Point processes and geometric inequalities

Latest papers

• Lévy Attention: Single-Pass Predictive Uncertainty for Continuous-Time Attention

  Sotirios P. Chatzis, Loukas Papadoulas · 20 August 2026

  Deep models for irregularly-sampled time series answer queries at arbitrary continuous timestamps, yet report nothing about how far each answer should be trusted. We show the attention layer itself can close that gap: with the right stochastic formulation, the pass that makes each prediction also re…

• Continuous-Time Reinforcement Learning for Controlled Hawkes Jump-Diffusions

  Tomasz R. Bielecki, Thibaut Mastrolia, Haoze Yan · 20 August 2026

  We study stochastic control of multivariate Hawkes-driven stochastic differential equations with machine learning algorithms in a non-Markovian setting. Due to the path dependence of the memory of the Hawkes intensity, this problem does not fall within classical stochastic control theory outside par…

• Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Run

  Yunbum Kook, Santosh S. Vempala · 18 August 2026

  For any convex body $\mathcal{K}\subset\mathbb{R}^{n}$ containing a unit ball, the spectral gap of Hit-and-Run is $Ω(1/(n^2 C_{\mathsf{PI}}))$, where $C_{\mathsf{PI}}$ is the Poincaré constant of the uniform distribution $π$ over $\mathcal{K}$. This implies that Hit-and-Run converges to a distributi…

• Certifying What Helps Customer-Return Timing: A Screen-and-Confirm Test for Conditioning Signals, and Why Decay Is Nearly Enough

  Sang Su Lee, Vineeth Loganathan, Shishir Dash, Vijay Raghavan · 13 August 2026

  Practitioners enrich customer-return models with ever more signals (lifetime value, category, recency/frequency, calendar, geography), and the temporal-point-process (TPP) literature follows suit with covariate- and external-covariate-conditioned intensities. But does any of it improve the timing, a…

• Existence-Field Diffusion Model for Spatial Point Processes with Variable Cardinality

  Xiaoyin Pan, Christian R. Shelton, Rakshith Mahishi, Chengkuan Hong · 30 July 2026

  We study generative modeling of spatial point processes (SPP), where both the number of points and their spatial configuration are governed by a joint distribution. While diffusion models have achieved strong performance in modeling complex distributions, extending them to variable-cardinality SPP r…

• Distributional Determinantal Point Process for Repulsive Clustering of Distributions

  Khai Nguyen, Yang Ni, Elizabeth Juarez-Colunga, Peter Mueller · 27 July 2026

  We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space. The dDPP is constructed via an L-ensemble with a sliced Wasserstein (SW) kernel between distributions. We show its valid…

• Smooth Neural Point Processes via B-Splines

  Michele Bellomo, Riccardo Ramaschi, Alberto Dolara, Tomaso Aste · 24 July 2026

  Temporal point processes (TPPs) provide a general and flexible framework for modeling sequences of events in continuous time. Neural networks have been successfully employed to model TPPs in a highly expressive and data-driven way. Neural TPPs are typically trained via Maximum Likelihood Estimation …

• Measuring Spatial Clustering via Metropolis-Hastings Diffusion Distance

  Thomas Weighill, Chidinma Williams · 17 July 2026

  We propose a novel measure of the discrepancy between two probability distributions $f$ and $g$ on a graph - which we call the diffusion distance - that measures the rate of convergence of $f$ to $g$ under a graph-constrained Markov chain with stationary distribution $g$. As a default choice for thi…

• GAttNHP: Group Attention Neural Hawkes Process for Extrapolation Reasoning in Temporal Knowledge Graphs

  Xiangni Tian, Kaixian Yu, Runpeng Dai, Niansheng Tang, Hongtu Zhu · 17 July 2026

  Temporal Knowledge Graphs (TKGs) record how facts evolve over time, but forecasting future events on a TKG remains difficult for three reasons: (i) long-range temporal dependencies are hard to encode; (ii) events on different chains mutually excite or inhibit one another in ways that snapshot-level …

• NeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process

  Neha Gupta, Aditya Maheshwari · 14 July 2026

  In this paper, we propose deep learning based NeuroMem-FHP framework for estimating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that captures long-range dependence through a fractional Mittag-Leffler excitation kernel. Two neural architectures, namely a Long …

• From Jumps to Signatures: a Generative Method for Temporal Point Processes

  Niels Cariou-Kotlarek, Vasileios Lampos · 9 July 2026

  Rough path signatures are a universal feature map for continuous paths and, via the expected signature, characterise path distributions. These guarantees do not directly extend to cadlag paths of Temporal Point Processes (TPPs), limiting the use of signature methods for event sequences. Furthermore,…

• Efficient Temporal Point Processes via Monotone Alternating Splines

  Cheng Wan, Quyu Kong, Feng Zhou · 3 July 2026

  Temporal point processes (TPPs) have widespread applications across various domains. Compared to modeling the conditional intensity of a TPP, modeling its cumulative conditional intensity function (CCIF) improves computational efficiency and eliminates numerical approximation errors. However, curren…

