Extends Neural ODEs to model discrete changes in continuous systems.
problem Lack of explicit termination time in existing Neural ODE formulations.
method Introduces neural event functions to implicitly define termination criteria.
result Models discrete changes in continuous systems without prior knowledge.
A simple guide to understanding hierarchical causality in complex systems.
problem Understanding hierarchical causality in complex systems.
method Formalizing hierarchical causality in terms of actors and agents, with three key structures.
result The system requires three additional structures: causation classes, aggregation operators, and discrete event-time maps.
Proposes OC4Seq for detecting anomalies in discrete event sequences.
problem Challenges in detecting anomalies in discrete event sequences, including data imbalance, discrete events, and sequential nature.
method Integrates anomaly detection with recurrent neural networks (RNNs) to embed sequences into latent spaces and designs a multi-scale RNN framework to capture multi-scale sequential patterns.
result OC4Seq consistently outperforms various baselines on three benchmark datasets.
New STH distance finds patterns in event timeseries without resampling.
problem Lack of efficient analysis methods for event and state timeseries.
method Define STE-ts, propose STH, leveraging both time and state duration.
result Improved precision and computation time compared to resampled metrics.
Unified framework detects changes in complex system models.
problem Accurate identification of dynamic changes in simulation models.
method Combines machine learning and process-driven simulation modeling.
result Significantly improves change point detection accuracy.
Modeling coating degradation with fewer data points.
problem Efficiently forecasting material degradation from high-frequency sensor data.
method Discrete degradation events using Hawkes processes.
result Forecasting future coating failure with superior performance.
New approach uses deep reinforcement learning for vehicle dispatching, reducing waiting times.
problem Dynamic vehicle dispatching problem in various contexts.
method Event-based semi-Markov decision process with deep q-learning.
result Deep reinforcement learning policies outperform heuristic methods in New York City data.
Neural surrogate predicts SPN rates from token trajectories.
problem Challenging parameter estimation in SPNs with covariates.
method 1D Convolutional Residual Network trained on Gillespie-simulated SPN realizations.
result Surrogate predicts rate-function coefficients with RMSE = 0.043.
Proposes ABIDES-Gym for financial markets simulation.
problem Training multi-agent systems in financial markets.
method Wrapping DEMAS into OpenAI Gym framework.
result Developed two financial markets OpenAI Gym environments.
Most real-world datasets, and particularly those collected from physical systems, are full of noise, packet loss, and other imperfections. However, most specification mining, anomaly detection and other such algorithms assume, or even require, perfect data quality to function properly. Such algorithms may work in lab c…
This paper explores neural models to improve modeling of Hawkes process intensity functions.
problem Traditional Hawkes process intensity function's parametrized kernel function biases future event predictions.
method Uses neural models to model the kernel function of Hawkes process intensity function.
result Neural models can better capture future event characteristics using past events data.
New methods for inferring, predicting, and estimating continuous-time, discrete-event processes.
problem Inferring, predicting, and estimating entropy rate of continuous-time, discrete-event processes.
method Bayesian structural inference extended with neural networks.
result Methods are competitive for prediction and entropy-rate estimation with state-of-the-art.
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they are affected by jumps. To this end, we introduce Neural Jump Stochastic Different…
Large volume of networked streaming event data are becoming increasingly available in a wide variety of applications, such as social network analysis, Internet traffic monitoring and healthcare analytics. Streaming event data are discrete observation occurred in continuous time, and the precise time interval between tw…
Research simulates Lloyd's of London's specialty insurance market dynamics.
problem Quantitative study of complex market phenomena in Lloyd's of London.
method Discrete Event Simulation (DES) framework for Lloyd's of London specialty insurance market.
result Model shows sophisticated exposure management reduces syndicate insolvency, and syndication enhances actuarial price accuracy.
The paper challenges the assumption of a unique global time in financial markets, highlighting market incompleteness.
problem The assumption of a unique global time in financial markets is challenged.
method The paper contrasts event-time, renewal, point-process, and order-flow descriptions of financial markets.
result Non-uniqueness of time leads to a more foundational form of market incompleteness.
