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Structure learning of directed acyclic graphs (DAGs) is a fundamental problem in many scientific endeavors. A new line of work, based on NOTEARS (Zheng et al., 2018), reformulates the structure learning problem as a continuous optimization one by leveraging an algebraic characterization of DAG constraint. The constrained problem is typically solved using the augmented Lagrangian method (ALM) which is often preferred to the quadratic penalty method (QPM) by virtue of its convergence result that does not require the penalty coefficient to go to infinity, hence avoiding ill-conditioning. In this work, we review the standard convergence result of the ALM and show that the required conditions are not satisfied in the recent continuous constrained formulation for learning DAGs. We demonstrate empirically that its behavior is akin to that of the QPM which is prone to ill-conditioning, thus motivating the use of second-order method in this setting. We also establish the convergence guarantee of QPM to a DAG solution, under mild conditions, based on a property of the DAG constraint term.
In deep learning with differential privacy (DP), the neural network achieves the privacy usually at the cost of slower convergence (and thus lower performance) than its non-private counterpart. This work gives the first convergence analysis of the DP
This paper presents a new conditional GAN (named convex relaxing CGAN or crCGAN) to replicate the conventional constrained topology optimization algorithms in an extremely effective and efficient process. The proposed crCGAN consists of a generator a
When training end-to-end learned models for lossy compression, one has to balance the rate and distortion losses. This is typically done by manually setting a tradeoff parameter $beta$, an approach called $beta$-VAE. Using this approach it is difficu
The communication between data-generating devices is partially responsible for a growing portion of the worlds power consumption. Thus reducing communication is vital, both, from an economical and an ecological perspective. For machine learning, on-d
The extrapolation strategy raised by Nesterov, which can accelerate the convergence rate of gradient descent methods by orders of magnitude when dealing with smooth convex objective, has led to tremendous success in training machine learning tasks. I