Fast nonconvex changepoint detection
In recent years, new technologies in neuroscience have made it possible to measure the activities of large numbers of neurons in behaving animals. For each neuron, a fluorescence trace is measured; this can be seen as a first-order approximation of the neuron's activity over time. Determining the exact time at which a neuron spikes on the basis of its fluorescence trace is an important open problem in the field of computational neuroscience. Recently, a convex optimization problem involving an L1 penalty was proposed for this task. In this talk, I slightly modify that proposal by replacing the L1 penalty with an L0 penalty.
Remarkably, it turns out that the resulting L0 optimization problem can be efficiently solved for the global optimum using an extremely simple and efficient dynamic programming algorithm. In addition to this basic algorithm, I develop a faster algorithm that can be used to deconvolve a fluorescence trace of 100 000 timesteps in less than a second. Furthermore, I present a modification to this algorithm that precludes the possibility of a “negative spike”. I demonstrate the performance of this algorithm for spike deconvolution on calcium imaging datasets that were recently released. This algorithm was used in the Allen Institute for Brain Science’s “platform paper” to decode neural activity from the Allen Brain Observatory.
I will also propose future work on FDR control for changepoint problems