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Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities.
A family of embedded Runge-Kutta formulae
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Random fields and diffusion processes
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Annealed importance sampling
Neal, R · 1998
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Asymptotic Statistics
van der Vaart, A · 2000
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Estimation of non-normalized statistical models by score matching
Hyvärinen, A · 2005
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MNIST handwritten digit database
LeCun, Y., Cortes, C., and Burges, C · 2010
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Density ratio estimation: A comprehensive review
Sugiyama, M., Suzuki, T., and Kanamori, T · 2010
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A connection between score matching and denoising autoencoders
Vincent, P · 2011
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Noise-contrastive estimation of unnormalized statistical models, with applications to natural image statistics
Gutmann, M. U. and Hyvärinen, A · 2012
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High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation
Izbicki, R., Lee, A., and Schafer, C · 2014
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Burda, Y., Grosse, R., and Salakhutdinov, R · 2015
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Deep Unsupervised Learning using Nonequilibrium Thermodynamics
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Deep Residual Learning for Image Recognition
He, K., Zhang, X., Ren, S., and Sun, J · 2016
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Multi-task learning using uncertainty to weigh losses for scene geometry and semantics
Kendall, A., Gal, Y., and Cipolla, R · 2017
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An overview of multi-task learning in deep neural networks
Ruder, S · 2017
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Flow contrastive estimation of energy-based models
Gao, R., Nijkamp, E., Kingma, D. P., Xu, Z., Dai, A. M., and Wu, Y. N · 2019
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Generative Adversarial Networks
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y · 2020
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Autoregressive Score Matching
Meng, C., Yu, L., Song, Y., Song, J., and Ermon, S · 2020
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Telescoping Density-Ratio Estimation
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Fourier features let networks learn high frequency functions in low dimensional domains
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Estimating the Density Ratio between Distributions with High Discrepancy using Multinomial Logistic Regression
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Generalization in diffusion models arises from geometry-adaptive harmonic representations
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Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Sampling
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