Learning from conditional distributions via dual embeddings

Bo Dai, Niao He, Yunpeng Pan, Byron Boots, Le Song

Research output: Contribution to conferencePaperpeer-review


Many machine learning tasks, such as learning with invariance and policy evaluation in reinforcement learning, can be characterized as problems of learning from conditional distributions. In such problems, each sample x itself is associated with a conditional distribution p(z|x) represented by samples {zi}Mi=1, and the goal is to learn a function f that links these conditional distributions to target values y. These problems become very challenging when we only have limited samples or in the extreme case only one sample from each conditional distribution. Commonly used approaches either assume that z is independent of x, or require an overwhelmingly large set of samples from each conditional distribution. To address these challenges, we propose a novel approach which employs a new min-max reformulation of the learning from conditional distribution problem. With such new reformulation, we only need to deal with the joint distribution p(z, x). We also design an efficient learning algorithm, Embedding-SGD, and establish theoretical sample complexity for such problems. Finally, our numerical experiments, on both synthetic and real-world datasets, show that the proposed approach can significantly improve over existing algorithms.

Original languageEnglish (US)
StatePublished - 2017
Externally publishedYes
Event20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017 - Fort Lauderdale, United States
Duration: Apr 20 2017Apr 22 2017


Conference20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017
CountryUnited States
CityFort Lauderdale

ASJC Scopus subject areas

  • Artificial Intelligence
  • Statistics and Probability

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