Result diversification (RD) is a crucial technique in Text-to-Image Retrieval for enhancing the efficiency of a practical application. Conventional methods focus solely on increasing the diversity metric of image appearances. However, the diversity metric and its desired value vary depending on the application, which limits the applications of RD. This paper proposes a novel task called CDR-CA (Contextual Diversity Refinement of Composite Attributes). CDR-CA aims to refine the diversities of multiple attributes, according to the application's context. To address this task, we propose Multi-Source DPPs, a simple yet strong baseline that extends the Determinantal Point Process (DPP) to multi-sources. We model MS-DPP as a single DPP model with a unified similarity matrix based on a manifold representation. We also introduce Tangent Normalization to reflect contexts. Extensive experiments demonstrate the effectiveness of the proposed method. Our code is publicly available at https://github.com/NEC-N-SOGI/msdpp.
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. However, these confidence estimates are often miscalibrated, as their architectures and loss functions are tailored to task performance rather than probabilistic foundation. Even with well calibrated predictions, object detectors fail to quantify uncertainty outside detected bounding boxes, i.e., the model does not make a probability assessment of whether an area without detected objects is truly free of obstacles. This poses a safety risk in applications such as automated driving, where uncertainty in empty areas remains unexplored. In this work, we propose an object detection model grounded in spatial statistics. Bounding box data matches realizations of a marked point process, commonly used to describe the probabilistic occurrence of spatial point events identified as bounding box centers, where marks are used to describe the spatial extension of bounding boxes and classes. Our statistical framework enables a likelihood-based training and provides well-defined confidence estimates for whether a region is drivable, i.e., free of objects. We demonstrate the effectiveness of our method through calibration assessments and evaluation of performance.
Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale to large datasets (which are common in modern applications), since it requires the solution of a linear system whose size scales quadratically with the number of samples in the dataset. We propose an approximate, distributed, accelerated sketch-and-project algorithm ($\texttt{ADASAP}$) for solving these linear systems, which improves scalability. We use the theory of determinantal point processes to show that the posterior mean induced by sketch-and-project rapidly converges to the true posterior mean. In particular, this yields the first efficient, condition number-free algorithm for estimating the posterior mean along the top spectral basis functions, showing that our approach is principled for GP inference. $\texttt{ADASAP}$ outperforms state-of-the-art solvers based on conjugate gradient and coordinate descent across several benchmark datasets and a large-scale Bayesian optimization task. Moreover, $\texttt{ADASAP}$ scales to a dataset with $> 3 \cdot 10^8$ samples, a feat which has not been accomplished in the literature.
Reliable uncertainty estimates are crucial in modern machine learning. Deep Gaussian Processes (DGPs) and Deep Sigma Point Processes (DSPPs) extend GPs hierarchically, offering promising methods for uncertainty quantification grounded in Bayesian principles. However, their empirical calibration and robustness under distribution shift relative to baselines like Deep Ensembles remain understudied. This work evaluates these models on regression (CASP dataset) and classification (ESR dataset) tasks, assessing predictive performance (MAE, Accu- racy), calibration using Negative Log-Likelihood (NLL) and Expected Calibration Error (ECE), alongside robustness under various synthetic feature-level distribution shifts. Results indicate DSPPs provide strong in-distribution calibration leveraging their sigma point approximations. However, compared to Deep Ensembles, which demonstrated superior robustness in both per- formance and calibration under the tested shifts, the GP-based methods showed vulnerabilities, exhibiting particular sensitivity in the observed metrics. Our findings underscore ensembles as a robust baseline, suggesting that while deep GP methods offer good in-distribution calibration, their practical robustness under distribution shift requires careful evaluation. To facilitate reproducibility, we make our code available at https://github.com/matthjs/xai-gp.
