[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86164-en":3,"doc-seo-86164-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86164,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","NeuroMem-FHP Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process","Proposes the NeuroMem-FHP deep learning framework to estimate parameters of the fractional Hawkes process (FHP), a self-exciting point process with long-range dependence via a fractional Mittag–Leffler excitation kernel. Two architectures—an LSTM and a Transformer—predict parameters (µ, γ, α, β) directly from inter-arrival time sequences without likelihood optimization. Synthetic-data experiments show strong gains over maximum likelihood estimation, with the Transformer achieving the best MSE. Ablation studies analyze hyperparameter effects, and validation on AAPL NBBO and Montgomery County 911 data reproduces empirical distribution, tail behavior, and temporal dependence.","arXiv :2607 . 1 1 177v 1 [ cs .LG] 13 Jul 2026  \nNeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process  \na  \n*  \nNeha Guptaa* , Aditya Maheshwarib  \nOperations Management and Quantitative Techniques Area, Indian Institute of Management Indore, Indore 453556, India. Corresponding author: [neha.gupta@iimidr.ac.in](neha.gupta@iimidr.ac.in)  \nb Operations Management and Quantitative Techniques Area, Indian Institute of Management Indore, Indore 453556, India. Email: [adityam@iimidr.ac.in](adityam@iimidr.ac.in)  \nAbstract. In this paper, we propose deep learning based NeuroMem-FHP framework for esti  \nmating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that  \ncaptures long-range dependence through a fractional Mittag–Leffler excitation kernel. Two neural  \narchitectures, namely a Long Short-Term Memory (LSTM) network and a Transformer, are devel  \noped to estimate the model parameters (µ,γ,α,β) directly from sequences of inter-arrival times  \nwithout requiring computationally intensive likelihood optimization. Experiments on synthetic  \ndata demonstrate that both neural models significantly outperform the classical Maximum Likeli  \nhood Estimation (MLE) method, with the Transformer achieving the highest estimation accuracy  \n(MSE = 0 . 1634), followed by the LSTM (MSE = 0 . 1752), compared to MLE (MSE = 2 .8032) . An  \nablation study further examines the effects of key hyperparameters on model performance. The  \nproposed framework is also validated on two real-world high-frequency datasets, namely AAPL  \nNBBO transaction data and Montgomery County 911 emergency call records. Using a predictive  \nvalidation approach, event sequences simulated from the estimated parameters closely reproduce  \nthe empirical distribution, tail behavior, and temporal dependence structure of the observed data.  \nThese results demonstrate that Transformer-based parameter estimation provides an accurate and  \nefficient alternative to conventional estimation techniques for FHP and offers a promising framework  \nfor modeling event-driven systems with long-memory dynamics.  \n1. Introduction  \nCounting processes with time-varying intensities have been found very useful in several applications (see [42, 34, 1]) . However, in many real-world applications, the occurrence of future events depends not only on time but also on the history of past events. In particular, the occurrence of the recent event increases the likelihood of observing subsequent events, leading to self-exciting behavior. To capture such history-dependent dynamics, the Hawkes process was first introduced in the early seventies by Hawkes (see [27, 26]) and found applications in various fields, for example, in modeling terrorist activities [50], finance (see [3, 23, 25, 4, 6, 7, 8]), and seismology (see [28, 45, 46]) . The Hawkes process is a self-exciting counting process with conditional stochastic intensity {Λ(t|Ht)}t≥0 , where Ht represents the history of the counting process and is given by  \nΛ(t|Ht) = µ + α Z0 t f (t − u) dN (u),  \nwhere µ > 0 is the baseline intensity, α > 0 is the jump size, f (t) is the kernel density function of a positive random variable, and N (t) is the counting process.  \nDespite its broad applicability, the classical Hawkes process employs an exponentially decaying selfexcitation kernel (see [3]), implying that the influence of past events diminishes rapidly over time and leading to short-range dependence. However, many real-world applications exhibit persistent temporal correlations and long-range dependence that cannot be adequately captured by exponential kernels. To overcome these limitations, fractional generalizations of Hawkes process have  \n2020 Mathematics Subject Classification. 60G55, 60G22, 62M09, 68T07 .  \nbeen developed. One formulation of the FHP replaces the exponential kernel with a Mittag-Lefflerself-exciting kernel, enabling power-law type memory effec","cbCaihmiEuMLtmID","https://ap.wps.com/l/cbCaihmiEuMLtmID","pdf",1677722,4,1,19,"English","en",105,"# Introduction\n## Self-exciting point processes and the Hawkes model\n## Fractional generalizations of Hawkes processes\n## Motivation for likelihood-free parameter estimation\n## Deep learning methods for stochastic process parameter inference","[{\"question\":\"What problem does NeuroMem-FHP address?\",\"answer\":\"It provides a deep learning approach for estimating parameters of the fractional Hawkes process without performing computationally intensive likelihood optimization.\"},{\"question\":\"Which neural network architectures are used to estimate FHP parameters?\",\"answer\":\"The framework uses two architectures: an LSTM network and a Transformer to estimate the parameters (µ, γ, α, β) from inter-arrival time sequences.\"},{\"question\":\"How is the proposed method validated beyond synthetic data?\",\"answer\":\"It is validated on two real-world high-frequency datasets—AAPL NBBO transaction data and Montgomery County 911 emergency call records—using a predictive validation strategy that matches empirical distribution and temporal dependence.\"}]",1784209030,48,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"neuromem-fhp-likelihood-free-deep-learning-framework-for-parameter-estimation-of-fractional-hawkes-process","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/neuromem-fhp-likelihood-free-deep-learning-framework-for-parameter-estimation-of-fractional-hawkes-process/86164/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does NeuroMem-FHP address?","Question",{"text":75,"@type":76},"It provides a deep learning approach for estimating parameters of the fractional Hawkes process without performing computationally intensive likelihood optimization.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which neural network architectures are used to estimate FHP parameters?",{"text":80,"@type":76},"The framework uses two architectures: an LSTM network and a Transformer to estimate the parameters (µ, γ, α, β) from inter-arrival time sequences.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the proposed method validated beyond synthetic data?",{"text":84,"@type":76},"It is validated on two real-world high-frequency datasets—AAPL NBBO transaction data and Montgomery County 911 emergency call records—using a predictive validation strategy that matches empirical distribution and temporal 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