Spatiotemporal point processes (STPPs) are probabilistic models for events occurring in continuous space and time. Real-world event data often exhibit intricate dependencies and heterogeneous dynamics. By incorporating modern deep learning techniques, STPPs can model these complexities more effectively than traditional approaches. Consequently, the fusion of neural methods with STPPs has become an active and rapidly evolving research area. In this review, we categorize existing approaches, unify key design choices, and explain the challenges of working with this data modality. We further highlight emerging trends and diverse application domains. Finally, we identify open challenges and gaps in the literature.

Flow-based generative models have recently shown impressive performance for conditional generation tasks, such as text-to-image generation. However, current methods transform a general unimodal noise distribution to a specific mode of the target data distribution. As such, every point in the initial source distribution can be mapped to every point in the target distribution, resulting in long average paths. To this end, in this work, we tap into a non-utilized property of conditional flow-based models: the ability to design a non-trivial prior distribution. Given an input condition, such as a text prompt, we first map it to a point lying in data space, representing an ``average" data point with the minimal average distance to all data points of the same conditional mode (e.g., class). We then utilize the flow matching formulation to map samples from a parametric distribution centered around this point to the conditional target distribution. Experimentally, our method significantly improves training times and generation efficiency (FID, KID and CLIP alignment scores) compared to baselines, producing high quality samples using fewer sampling steps.

A common pursuit in modern statistical learning is to attain satisfactory generalization out of the source data distribution (OOD). In theory, the challenge remains unsolved even under the canonical setting of covariate shift for the linear model. This paper studies the foundational (high-dimensional) linear regression where the ground truth variables are confined to an ellipse-shape constraint and addresses two fundamental questions in this regime: (i) given the target covariate matrix, what is the min-max \emph{optimal} algorithm under covariate shift? (ii) for what kinds of target classes, the commonly-used SGD-type algorithms achieve optimality? Our analysis starts with establishing a tight lower generalization bound via a Bayesian Cramer-Rao inequality. For (i), we prove that the optimal estimator can be simply a certain linear transformation of the best estimator for the source distribution. Given the source and target matrices, we show that the transformation can be efficiently computed via a convex program. The min-max optimal analysis for SGD leverages the idea that we recognize both the accumulated updates of the applied algorithms and the ideal transformation as preconditions on the learning variables. We provide sufficient conditions when SGD with its acceleration variants attain optimality.

Clustering is a key component in any data analysis toolbox.

Submodular optimization has found many applications in machine learning and beyond. We carry out the first systematic investigation of inference in probabilistic models defined through submodular functions, generalizing regular pairwise MRFs and Determinantal Point Processes.

We introduce a new sequential Monte Carlo algorithm we call the particle cascade. The particle cascade is an asynchronous, anytime alternative to traditional sequential Monte Carlo algorithms that is amenable to parallel and distributed implementations. It uses no barrier synchronizations which leads to improved particle throughput and memory efficiency. It is an anytime algorithm in the sense that it can be run forever to emit an unbounded number of particles while keeping within a fixed memory budget. We prove that the particle cascade provides an unbiased marginal likelihood estimator which can be straightforwardly plugged into existing pseudo-marginal methods.

This paper introduces an integrated Bayesian model that combines line integral measurements and point values using Gaussian Process (GP). The proposed method leverages Gaussian Process Regression (GPR) to incorporate point values into 2D profiles and employs coordinate mapping to integrate magnetic flux information for 2D inversion. The average relative error of the reconstructed profile, using the integrated Bayesian tomography model with normalized magnetic flux, is as low as 3.60*10^(-4). Additionally, sensitivity tests were conducted on the number of grids, the standard deviation of synthetic diagnostic data, and noise levels, laying a solid foundation for the application of the model to experimental data. This work not only achieves accurate 2D inversion using the integrated Bayesian model but also provides a robust framework for decoupling pressure information from equilibrium reconstruction, thus making it possible to optimize equilibrium reconstruction using inversion results.

We analyze the performance of heterogeneous learning agents in asset markets with stochastic payoffs. Our agents aim to maximize the expected growth rate of their wealth but have different theories on how to learn this best. We focus on comparing Bayesian and no-regret learners in market dynamics. Bayesian learners with a prior over a finite set of models that assign positive prior probability to the correct model have posterior probabilities that converge exponentially to the correct model. Consequently, they survive even in the presence of agents who invest according to the correct model of the stochastic process. Bayesians with a continuum prior converge to the correct model at a rate of $O((\log T)/T)$. Online learning theory provides no-regret algorithms for maximizing the log of wealth in this setting, achieving a worst-case regret bound of $O(\log T)$ without assuming a steady underlying stochastic process but comparing to the best fixed investment rule. This regret, as we observe, is of the same order of magnitude as that of a Bayesian learner with a continuum prior. However, we show that even such low regret may not be sufficient for survival in asset markets: an agent can have regret as low as $O(\log T)$, but still vanish in market dynamics when competing against agents who invest according to the correct model or even against a perfect Bayesian with a finite prior. On the other hand, we show that Bayesian learning is fragile, while no-regret learning requires less knowledge of the environment and is therefore more robust. Any no-regret learner will drive out of the market an imperfect Bayesian whose finite prior or update rule has even small errors. We formally establish the relationship between notions of survival, vanishing, and market domination studied in economics and the framework of regret minimization, thus bridging these theories.

This paper investigates the integration of data sensor fusion in digital twin technology to bolster home environment capabilities, particularly in the context of challenges brought on by the coronavirus pandemic and its economic effects. The study underscores the crucial role of digital transformation in not just adapting to, but also mitigating disruptions during the fourth industrial revolution. Using the Wit Motion sensor, data was collected for activities such as walking, working, sitting, and lying, with sensors measuring accelerometers, gyroscopes, and magnetometers. The research integrates Cyber-physical systems, IoT, AI, and robotics to fortify digital twin capabilities. The paper compares sensor fusion methods, including feature-level fusion, decision-level fusion, and Kalman filter fusion, alongside machine learning models like SVM, GBoost, and Random Forest to assess model effectiveness. Results show that sensor fusion significantly improves the accuracy and reliability of these models, as it compensates for individual sensor weaknesses, particularly with magnetometers. Despite higher accuracy in ideal conditions, integrating data from multiple sensors ensures more consistent and reliable results in real-world settings, thereby establishing a robust system that can be confidently applied in practical scenarios.

We have seen rapid progress in the field of Artificial Intelligence (AI). If this progress continues, perhaps one day we will create powerful artificial agents. If we do so, how do we ensure that such AI agents do not go out of control? One approach is to make sure that we can switch off AI agents when they act against our interests. Put another way, we want to make sure that AI agents will defer to us.