Realistic crowd simulations are essential for immersive virtual environments, relying on both individual behaviors (microscopic dynamics) and overall crowd patterns (macroscopic characteristics). While recent data-driven methods like deep reinforcement learning improve microscopic realism, they often overlook critical macroscopic features such as crowd density and flow, which are governed by spatio-temporal spawn dynamics, namely, when and where agents enter a scene. Traditional methods, like random spawn rates, stochastic processes, or fixed schedules, are not guaranteed to capture the underlying complexity or lack diversity and realism. To address this issue, we propose a novel approach called nTPP-GMM that models spatio-temporal spawn dynamics using Neural Temporal Point Processes (nTPPs) that are coupled with a spawn-conditional Gaussian Mixture Model (GMM) for agent spawn and goal positions. We evaluate our approach by orchestrating crowd simulations of three diverse real-world datasets with nTPP-GMM. Our experiments demonstrate the orchestration with nTPP-GMM leads to realistic simulations that reflect real-world crowd scenarios and allow crowd analysis.
Marked temporal point processes (MTPPs) have been shown to be extremely effective in modeling continuous time event sequences (CTESs). In this work, we present adversarial attacks designed specifically for MTPP models. A key criterion for a good adversarial attack is its imperceptibility. For objects such as images or text, this is often achieved by bounding perturbation in some fixed $L_p$ norm-ball. However, similarly minimizing distance norms between two CTESs in the context of MTPPs is challenging due to their sequential nature and varying time-scales and lengths. We address this challenge by first permuting the events and then incorporating the additive noise to the arrival timestamps. However, the worst case optimization of such adversarial attacks is a hard combinatorial problem, requiring exploration across a permutation space that is factorially large in the length of the input sequence. As a result, we propose a novel differentiable scheme PERMTPP using which we can perform adversarial attacks by learning to minimize the likelihood, while minimizing the distance between two CTESs. Our experiments on four real-world datasets demonstrate the offensive and defensive capabilities, and lower inference times of PERMTPP.
An event sequence generated by a temporal point process is often associated with a hidden and structured event branching process that captures the triggering relations between its historical and current events. In this study, we design a new plug-and-play module based on the Bregman ADMM (BADMM) algorithm, which infers event branches associated with event sequences in the maximum likelihood estimation framework of temporal point processes (TPPs). Specifically, we formulate the inference of event branches as an optimization problem for the event transition matrix under sparse and low-rank constraints, which is embedded in existing TPP models or their learning paradigms. We can implement this optimization problem based on subspace clustering and sparse group-lasso, respectively, and solve it using the Bregman ADMM algorithm, whose unrolling leads to the proposed BADMM module. When learning a classic TPP (e.g., Hawkes process) by the expectation-maximization algorithm, the BADMM module helps derive structured responsibility matrices in the E-step. Similarly, the BADMM module helps derive low-rank and sparse attention maps for the neural TPPs with self-attention layers. The structured responsibility matrices and attention maps, which work as learned event transition matrices, indicate event branches, e.g., inferring isolated events and those key events triggering many subsequent events. Experiments on both synthetic and real-world data show that plugging our BADMM module into existing TPP models and learning paradigms can improve model performance and provide us with interpretable structured event branches. The code is available at \url{https://github.com/qingmeiwangdaily/BADMM_TPP}.
Determinantal point processes (DPPs) are random configurations of points with tunable negative dependence. Because sampling is tractable, DPPs are natural candidates for subsampling tasks, such as minibatch selection or coreset construction. A \emph{coreset} is a subset of a (large) training set, such that minimizing an empirical loss averaged over the coreset is a controlled replacement for the intractable minimization of the original empirical loss. Typically, the control takes the form of a guarantee that the average loss over the coreset approximates the total loss uniformly across the parameter space. Recent work has provided significant empirical support in favor of using DPPs to build randomized coresets, coupled with interesting theoretical results that are suggestive but leave some key questions unanswered. In particular, the central question of whether the cardinality of a DPP-based coreset is fundamentally smaller than one based on independent sampling remained open. In this paper, we answer this question in the affirmative, demonstrating that \emph{DPPs can provably outperform independently drawn coresets}. In this vein, we contribute a conceptual understanding of coreset loss as a \emph{linear statistic} of the (random) coreset. We leverage this structural observation to connect the coresets problem to a more general problem of concentration phenomena for linear statistics of DPPs, wherein we obtain \emph{effective concentration inequalities that extend well-beyond the state-of-the-art}, encompassing general non-projection, even non-symmetric kernels. The latter have been recently shown to be of interest in machine learning beyond coresets, but come with a limited theoretical toolbox, to the extension of which our result contributes. Finally, we are also able to address the coresets problem for vector-valued objective functions, a novelty in the coresets literature.
