We introduce two new particle-based algorithms for learning latent variable models via marginal maximum likelihood estimation, including one which is entirely tuning-free. Our methods are based on the perspective of marginal maximum likelihood estimation as an optimization problem: namely, as the minimization of a free energy functional. One way to solve this problem is via the discretization of a gradient flow associated with the free energy. We study one such approach, which resembles an extension of Stein variational gradient descent, establishing a descent lemma which guarantees that the free energy decreases at each iteration. This method, and any other obtained as the discretization of the gradient flow, necessarily depends on a learning rate which must be carefully tuned by the practitioner in order to ensure convergence at a suitable rate. With this in mind, we also propose another algorithm for optimizing the free energy which is entirely learning rate free, based on coin betting techniques from convex optimization. We validate the performance of our algorithms across several numerical experiments, including several high-dimensional settings. Our results are competitive with existing particle-based methods, without the need for any hyperparameter tuning.

翻译：我们提出了两种新的基于粒子的算法，用于通过边际最大似然估计学习潜变量模型，其中一种算法完全无需调参。我们的方法基于边际最大似然估计作为优化问题的视角：即将其视为自由能泛函的最小化。解决该问题的一种途径是对与自由能相关的梯度流进行离散化。我们研究了其中一种方法，它类似于斯坦因变分梯度下降的推广，并建立了一个保证自由能在每次迭代中递减的下降引理。该方法以及通过梯度流离散化得到的任何其他方法，都必然依赖于学习率，该学习率必须由实践者仔细调参以确保以合适的速率收敛。基于此，我们还提出了一种优化自由能的算法，该算法基于凸优化中的硬币投注技术，完全无需学习率。我们通过多项数值实验验证了算法的性能，包括若干高维场景。我们的结果与现有基于粒子的方法相比具有竞争力，且无需任何超参数调参。