratio trick (Goodfellow et al., 2014, Good-fellow, 2014, Sugiyama et al., 2012) leverages the power of classiﬁers in order to estimate density ratios.”
Bias Correction of Learned Generative Models using Likelihood-Free Importance Weighting (2019, methodology): “As shown in prior work, the output of such classifiers can be used to extract density ratios [9].”
Variational Autoencoder with Implicit Optimal Priors (2018, methodology): “In this paper, we introduce the density ratio trick (Sugiyama, Suzuki, and Kanamori 2012; Goodfellow et al. 2014), which can estimate the ratio of two distributions without modeling each distribution explicitly.”
Multi-label Contrastive Predictive Coding (2020, background): “The above theorem extends existing variational lower bound estimators of KL divergences (that are generally interpreted as binary classification [46, 39]) into a family of lower bounds that can be interpreted as multi-label classification.”
Constructive setting for problems of density ratio estimation (2015, background): “However, this naive approach is not reliable in high-dimensional problems since division by an estimated quantity can greatly magnify the estimation error [6].”
Likelihood-Free Inference by Ratio Estimation (2016, methodology): “There are several methods in the literature available for the estimation of density ratios (e.g. Gutmann and Hirayama, 2011; Sugiyama et al., 2012; Izbicki et al., 2014), of which estimation through logistic regression is widely used and has some favourable asymptotic properties (Geyer, 1994; Qin, 1”
Data Selection for Language Models via Importance Resampling (2023, methodology): “Many methods tackle the high-dimensional importance weight estimation problem [79; 67; 12; 13].”
Under Review as a Conference Paper at Iclr 2017 Learning in Implicit Generative Models (2017, methodology): “There are four general approaches to consider (Sugiyama et al., 2012a): 1) class-probability estimation, 2) divergence minimisation, 3) ratio matching, and 4) moment matching.”