Attention guides our gaze to fixate the proper location of the scene and holds it in that location for the deserved amount of time given current processing demands, before shifting to the next one. As such, gaze deployment crucially is a temporal process. Existing computational models have made significant strides in predicting spatial aspects of observer's visual scanpaths (where to look), while often putting on the background the temporal facet of attention dynamics (when). In this paper we present TPP-Gaze, a novel and principled approach to model scanpath dynamics based on Neural Temporal Point Process (TPP), that jointly learns the temporal dynamics of fixations position and duration, integrating deep learning methodologies with point process theory. We conduct extensive experiments across five publicly available datasets. Our results show the overall superior performance of the proposed model compared to state-of-the-art approaches. Source code and trained models are publicly available at: https://github.com/phuselab/tppgaze.
Retrieving temporal event sequences from textual descriptions is crucial for applications such as analyzing e-commerce behavior, monitoring social media activities, and tracking criminal incidents. To advance this task, we introduce TESRBench, a comprehensive benchmark for temporal event sequence retrieval (TESR) from textual descriptions. TESRBench includes diverse real-world datasets with synthesized and reviewed textual descriptions, providing a strong foundation for evaluating retrieval performance and addressing challenges in this domain. Building on this benchmark, we propose TPP-Embedding, a novel model for embedding and retrieving event sequences. The model leverages the TPP-LLM framework, integrating large language models (LLMs) with temporal point processes (TPPs) to encode both event texts and times. By pooling representations and applying a contrastive loss, it unifies temporal dynamics and event semantics in a shared embedding space, aligning sequence-level embeddings of event sequences and their descriptions. TPP-Embedding demonstrates superior performance over baseline models across TESRBench datasets, establishing it as a powerful solution for the temporal event sequence retrieval task.
Learning continuous-time point processes is essential to many discrete event forecasting tasks. However, integration poses a major challenge, particularly for spatiotemporal point processes (STPPs), as it involves calculating the likelihood through triple integrals over space and time. Existing methods for integrating STPP either assume a parametric form of the intensity function, which lacks flexibility; or approximating the intensity with Monte Carlo sampling, which introduces numerical errors. Recent work by Omi et al. [2019] proposes a dual network approach for efficient integration of flexible intensity function. However, their method only focuses on the 1D temporal point process. In this paper, we introduce a novel paradigm: AutoSTPP (Automatic Integration for Spatiotemporal Neural Point Processes) that extends the dual network approach to 3D STPP. While previous work provides a foundation, its direct extension overly restricts the intensity function and leads to computational challenges. In response, we introduce a decomposable parametrization for the integral network using ProdNet. This approach, leveraging the product of simplified univariate graphs, effectively sidesteps the computational complexities inherent in multivariate computational graphs. We prove the consistency of AutoSTPP and validate it on synthetic data and benchmark real-world datasets. AutoSTPP shows a significant advantage in recovering complex intensity functions from irregular spatiotemporal events, particularly when the intensity is sharply localized. Our code is open-source at https://github.com/Rose-STL-Lab/AutoSTPP.
Score matching estimators have gained widespread attention in recent years partly because they are free from calculating the integral of normalizing constant, thereby addressing the computational challenges in maximum likelihood estimation (MLE). Some existing works have proposed score matching estimators for point processes. However, this work demonstrates that the incompleteness of the estimators proposed in those works renders them applicable only to specific problems, and they fail for more general point processes. To address this issue, this work introduces the weighted score matching estimator to point processes. Theoretically, we prove the consistency of our estimator and establish its rate of convergence. Experimental results indicate that our estimator accurately estimates model parameters on synthetic data and yields results consistent with MLE on real data. In contrast, existing score matching estimators fail to perform effectively. Codes are publicly available at \url{https://github.com/KenCao2007/WSM_TPP}.
