Abstract The problem of sequentially transferring a data-predictive probability distribution from a source to a target Bayesian filter is addressed in this paper. In many practical settings, this transfer is incompletely modelled, since the stochastic dependence structure between the filters typically cannot be fully specified. We therefore adopt fully probabilistic design to select the optimal transfer mechanism. We relax the target observation model via a scale-mixing parameter, which proves vital in successfully transferring the first and second moments of the source data predictor. This sensitivity to the transferred second moment ensures that imprecise predictors are rejected, achieving robust transfer. Indeed, Student-t state and observation models are adopted for both learning processes, in order to handle outliers in all hidden and observed variables. A recursive outlier-robust Bayesian transfer learning algorithm is recovered via a local variational Bayes approximation. The outlier rejection and positive transfer properties of the resulting algorithm are clearly demonstrated in a simulated planar position-velocity system, as is the key property of imprecise knowledge rejection (robust transfer), unavailable in current Bayesian transfer algorithms. Performance comparison with particle filter variants demonstrates the successful convergence of our robust variational Bayes transfer learning algorithm in sequential processing.

中文翻译：

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Student-t 过滤器之间的贝叶斯迁移学习

摘要 本文解决了从源到目标贝叶斯滤波器顺序传输数据预测概率分布的问题。在许多实际设置中，这种传输是不完全建模的，因为通常无法完全指定过滤器之间的随机依赖结构。因此，我们采用完全概率设计来选择最佳传输机制。我们通过尺度混合参数放松目标观测模型，这证明对于成功传递源数据预测器的一阶和二阶矩至关重要。这种对传递的二阶矩的敏感性确保拒绝不精确的预测变量，实现稳健的传递。事实上，两种学习过程都采用了 Student-t 状态和观察模型，为了处理所有隐藏变量和观察变量中的异常值。通过局部变分贝叶斯近似恢复递归异常值稳健贝叶斯转移学习算法。结果算法的异常值拒绝和正转移特性在模拟的平面位置-速度系统中得到了清晰的证明，这是不精确知识拒绝（鲁棒转移）的关键特性，在当前的贝叶斯转移算法中是不可用的。与粒子滤波器变体的性能比较表明，我们的稳健变分贝叶斯转移学习算法在顺序处理中的成功收敛。结果算法的异常值拒绝和正转移特性在模拟的平面位置-速度系统中得到了清晰的证明，这是不精确知识拒绝（鲁棒转移）的关键特性，在当前的贝叶斯转移算法中是不可用的。与粒子滤波器变体的性能比较表明，我们的稳健变分贝叶斯转移学习算法在顺序处理中的成功收敛。结果算法的异常值拒绝和正转移特性在模拟的平面位置-速度系统中得到了清晰的证明，这是不精确知识拒绝（鲁棒转移）的关键特性，在当前的贝叶斯转移算法中是不可用的。与粒子滤波器变体的性能比较表明，我们的稳健变分贝叶斯转移学习算法在顺序处理中的成功收敛。