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In this work, we propose an infinite restricted Boltzmann machine~(RBM), whose maximum likelihood estimation~(MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of finite models of increasing complexity. As a side benefit, this can be used to easily and efficiently identify an appropriate number of hidden units during the optimization. The resulting model can also be used as an initialization for typical state-of-the-art RBM training algorithms such as contrastive divergence, leading to models with consistently higher test likelihood than random initialization.
We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block Frank-Wolfe al
Dictionary learning is a widely used unsupervised learning method in signal processing and machine learning. Most existing works of dictionary learning are in an offline manner. There are mainly two offline ways for dictionary learning. One is to do
We unveil the connections between Frank Wolfe (FW) type algorithms and the momentum in Accelerated Gradient Methods (AGM). On the negative side, these connections illustrate why momentum is unlikely to be effective for FW type algorithms. The encoura
In this paper, we study the properties of the Frank-Wolfe algorithm to solve the ExactSparse reconstruction problem. We prove that when the dictionary is quasi-incoherent, at each iteration, the Frank-Wolfe algorithm picks up an atom indexed by the s
Action-constrained reinforcement learning (RL) is a widely-used approach in various real-world applications, such as scheduling in networked systems with resource constraints and control of a robot with kinematic constraints. While the existing proje