Temporal point processes (TPPs) are widely used to model the timing and occurrence of events in domains such as social networks, transportation systems, and e-commerce. In this paper, we introduce TPP-LLM, a novel framework that integrates large language models (LLMs) with TPPs to capture both the semantic and temporal aspects of event sequences. Unlike traditional methods that rely on categorical event type representations, TPP-LLM directly utilizes the textual descriptions of event types, enabling the model to capture rich semantic information embedded in the text. While LLMs excel at understanding event semantics, they are less adept at capturing temporal patterns. To address this, TPP-LLM incorporates temporal embeddings and employs parameter-efficient fine-tuning (PEFT) methods to effectively learn temporal dynamics without extensive retraining. This approach improves both predictive accuracy and computational efficiency. Experimental results across diverse real-world datasets demonstrate that TPP-LLM outperforms state-of-the-art baselines in sequence modeling and event prediction, highlighting the benefits of combining LLMs with TPPs.
Quantifying the predictive capacity of a neural system, intended as the capability to store information and actively use it for dynamic system evolution, is a key component of neural information processing. Information storage (IS), the main measure quantifying the active utilization of memory in a dynamic system, is only defined for discrete-time processes. While recent theoretical work laid the foundations for the continuous-time analysis of the predictive capacity stored in a process, methods for the effective computation of the related measures are needed to favor widespread utilization on neural data. This work introduces a method for the model-free estimation of the so-called memory utilization rate (MUR), the continuous-time counterpart of the IS, specifically designed to quantify the predictive capacity stored in neural point processes. The method employs nearest-neighbor entropy estimation applied to the inter-spike intervals measured from point-process realizations to quantify the extent of memory used by a spike train. An empirical procedure based on surrogate data is implemented to compensate the estimation bias and detect statistically significant levels of memory. The method is validated in simulated Poisson processes and in realistic models of coupled cortical dynamics and heartbeat dynamics. It is then applied to real spike trains reflecting central and autonomic nervous system activities: in spontaneously growing cortical neuron cultures, the MUR detected increasing memory utilization across maturation stages, associated to emergent bursting synchronized activity; in the study of the neuro-autonomic modulation of human heartbeats, the MUR reflected the sympathetic activation occurring with postural but not with mental stress. The proposed approach offers a computationally reliable tool to analyze spike train data in computational neuroscience and physiology.
Long-horizon event forecasting is critical across various domains, including retail, finance, healthcare, and social networks. Traditional methods, such as Marked Temporal Point Processes (MTPP), often rely on autoregressive models to predict multiple future events. However, these models frequently suffer from issues like converging to constant or repetitive outputs, which limits their effectiveness and general applicability. To address these challenges, we introduce DeTPP (Detection-based Temporal Point Processes), a novel approach inspired by object detection techniques from computer vision. DeTPP employs a unique matching-based loss function that selectively prioritizes reliably predictable events, improving the accuracy and diversity of predictions during inference. Our method establishes a new state-of-the-art in long-horizon event forecasting, achieving up to a 77% relative improvement over existing MTPP and next-K methods. The proposed hybrid approach enhances the accuracy of next event prediction by up to 2.7% on a large transactional dataset. Notably, DeTPP is also among the fastest methods for inference. The implementation of DeTPP is publicly available on GitHub.
A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the cumulative intensity function) in the likelihood resulting in doubly intractable posterior distribution. Here, we propose a nonparametric Bayesian approach for estimating the intensity function of an inhomogeneous Poisson process without reliance on large data augmentation or approximations of the likelihood function. We propose to jointly model the intensity and the cumulative intensity function as a transformed Gaussian process, allowing us to directly bypass the need of approximating the cumulative intensity function in the likelihood. We propose an exact MCMC sampler for posterior inference and evaluate its performance on simulated data. We demonstrate the utility of our method in three real-world scenarios including temporal and spatial event data, as well as aggregated time count data collected at multiple resolutions. Finally, we discuss extensions of our proposed method to other point processes.
