Density-Ratio Estimation
Many problems about the difference between two probability distributions can be solved from the ratio alone, without recovering either distribution. Density-ratio estimation gets that ratio straight from the data, and it is the shared foundation under anomaly detection, adaptation to covariate shift, and the weighting used in causal inference. The main result here is Non-negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation (Kato and Teshima, 2021), published at ICML 2021.
Problems addressed
Estimating each density and then dividing is unstable, because error in the denominator swings the ratio a long way. So these methods estimate the ratio itself, as a single function. The estimation can be written uniformly as the minimization of a Bregman divergence, and many existing methods come out as special cases of it. We showed that this formulation, once a deep neural network is put inside it, overfits in a particular way, with the training loss alone dropping unnaturally, and we stabilized it with a non-negativity correction.
More recently we showed that Riesz regression, which causal inference uses for bias correction, has the same structure as density-ratio estimation, and that result ties the two fields together (Riesz Regression As Direct Density Ratio Estimation). The Generalized Riesz Regression page covers this direction as a whole.
Research thread
- 2023
- Unified Perspective on Probability Divergence via Maximum Likelihood Density Ratio Estimation (AISTATS 2023). Unifies the estimation of probability divergences as maximum likelihood estimation of a density ratio.
- 2021
- Density-Ratio Based Personalised Ranking from Implicit Feedback (WWW 2021). Recommendation from implicit feedback, formulated through a density ratio.
- 2020
- Off-Policy Evaluation and Learning for External Validity under a Covariate Shift (NeurIPS 2020). An application to correcting covariate shift.
Relation to earlier work
The methodology of solving learning problems through an estimated density ratio was established by a line of work from Masashi Sugiyama and coauthors, and it is collected in the textbook by Sugiyama, Suzuki, and Kanamori (2012, Density Ratio Estimation in Machine Learning). Direct estimation under squared loss, uLSIF (Kanamori, Hido, and Sugiyama, 2009, A Least-squares Approach to Direct Importance Estimation), is a representative method. Our work finds what breaks when the methodology is carried over to deep models, corrects it, and builds the bridge to causal inference.