Spatio-temporal point processes (STPPs) are potent mathematical tools for modeling and predicting events with both temporal and spatial features. Despite their versatility, most existing methods for learning STPPs either assume a restricted form of the spatio-temporal distribution, or suffer from inaccurate approximations of the intractable integral in the likelihood training objective. These issues typically arise from the normalization term of the probability density function. Moreover, existing works only provide point prediction for events without quantifying their uncertainty, such as confidence intervals for the event’s arrival time and confidence regions for the event’s location, which is crucial given the considerable randomness of the data. To tackle these challenges, we introduce SMASH: a Score MAtching-based pSeudolikeliHood estimator for learning marked STPPs. Specifically, our framework adopts a normalization-free objective by estimating the pseudolikelihood of marked STPPs through score-matching and predicts confidence intervals/regions for event time and location by generating samples through a score-based sampling algorithm. The superior performance of our proposed framework is demonstrated through extensive experiments on both point and confidence interval/region prediction of events.

In this paper, we consider the quickest detection problem in high-dimensional streaming data, where the unknown regression coefficients might change at some unknown time. We propose a quickest detection algorithm based on the implicit regularization algorithm via gradient descent, and provide theoretical guarantees on the average run length to false alarm and detection delay. Numerical studies are conducted to validate the theoretical results.

We consider the linear discriminant analysis problem in the high-dimensional settings. In this work, we propose PANDA(PivotAl liNear Discriminant Analysis), a tuning insensitive method in the sense that it requires very little effort to tune the parameters. Moreover, we prove that PANDA achieves the optimal convergence rate in terms of both the estimation error and misclassification rate. Our theoretical results are backed up by thorough numerical studies using both simulated and real datasets. In comparison with the existing methods, we observe that our proposed PANDA yields equal or better performance, and requires substantially less effort in parameter tuning.

We study the multi-stream quickest detection problem under the active learning setup, It is assumed that there are p local streams in a system and s ≤ p unknown local streams are affected by an undesired event at some unknown time, but one is only able to take observations from r of these p local streams at each time instant. The objective is how to adaptively sample from these p local streams and how to use the observed data to raise a correct global alarm as quickly as possible. In this paper, we develop the first asymptotic optimality theory in the active quickest detection literature for the case when s = r = 2. To be more concrete, we propose to combine three ideas to develop efficient active quickest detection algorithms: (1) win-stay, lose-switch sampling strategy; (2) local CUSUM statistics for local monitoring; and (3) the SUM-Shrinkage technique to fuse local statistics into a global decision. We show that our proposed algorithms are asymptotically optimal in the sense of minimizing detection delay up to the second order subject to the false alarm constraint. Numerical studies are conducted to validate our theoretical results.

The multi-stream quickest detection problem with unknown post-change parameters is studied under the sampling control constraint, where there are$M$local processes in a system but one is only able to take observations from one of these$M$local processes at each time instant. The objective is to raise a correct alarm as quickly as possible once the change occurs subject to both false alarm and sampling control constraints. We propose an efficient myopic-sampling-based quickest detection algorithm under sampling control constraint, and show it is asymptotically optimal in the sense of minimizing the detection delay under our context when the number$M$of processes is fixed. Simulation studies are conducted to validate our theoretical results.

In multi-stream sequential change-point detection it is assumed that there are$M$processes in a system and at some unknown time, an occurring event changes the distribution of the samples of a particular process. In this article, we consider this problem under a sampling control constraint when one is allowed, at each point in time, to sample a single process. The objective is to raise an alarm as quickly as possible subject to a proper false alarm constraint. We show that under sampling control, a simple myopic-sampling-based sequential change-point detection strategy is second-order asymptotically optimal when the number$M$of processes is fixed. This means that the proposed detector, even by sampling with a rate$1/M$of the full rate, enjoys the same detection delay, up to some additive finite constant, as the optimal procedure. Simulation experiments corroborate our theoretical results.

In the sequential change-point detection problem for multi-stream data, it is assumed that there are M processes in a system and at some unknown time, an occurring event impacts one unknown local process in the sense of changing the distribution of observations from that affected local process. In this paper, we consider such problem under the sampling control constraint, in which one is able to take observations from only one of the local processes at each time step. Our objective is to design an adaptive sampling policy and a stopping time policy that is able to raise a correct alarm as quickly as possible subject to the false alarm and sampling control constraint. We develop an efficient sequential change-point detection algorithm under the sampling control that turns out to be second-order asymptotically optimal under the full data scenario. That is, with the sampling rate that is only 1/M of the full data scenario, our proposed algorithm has the same performance up to second-order as the optimal procedure under the full data scenario.