Expectation maximization (EM) is a technique for estimating maximum-likelihood parameters of a latent variable model given observed data by alternating between taking expectations of sufficient statistics, and maximizing the expected log likelihood. For situations where sufficient statistics are intractable, stochastic approximation EM (SAEM) is often used, which uses Monte Carlo techniques to approximate the expected log likelihood. Two common implementations of SAEM, Batch EM (BEM) and online EM (OEM), are parameterized by a “learning rate”, and their efficiency depend strongly on this parameter. We propose an extension to the OEM algorithm, termed Introspective Online Expectation Maximization (IOEM), which removes the need for specifying this parameter by adapting the learning rate to trends in the parameter updates. We show that our algorithm matches the efficiency of the optimal BEM and OEM algorithms in multiple models, and that the efficiency of IOEM can exceed that of BEM/OEM methods with optimal learning rates when the model has many parameters. Finally we use IOEM to fit two models to a financial time series. A Python implementation is available at https://github.com/luntergroup/IOEM.git.

中文翻译：

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通过在线蒙特卡罗期望最大化中的自适应学习，对状态空间模型进行有效推理。


期望最大化 (EM) 是一种通过在获取足够统计数据的期望和最大化期望对数似然之间交替来估计给定观测数据的潜在变量模型的最大似然参数的技术。对于难以处理足够的统计数据的情况，通常使用随机近似 EM (SAEM)，它使用蒙特卡罗技术来近似预期的对数似然。 SAEM 的两种常见实现，批量 EM (BEM) 和在线 EM (OEM)，通过“学习率”进行参数化，它们的效率很大程度上取决于该参数。我们提出了 OEM 算法的扩展，称为内省在线期望最大化（IOEM），它通过使学习率适应参数更新的趋势来消除指定此参数的需要。我们表明，我们的算法在多个模型中与最佳 BEM 和 OEM 算法的效率相匹配，并且当模型具有许多参数时，IOEM 的效率可以超过具有最佳学习率的 BEM/OEM 方法。最后，我们使用 IOEM 将两个模型拟合到金融时间序列。 Python 实现可在 https://github.com/luntergroup/IOEM.git 上找到。