PyDTS analyzes survival data with discrete intervals and competing risks.
problem Discrete-time survival analysis with competing risks and optional penalization.
method Regularized estimation methods, model evaluation metrics, variable screening tools, and simulation module.
result Supports research and development in discrete-time survival analysis.
A system is presented that segments, clusters and predicts musical audio in an unsupervised manner, adjusting the number of (timbre) clusters instantaneously to the audio input. A sequence learning algorithm adapts its structure to a dynamically changing clustering tree. The flow of the system is as follows: 1) segment…
Paper uncovers causal structures in Hawkes processes with latent subprocesses.
problem Tackles latent subprocesses in Hawkes processes with complex event-driven interactions.
method Proposes a two-phase iterative algorithm that infers causal relationships and identifies latent subprocesses.
result Successfully recovers causal structures in datasets with latent subprocesses.
PRAGMA models financial event sequences for various banking tasks.
problem Handling diverse financial data for multiple applications.
method Pre-training a Transformer model on a large banking event corpus with a self-supervised objective.
result PRAGMA achieves superior performance across multiple financial domains from raw event sequences.
New model for multivariate discrete event data with flexible interactions.
problem Modeling multivariate discrete event data with categorical interactions.
method Developed a new modeling approach with convex constraints, two estimation procedures (LS and ML).
result Proposed model can capture arbitrary shapes of historical event influence.
A new model predicts discrete events with flexible, nonparametric baseline and excitation.
problem Limited flexibility in discrete Hawkes models for event prediction.
method Gaussian Process Discrete Hawkes Process (GP-DHP) with collapsed latent representation.
result Improves predictive log-likelihood for diverse event patterns.
MOB-dS uses permutation to correct for dependency in discrete survival data.
problem Identifying subgroups in discrete event time data with potential spurious results.
method Model-based recursive partitioning (MOB) with modified data matrix and permutation test.
result MOB-dS controls type I error rate better than standard MOB for discrete survival data.
Process Monitoring involves tracking a system's behaviors, evaluating the current state of the system, and discovering interesting events that require immediate actions. In this paper, we consider monitoring temporal system state sequences to help detect the changes of dynamic systems, check the divergence of the syste…
Exact results on power-law distributions in systems with resets.
problem Understanding power-law distributions in systems with resets.
method Exact mathematical analysis of multiplicative processes with resets.
result Power-law distributions are built up over time and their moments behave quantitatively determined by parameters.
Paper introduces a neural network-based non-stationary influence kernel for complex event data.
problem Modeling complex, non-stationary, and dependent discrete event data.
method Neural Spectral Marked Point Processes (NSMPP) with a versatile non-stationary influence kernel.
result NSMPP outperforms state-of-the-art models on synthetic and real data.
Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using this framework we describe some new global controllability tests for hybrid contr…
New test identifies risk spillovers in financial markets using extreme events.
problem Identifying risk spillovers in financial markets for systemic risk assessment.
method Novel Granger causality test in tail events using likelihood ratio statistic.
result Good size and power, especially for large sample size, inferring correct time scale.
TriTPP models enable faster and more flexible event data modeling.
problem Inflexibility and slow sampling in traditional TPP models.
method Triangular Maps and Normalizing Flows for parallel sampling and likelihood computation.
result TriTPP models achieve orders of magnitude faster sampling while maintaining flexibility.
Paper solves POMDPs in continuous time and discrete spaces.
problem Optimal decision making in discrete state and action space systems under partial observability.
method Combining optimal filtering theory and deep learning to solve a Hamilton-Jacobi-Bellman equation.
result Derives a mathematical description and solution approach for continuous-time POMDPs.
SurvSurf predicts first hitting times for intermittent events without monotonic violations.
problem Predicting first hitting times for intermittent events with monotonicity guarantees.
method Partially monotonic neural network for sequential events, incorporating unobserved events.
result SurvSurf outperforms existing models in MSE and IBS metrics.
Efficiently models event-based data with general parametric kernels.
problem Inference for Hawkes processes with general parametric kernels requires large datasets.
method Developed a fast ℓ2 gradient-based solver using a discretized version of events. result Improved estimation of pattern latency in brain signals.
