Infinity Learning: Learning Markov Chains from Aggregate Steady-State Observations
Infinity Learning: Learning Markov Chains from Aggregate Steady-State Observations
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DOI：
10.1609/aaai.v34i04.5806
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
Jianfei Gao;Mohamed Zahran;Amit Sheoran;S. Fahmy;Bruno Ribeiro
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文献类型：
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作者：
Jianfei Gao;Mohamed Zahran;Amit Sheoran;S. Fahmy;Bruno Ribeiro
我们考虑学习参数连续时间马尔可夫链（CTMC）序列模型的任务，而训练数据完全由总体稳态统计数据组成，我们假设我们希望预测的状态在训练数据中均不在训练速度，并均不在训练率。未观察到的国家的国家分布。通过稳态计算，即使只能观察到CTMC状态的子集，我们也可以将∞-SGD应用于现实世界测试床和合成实验，表明其准确性，可以将稳态分布推送到未观察的状态下（在繁重的载荷下训练时），甚至在困难的场景中训练时，
We consider the task of learning a parametric Continuous Time Markov Chain (CTMC) sequence model without examples of sequences, where the training data consists entirely of aggregate steady-state statistics. Making the problem harder, we assume that the states we wish to predict are unobserved in the training data. Specifically, given a parametric model over the transition rates of a CTMC and some known transition rates, we wish to extrapolate its steady state distribution to states that are unobserved. A technical roadblock to learn a CTMC from its steady state has been that the chain rule to compute gradients will not work over the arbitrarily long sequences necessary to reach steady state —from where the aggregate statistics are sampled. To overcome this optimization challenge, we propose ∞-SGD, a principled stochastic gradient descent method that uses randomly-stopped estimators to avoid infinite sums required by the steady state computation, while learning even when only a subset of the CTMC states can be observed. We apply ∞-SGD to a real-world testbed and synthetic experiments showcasing its accuracy, ability to extrapolate the steady state distribution to unobserved states under unobserved conditions (heavy loads, when training under light loads), and succeeding in difficult scenarios where even a tailor-made extension of existing methods fails.