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Abstract This paper studies a statistical learning model where the model coefficients have a pre-determined non-overlapping group sparsity structure. We consider a combination of a loss function and a regularizer to recover the desired group sparsity patterns, which can embrace many existing works. We analyze directional stationary solutions of the proposed formulation, obtaining a sufficient condition for a directional stationary solution to achieve optimality and establishing a bound of the distance from the solution to a reference point. We develop an efficient algorithm that adopts an alternating direction method of multiplier (ADMM), showing that the iterates converge to a directional stationary solution under certain conditions. In the numerical experiment, we implement the algorithm for generalized linear models with convex and nonconvex group regularizers to evaluate the model performance on various data types, noise levels, and sparsity settings.
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DeepHoyer: Learning Sparser Neural Network with Differentiable Scale-Invariant Sparsity Measures
In seeking for sparse and efficient neural network models, many previous works investigated on enforcing `1 or `0 regularizers to encourage weight sparsity during training. The `0 regularizer measures the parameter sparsity directly and is invariant to the scaling of parameter values. But it cannot provide useful gradients and therefore requires complex optimization techniques. The `1 regularizer is almost everywhere differentiable and can be easily optimized with gradient descent. Yet it is not scale-invariant and causes the same shrinking rate to all parameters, which is inefficient in increasing sparsity. Inspired by the Hoyer measure (the ratio between `1 and `2 norms) used in traditional compressed sensing problems, we present DeepHoyer, a set of sparsity-inducing regularizers that are both differentiable almost everywhere and scale-invariant. Our experiments show that enforcing DeepHoyer regularizers can produce even sparser neural network models than previous works, under the same accuracy level. We also show that DeepHoyer can be applied to both element-wise and structural pruning. The codes are available at https://github.com/yanghr/DeepHoyer.
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- PAR ID:
- 10179709
- Date Published:
- Journal Name:
- International Conference on Learning Representations
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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