• HawkesNest: A Multi-Axis Synthetic Benchmark for Spatiotemporal Pattern Complexity

  Yahya Aalaila, Sumantrak Mukherjee, Gerrit Gro{\ss}mann, Sebastian Vollmer · 16 June 2026

  Evaluation of spatiotemporal point process (STPP) models relies heavily on opaque real-world datasets, where latent generative structure is unknown and model failures are difficult to attribute. We introduce HawkesNest, a generator-aligned benchmark for controlled spatiotemporal pattern complexity b…

• GLIDE: Graph-guided Leap Inference for Diffusion Estimation of Spatio-Temporal Point Processes

  Guanyu Zhou, Yao Liu, Yanglei Gan, Yuxiang Cai, Peng He, Run Lin, Yuxiang Liu, Qiao Liu · 2 June 2026

  Spatio-temporal point processes (STPPs) provide a principled framework for modeling asynchronous events in continuous time and space. Recent diffusion-based approaches offer a flexible alternative to deterministic prediction by modeling complex conditional distributions, but their application to STP…

• Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Events

  Keyan Chen, Qiwei Yuan, Zhitong Xu, Bin Shen, Shandian Zhe · 5 May 2026

  Events in spatiotemporal systems are ubiquitous, yet modeling their complex distributions remains challenging. Existing point process models often rely on strong structural assumptions and are typically limited to autoregressive, event-by-event prediction. As a result, they struggle to support broad…

• Modeling Patient Care Trajectories with Transformer Hawkes Processes

  Saumya Pandey, Varun Chandola · 8 April 2026

  Patient healthcare utilization consists of irregularly time-stamped events, such as outpatient visits, inpatient admissions, and emergency encounters, forming individualized care trajectories. Modeling these trajectories is crucial for understanding utilization patterns and predicting future care ne…

• Massively Parallel Exact Inference for Hawkes Processes

  Ahmer Raza, Hudson Smith · 3 April 2026

  Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as $O(N^2)$ in the number of events. The canonical linear exponential Hawkes process admits a faster $O(N)$ recurrence, but prior work evaluates this recurrence se…

• The Geometry of Efficient Nonconvex Sampling

  Santosh S. Vempala, Andre Wibisono · 27 March 2026

  We present an efficient algorithm for uniformly sampling from an arbitrary compact body $\mathcal{X} \subset \mathbb{R}^n$ from a warm start under isoperimetry and a natural volume growth condition. Our result provides a substantial common generalization of known results for convex bodies and star-s…

• Random Scaling and Momentum for Non-smooth Non-convex Optimization

  Qinzi Zhang, Ashok Cutkosky · 17 March 2026

  Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which classical analysis applies only if the loss is either convex or…

• Towards Reliable Detection of Empty Space: Conditional Marked Point Processes for Object Detection

  Tobias J. Riedlinger, Kira Maag, Hanno Gottschalk · 16 March 2026

  Deep neural networks have set the state-of-the-art in computer vision tasks such as bounding box detection and semantic segmentation. Object detectors and segmentation models assign confidence scores to predictions, reflecting the model's uncertainty in object detection or pixel-wise classification.…

• Causal Structure Learning in Hawkes Processes with Complex Latent Confounder Networks

  Songyao Jin, Biwei Huang · 3 March 2026

  Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed subprocesses, real-world systems are often only partially observed, wit…

• Multivariate Spatio-Temporal Neural Hawkes Processes

  Christopher Chukwuemeka, Hojun You, Mikyoung Jun · 2 March 2026

  We propose a Multivariate Spatio-Temporal Neural Hawkes Process for modeling complex multivariate event data with spatio-temporal dynamics. The proposed model extends continuous-time neural Hawkes processes by integrating spatial information into latent state evolution through learned temporal and s…

• A Nonparametric Discrete Hawkes Model with a Collapsed Gaussian-Process Prior

  Trinnhallen Brisley, Gordon Ross, Daniel Paulin · 11 February 2026

  Hawkes process models are used in settings where past events increase the likelihood of future events occurring. Many applications record events as counts on a regular grid, yet discrete-time Hawkes models remain comparatively underused and are often constrained by fixed-form baselines and excitatio…

• Scalable spatial point process models for forensic footwear analysis

  Alokesh Manna, Neil Spencer, Dipak K. Dey · 10 February 2026

  Shoe print evidence recovered from crime scenes plays a key role in forensic investigations. By examining shoe prints, investigators can determine details of the footwear worn by suspects. However, establishing that a suspect's shoes match the make and model of a crime scene print may not be suffici…

• A Representer Theorem for Hawkes Processes via Penalized Least Squares Minimization

  Hideaki Kim, Tomoharu Iwata · 6 February 2026

  The representer theorem is a cornerstone of kernel methods, which aim to estimate latent functions in reproducing kernel Hilbert spaces (RKHSs) in a nonparametric manner. Its significance lies in converting inherently infinite-dimensional optimization problems into finite-dimensional ones over dual …