Trajectory Inference with Smooth Schrödinger Bridges
This work addresses trajectory inference for applications like single-cell RNAseq analysis, representing an incremental improvement with a novel method for a known bottleneck.
The authors tackled the problem of trajectory inference and particle tracking by introducing Smooth Schrödinger Bridges, which generalize prior work to use smooth Gaussian processes for more regular and interpretable trajectories. They developed a practical algorithm that outperforms existing methods on simulated and real single-cell RNAseq datasets.
Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schrödinger Bridges. Our proposal generalizes prior work by allowing the reference process in the Schrödinger Bridge problem to be a smooth Gaussian process, leading to more regular and interpretable trajectories in applications. Though naïvely smoothing the reference process leads to a computationally intractable problem, we identify a class of processes (including the Matérn processes) for which the resulting Smooth Schrödinger Bridge problem can be lifted to a simpler problem on phase space, which can be solved in polynomial time. We develop a practical approximation of this algorithm that outperforms existing methods on numerous simulated and real single-cell RNAseq datasets. The code can be found at https://github.com/WanliHongC/Smooth_SB