Police patrol units need to split their time between performing preventive patrol and being dispatched to serve emergency incidents. In the existing literature, patrol and dispatch decisions are often studied separately. We consider joint optimization of these two decisions to improve police operations efficiency and reduce response time to emergency calls. Methodology/results: We propose a novel method for jointly optimizing multi-agent patrol and dispatch to learn policies yielding rapid response times. Our method treats each patroller as an independent Q-learner (agent) with a shared deep Q-network that represents the state-action values. The dispatching decisions are chosen using mixed-integer programming and value function approximation from combinatorial action spaces. We demonstrate that this heterogeneous multi-agent reinforcement learning approach is capable of learning joint policies that outperform those optimized for patrol or dispatch alone. Managerial Implications: Policies jointly optimized for patrol and dispatch can lead to more effective service while targeting demonstrably flexible objectives, such as those encouraging efficiency and equity in response.

Posterior sampling in high-dimensional spaces using generative models holds significant promise for various applications, including but not limited to inverse problems and guided generation tasks. Despite many recent developments, generating diverse posterior samples remains a challenge, as existing methods require restarting the entire generative process for each new sample, making the procedure computationally expensive. In this work, we propose efficient posterior sampling by simulating Langevin dynamics in the noise space of a pre-trained generative model. By exploiting the mapping between the noise and data spaces which can be provided by distilled flows or consistency models, our method enables seamless exploration of the posterior without the need to re-run the full sampling chain, drastically reducing computational overhead. Theoretically, we prove a guarantee for the proposed noise-space Langevin dynamics to approximate the posterior, assuming that the generative model sufficiently approximates the prior distribution. Our framework is experimentally validated on image restoration tasks involving noisy linear and nonlinear forward operators applied to LSUN-Bedroom (256 x 256) and ImageNet (64 x 64) datasets. The results demonstrate that our approach generates high-fidelity samples with enhanced semantic diversity even under a limited number of function evaluations, offering superior efficiency and performance compared to existing diffusion-based posterior sampling techniques.

Point process models are widely used for continuous asynchronous event data, where each data point includes time and additional information called "marks", which can be locations, nodes, or event types. This paper presents a novel point process model for discrete event data over graphs, where the event interaction occurs within a latent graph structure. Our model builds upon Hawkes's classic influence kernel-based formulation in the original self-exciting point processes work to capture the influence of historical events on future events' occurrence. The key idea is to represent the influence kernel by Graph Neural Networks (GNN) to capture the underlying graph structure while harvesting the strong representation power of GNNs. Compared with prior works focusing on directly modeling the conditional intensity function using neural networks, our kernel presentation herds the repeated event influence patterns more effectively by combining statistical and deep models, achieving better model estimation/learning efficiency and superior predictive performance. Our work significantly extends the existing deep spatio-temporal kernel for point process data, which is inapplicable to our setting due to the fundamental difference in the nature of the observation space being Euclidean rather than a graph. We present comprehensive experiments on synthetic and real-world data to show the superior performance of the proposed approach against the state-of-the-art in predicting future events and uncovering the relational structure among data.

Learning to differentiate model distributions from observed data is a fundamental problem in statistics and machine learning, and high-dimensional data remains a challenging setting for such problems. Metrics that quantify the disparity in probability distributions, such as the Stein discrepancy, play an important role in high-dimensional statistical testing. This paper presents a method based on neural network Stein critics to distinguish between data sampled from an unknown probability distribution and a nominal model distribution with a novel staging of the weight of regularization. The benefit of using staged L 2 regularization in training such critics is demonstrated on evaluating generative models of image data.

Learning to differentiate model distributions from observed data is a fundamental problem in statistics and machine learning, and high-dimensional data remains a challenging setting for such problems. Metrics that quantify the disparity in probability distributions, such as the Stein discrepancy, play an important role in high-dimensional statistical testing. In this paper, we investigate the role of $L^{2}$ regularization in training a neural network Stein critic so as to distinguish between data sampled from an unknown probability distribution and a nominal model distribution. Making a connection to the Neural Tangent Kernel (NTK) theory, we develop a novel staging procedure for the weight of regularization over training time, which leverages the advantages of highly-regularized training at early times. Theoretically, we prove the approximation of the training dynamic by the kernel optimization, namely the “lazy training”, when the $L^{2}$ regularization weight is large, and training on $n$ samples converge at a rate of ${O}(n^{-1/2})$ up to a log factor. The result guarantees learning the optimal critic assuming sufficient alignment with the leading eigen-modes of the zero-time NTK. The benefit of the staged $L^{2}$ regularization is demonstrated on simulated high dimensional data and an application to evaluating generative models of image data.

Matrix data has been applied to a wide variety of scientific and engineering problems, including image processing, recommendation systems, and network modeling. Much effort has been on modeling individual matrix data using optimization and factorization. However, there has been relatively little research on modeling sequential and streaming observations for matrix data. To this end, we propose a novel Bayesian assimilation approach to model sequential low-rank matrix observations for online anomaly identification. By exploiting the posterior distributional properties of low-rank matrix subspaces, we track the subspace evolution and carry out uncertainty quantification with a computationally efficient procedure. It also enables identifying the changes in streaming matrices in real-time. We evaluate the performance of our method via an application of change identification in piezoresponse force microscopy data for material science studies.

With the increased extent of synchrophasor-based wide area monitoring systems in modern large-scale power systems, more data-limited classification of fault events in smart grids becomes possible. Recent works have identified and ex-ploited the low-rank property of synchrophasor data and power system dynamics for fault type classification. We develop a new methodology for modeling particular types of power grid faults from a tensor perspective, taking advantage of this well-known low-rank property, and classifying observed faults into categories by comparing to these low-rank representations. Using simulated data from the IEEE 39-bus system, we demonstrate that this approach is robust to limited temporal observation and sparse embedding of measurement units on the grid.