In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the explicit representation of the chemical master equation solution. An additional advantage of representing the probability mass function in the tensor train format is that parametric dependency can be easily incorporated by introducing a tensor product basis expansion in the parameter space. Time is treated as an additional dimension of the tensor and a linear system is derived to solve the chemical master equation in time. We exemplify the tensor-train method by performing inference tasks such as smoothing and parameter inference using the tensor-train framework. A very high compression ratio is observed for storing the probability mass function of the solution. Since all linear algebra operations are performed in the tensor-train format, a significant reduction of the computational time is observed as well.

翻译：在这项工作中,我们用高压培训格式对化学主方程式进行贝耶斯式推论任务。 电压培训近似值已证明非常有效, 代表化学主方程式溶液的清晰表示产生的高维数据。 在高压列列方程式中代表概率质量函数的另一个好处是,通过在参数空间中引入强压产品基扩展,参数依赖性可以很容易地纳入参数。 时间被作为强压的附加维度处理,并且将一个线性系统用来及时解决化学主方程式。 我们通过使用高压技术框架进行光滑和参数推导等推推法,来举例说明了抗拉- 和参数引力法方法。 在存储溶液的概率质量函数时,观察到了非常高的压缩率。 由于所有线性测算器操作都是以高压系统格式进行的,因此也观察到了计算时间的显著缩短。