Learning latent variable structured prediction models with Gaussian perturbations
This work addresses a specific bottleneck in machine learning for structured prediction with latent variables, offering an incremental improvement over existing methods.
The paper tackles the non-convexity and computational challenges in structured prediction with latent variables by introducing a new family of loss functions under Gaussian perturbations, showing that this approach provides a tighter upper bound for the Gibbs decoder distortion and enables faster objective evaluation, as demonstrated in synthetic experiments and a computer vision application.
The standard margin-based structured prediction commonly uses a maximum loss over all possible structured outputs. The large-margin formulation including latent variables not only results in a non-convex formulation but also increases the search space by a factor of the size of the latent space. Recent work has proposed the use of the maximum loss over random structured outputs sampled independently from some proposal distribution, with theoretical guarantees. We extend this work by including latent variables. We study a new family of loss functions under Gaussian perturbations and analyze the effect of the latent space on the generalization bounds. We show that the non-convexity of learning with latent variables originates naturally, as it relates to a tight upper bound of the Gibbs decoder distortion with respect to the latent space. Finally, we provide a formulation using random samples that produces a tighter upper bound of the Gibbs decoder distortion up to a statistical accuracy, which enables a faster evaluation of the objective function. We illustrate the method with synthetic experiments and a computer vision application.