Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders

By Eleni Sgouritsa, Dominik Janzing, Jan Peters, Bernhard Schölkopf. 2013

16 citations recorded by the source corpus.

We propose a kernel method to identify finite mixtures of nonparametric product distributions. It is based on a Hilbert space embedding of the joint distribution. The rank of the constructed tensor is equal to the number of mixture components. We present an algorithm to recover the components by partitioning the data points into clusters such that the variables are jointly conditionally independent given the cluster. This method can be used to identify finite confounders.

Subfields: Artificial Intelligence, Computational Mathematics, Probabilistic & Bayesian Methods, Causal Inference & Discovery

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Bernhard Schölkopf
2. Kenji Fukumizu
3. Bharath K. Sriperumbudur
4. Krikamol Muandet
5. Arthur Gretton
6. Le Song
7. Bo Dai
8. David Lopez-Paz

In Computational Mathematics

1. Bo Dai
2. Kenji Fukumizu
3. Bernhard Schölkopf
4. Le Song
5. Anima Anandkumar
6. Bo Xie
7. Krikamol Muandet
8. Bharath K. Sriperumbudur

In Probabilistic & Bayesian Methods

1. Krikamol Muandet
2. Kenji Fukumizu
3. Bharath K. Sriperumbudur
4. Bernhard Schölkopf
5. Arthur Gretton
6. Le Song
7. Bo Dai
8. Yu Nishiyama

In Causal Inference & Discovery

1. Krikamol Muandet
2. Bharath K. Sriperumbudur
3. Kenji Fukumizu
4. Bernhard Schölkopf
5. Le Song
6. Bo Dai
7. David Lopez-Paz
8. Dominik Janzing

Citations in the corpus

• Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “…(Gretton et al. 2012a), independence and conditional independence tests (Fukumizu et al. 2008, Zhang et al. 2011, Doran et al. 2014), causal inference (Sgouritsa et al. 2013, Chen et al. 2014), adaptive MCMC (Sejdinovic et al. 2014), and approximate Bayesian computation (Fukumizu et al. 2013).”
• Nonparametric Estimation of Multi-View Latent Variable Models (2013, result): “However, none of the previous works explicitly recovers the actual parameters of the models Song et al. (2011); Song & Dai (2013); Sgouritsa et al. (2013).”