Sequential Detection of Regime Changes in Neural Data

The problem of detecting changes in firing patterns in neural data is studied. The problem is formulated as a quickest change detection problem. Important algorithms from the literature are reviewed. A new algorithmic technique is discussed to detect deviations from learned baseline behavior. The algorithms studied can be applied to both spike and local field potential data. The algorithms are applied to mice spike data to verify the presence of behavioral learning

Minimax-Optimal Algorithms for Detecting Changes in Statistically Periodic Random Processes

Theory and algorithms are developed for detecting changes in the distribution of statistically periodic random processes. The statistical periodicity is modeled using independent and periodically identically distributed processes, a new class of stochastic processes proposed by us. An algorithm is developed that is minimax asymptotically optimal as the false alarm rate goes to zero. Algorithms are also developed for the cases when the post-change distribution is not known or when there are multiple streams of observations. The modeling is inspired by real datasets encountered in cyber-physical systems, biology, and medicine. The developed algorithms are applied to sequences of Instagram counts collected around a 5K run in New York City to detect the run.Comment: arXiv admin note: text overlap with arXiv:1810.12760, arXiv:1807.0694

A Bayesian Theory of Change Detection in Statistically Periodic Random Processes

A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. A novel Bayesian theory is developed for detecting a change in the distribution of an i.p.i.d. process. It is shown that the Bayesian change point problem can be expressed as a problem of optimal control of a Markov decision process (MDP) with periodic transition and cost structures. Optimal control theory is developed for periodic MDPs for discounted and undiscounted total cost criteria. A fixed-point equation is obtained that is satisfied by the optimal cost function. It is shown that the optimal policy for the MDP is nonstationary but periodic in nature. A value iteration algorithm is obtained to compute the optimal cost function. The results from the MDP theory are then applied to detect changes in i.p.i.d. processes. It is shown that while the optimal change point algorithm is a stopping rule based on a periodic sequence of thresholds, a single-threshold policy is asymptotically optimal, as the probability of false alarm goes to zero. Numerical results are provided to demonstrate that the asymptotically optimal policy is not strictly optimal