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Decoupled Variational Gaussian Inference
Mohammad Emtiyaz Khan

Thu Dec 11 11:00 AM -- 03:00 PM (PST) @ Level 2, room 210D #None
Variational Gaussian (VG) inference methods that optimize a lower bound to the marginal likelihood are a popular approach for Bayesian inference. These methods are fast and easy to use, while being reasonably accurate. A difficulty remains in computation of the lower bound when the latent dimensionality $L$ is large. Even though the lower bound is concave for many models, its computation requires optimization over $O(L^2)$ variational parameters. Efficient reparameterization schemes can reduce the number of parameters, but give inaccurate solutions or destroy concavity leading to slow convergence. We propose decoupled variational inference that brings the best of both worlds together. First, it maximizes a Lagrangian of the lower bound reducing the number of parameters to $O(N)$, where $N$ is the number of data examples. The reparameterization obtained is unique and recovers maxima of the lower-bound even when the bound is not concave. Second, our method maximizes the lower bound using a sequence of convex problems, each of which is parallellizable over data examples and computes gradient efficiently. Overall, our approach avoids all direct computations of the covariance, only requiring its linear projections. Theoretically, our method converges at the same rate as existing methods in the case of concave lower bounds, while remaining convergent at a reasonable rate for the non-concave case.

Author Information

Emtiyaz Khan (RIKEN)

Emtiyaz Khan (also known as Emti) is a team leader at the RIKEN center for Advanced Intelligence Project (AIP) in Tokyo where he leads the Approximate Bayesian Inference Team. He is also a visiting professor at the Tokyo University of Agriculture and Technology (TUAT). Previously, he was a postdoc and then a scientist at Ecole Polytechnique Fédérale de Lausanne (EPFL), where he also taught two large machine learning courses and received a teaching award. He finished his PhD in machine learning from University of British Columbia in 2012. The main goal of Emti’s research is to understand the principles of learning from data and use them to develop algorithms that can learn like living beings. For the past 10 years, his work has focused on developing Bayesian methods that could lead to such fundamental principles. The approximate Bayesian inference team now continues to use these principles, as well as derive new ones, to solve real-world problems.

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