New method for discrete-time survival analysis with competing risks.
problem Discrete failure time data in survival analysis.
method Proposes a new estimation procedure for discrete-time survival analysis with competing events.
result Offers advantages over existing procedures and integrates regularized regression methods.
We present the Infinite Latent Events Model, a nonparametric hierarchical Bayesian distribution over infinite dimensional Dynamic Bayesian Networks with binary state representations and noisy-OR-like transitions. The distribution can be used to learn structure in discrete timeseries data by simultaneously inferring a s…
This paper analyzes OCBA algorithms' convergence rates for DEDS optimization.
problem Optimizing discrete-event dynamic systems with limited computing resources.
method Characterizes convergence rates of two OCBA algorithms under different performance measures.
result OCBA algorithms achieve optimal convergence rates under probability of correct selection and expected opportunity cost measures.
Myopic procedures are shown to be asymptotically optimal in ranking and selection problems.
problem Selecting the best design from a set with unknown mean performance.
method Myopic procedures that iteratively improve an approximation of the objective measure.
result Myopic procedures satisfy optimality conditions of ranking and selection problems.
Smooth fractal trees via analytic generators, preserving combinatorial and geometric properties.
problem Constructing smooth fractal trees from discrete models.
method Using analytic generator fields to integrate smooth vector fields in an internal state space, generating geometric curves as projections of generator trajectories.
result Analytic generators can represent any discrete tree specification and preserve the asymptotic limit geometry.
A new method prices time-to-event cash flows using survival analysis.
problem Pricing insurance investment portfolios with time-to-event cash flows.
method Discrete-time survival analysis framework, hazard rate estimators, asymptotic multivariate normality.
result Pricing model yields estimates closer to actual cash flows than non-random models.
New framework models time-uncertain point processes for better event prediction.
problem Uncertainty in event times in point processes.
method Formulated and discretized continuous-time Hawkes processes with time grid, enabling optimization methods for inference.
result Parameter recovery with O(1/k) convergence rate using gradient descent and VI. CyPhERS provides real-time event info for CPSs, avoiding downtime.
problem Real-time event identification in CPSs is challenging due to complex interdependencies and rare events.
method CyPhERS integrates cyber and physical components, generating event signatures for known and unknown events.
result Event signatures provide relevant and inferable information on both known and unknown event types.
Framework preserves emergent physics in non-equilibrium systems from particle trajectories.
problem Linking short spatiotemporal scales to emergent bulk physics in multiscale systems.
method Metriplectic bracket formalism for structure-preserving coarse-graining.
result Preservation of thermodynamic laws and conservation in machine-learned dynamics.
Deep-PrAE improves rare-event simulation for black-box systems.
problem Evaluating rare safety-critical events in learning-based systems.
method Combines deep neural networks with IS to create statistically guaranteed estimations.
result Deep-PrAE provides accurate bounds on safety-critical event probabilities.
This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian latent variable modeling, an alternating chain of discrete Poisson and continuous …
New method quantifies resilience of electric distribution systems from historical data.
problem Large blackouts caused by extreme winds have significant costs and impacts.
method Formulate large event risk from utility outage data, quantify resilience improvements through investments.
result Investments in wind hardening and faster restoration can reduce the probability of large cost events.
Method infers causal structure from system behaviors using RKHS and kernel ε-machines.
problem Discovering causal structure in systems with varying external and measurement noise.
method Combines causal states and RKHS for efficient representation and inference of causal structure.
result Robustly estimates causal structure in high-dimensional data with varying noise.
Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help us predict which type of event will happen next and when. We model streams of d…
Proposes a method to ensure accurate estimation of rare events in AI systems.
problem Lack of efficiency guarantees in black-box systems for rare-event simulation.
method Integrates deep learning with importance sampling to create a statistically guaranteed estimator.
result Demonstrates effective estimation of rare-event probabilities in AI systems.
This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and the key concepts in point processes. We then introduce the Hawkes process, its event intensity function, as…