Accurately forecasting multiple future events within a given time horizon is crucial for finance, retail, social networks, and healthcare applications. Event timing and labels are typically modeled using Marked Temporal Point Processes (MTPP), with evaluations often focused on next-event prediction quality. While some studies have extended evaluations to a fixed number of future events, we demonstrate that this approach leads to inaccuracies in handling false positives and false negatives. To address these issues, we propose a novel evaluation method inspired by object detection techniques from computer vision. Specifically, we introduce Temporal mean Average Precision (T-mAP), a temporal variant of mAP, which overcomes the limitations of existing long-horizon evaluation metrics. Our extensive experiments demonstrate that models with strong next-event prediction accuracy can yield poor long-horizon forecasts and vice versa, indicating that specialized methods are needed for each task. To support further research, we release HoTPP, the first benchmark designed explicitly for evaluating long-horizon MTPP predictions. HoTPP includes large-scale datasets with up to 43 million events and provides optimized procedures for both autoregressive and parallel inference, paving the way for future advancements in the field.
We consider the problem of multi-objective optimization (MOO) of expensive black-box functions with the goal of discovering high-quality and diverse Pareto fronts where we are allowed to evaluate a batch of inputs. This problem arises in many real-world applications including penicillin production where diversity of solutions is critical. We solve this problem in the framework of Bayesian optimization (BO) and propose a novel approach referred to as Pareto front-Diverse Batch Multi-Objective BO (PDBO). PDBO tackles two important challenges: 1) How to automatically select the best acquisition function in each BO iteration, and 2) How to select a diverse batch of inputs by considering multiple objectives. We propose principled solutions to address these two challenges. First, PDBO employs a multi-armed bandit approach to select one acquisition function from a given library. We solve a cheap MOO problem by assigning the selected acquisition function for each expensive objective function to obtain a candidate set of inputs for evaluation. Second, it utilizes Determinantal Point Processes (DPPs) to choose a Pareto-front-diverse batch of inputs for evaluation from the candidate set obtained from the first step. The key parameters for the methods behind these two steps are updated after each round of function evaluations. Experiments on multiple MOO benchmarks demonstrate that PDBO outperforms prior methods in terms of both the quality and diversity of Pareto solutions.
We introduce a novel statistical framework for the analysis of replicated point processes that allows for the study of point pattern variability at a population level. By treating point process realizations as random measures, we adopt a functional analysis perspective and propose a form of functional Principal Component Analysis (fPCA) for point processes. The originality of our method is to base our analysis on the cumulative mass functions of the random measures which gives us a direct and interpretable analysis. Key theoretical contributions include establishing a Karhunen-Lo\`{e}ve expansion for the random measures and a Mercer Theorem for covariance measures. We establish convergence in a strong sense, and introduce the concept of principal measures, which can be seen as latent processes governing the dynamics of the observed point patterns. We propose an easy-to-implement estimation strategy of eigenelements for which parametric rates are achieved. We fully characterize the solutions of our approach to Poisson and Hawkes processes and validate our methodology via simulations and diverse applications in seismology, single-cell biology and neurosiences, demonstrating its versatility and effectiveness. Our method is implemented in the pppca R-package.
We introduce squared neural Poisson point processes (SNEPPPs) by parameterising the intensity function by the squared norm of a two layer neural network. When the hidden layer is fixed and the second layer has a single neuron, our approach resembles previous uses of squared Gaussian process or kernel methods, but allowing the hidden layer to be learnt allows for additional flexibility. In many cases of interest, the integrated intensity function admits a closed form and can be computed in quadratic time in the number of hidden neurons. We enumerate a far more extensive number of such cases than has previously been discussed. Our approach is more memory and time efficient than naive implementations of squared or exponentiated kernel methods or Gaussian processes. Maximum likelihood and maximum a posteriori estimates in a reparameterisation of the final layer of the intensity function can be obtained by solving a (strongly) convex optimisation problem using projected gradient descent. We demonstrate SNEPPPs on real, and synthetic benchmarks, and provide a software implementation. https://github.com/RussellTsuchida/snefy