Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion, and multiplication of large matrices or Monte Carlo estimation, neither of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we frame the standard Bayesian filtering problem as optimization over a time-varying objective. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems.

翻译：贝叶斯滤波通过反演显式生成模型，将含噪测量值转换为状态估计，从而近似时变系统的真实潜在行为。该过程通常需要存储、求逆和乘法运算大型矩阵，或采用蒙特卡洛估计，但对于高维状态空间（如人工神经网络的权重空间）而言，这两种方法均不实用。本文将标准贝叶斯滤波问题重新表述为时变目标函数上的优化问题。我们不维护滤波方程所需的矩阵或模拟粒子，而是通过指定一个优化器来隐式定义贝叶斯滤波器。在线性高斯设定下，我们证明每个卡尔曼滤波器均可等效为K步梯度下降的形式。在非线性设定中，实验表明我们的框架所生成的滤波器高效、鲁棒且可扩展至高维系统，与标准贝叶斯滤波解决方案工具箱相比表现优异。我们认为，调优优化器比指定正确的滤波方程更为简便，使得本框架成为高维滤波问题的理想选择。