arXiv research

Develops quasi-likelihood analysis for marked point processes and applies it to Hawkes processes.

The paper extends intensity models for limit order books using marked point processes.

We introduce a class of hybrid marked point processes, which encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class amalgamates such existing processes, it also contains novel processes with complex dynamics. These processes are defined implicitly via their intensity and a…

The paper models user-advertiser interactions using point processes.

A new method clusters rows of a matrix of point processes.

Paper introduces a neural network-based non-stationary influence kernel for complex event data.

Neural marked point processes show saturation with complexity, leading to new simple architectures.

New model captures time and mark inter-dependence in TPPs.

New method models MTPP without predefined intensity functions.

Framework handles both exchangeable and non-exchangeable event sequences without tuning.

This paper introduces the factorial marked temporal point process model and presents efficient learning methods. In conventional (multi-dimensional) marked temporal point process models, event is often encoded by a single discrete variable i.e. a marker. In this paper, we describe the factorial marked point processes w…

A new framework generates high-dimensional event sequences efficiently.

Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of point patterns, produces characteristics (marks) of the points. One aims at learnin…

In a wide variety of applications, humans interact with a complex environment by means of asynchronous stochastic discrete events in continuous time. Can we design online interventions that will help humans achieve certain goals in such asynchronous setting? In this paper, we address the above problem from the perspect…

A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.

We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of the…

A new method uses Transformers for efficient prediction of marked point processes.

Proposes a new framework to disentangle event influences in MTPP.

Methodology for estimating marked Hawkes processes with neural networks.

We classify GL(2,R) invariant point markings over components of strata of Abelian differentials. Such point markings exist only when the component is hyperelliptic and arise from marking Weierstrass points or two points exchanged by the hyperelliptic involution. We show that these point markings can be used to determin…

This paper deals with numerical solutions of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of t…

We show that all GL(2,R) equivariant point markings over orbit closures of translation surfaces arise from branched covering constructions and periodic points, completely classify such point markings over strata of quadratic differentials, and give applications to the finite blocking problem.

This paper models how features influence event triggers in high-dimensional networks.

Differentiable adversarial attacks improve model robustness in MTPP models.

We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth. We consider a market model with jumps driven by (multivariate) marked point processes and so-called non-linear wealth dynamics which allows to take …

A new method uses BSDEs to solve optimal reinsurance under partial information.

We introduce a new model in order to describe the fluctuation of tick-by-tick financial time series. Our model, based on marked point process, allows us to incorporate in a unique process the duration of the transaction and the corresponding volume of orders. The model is motivated by the fact that the "excitation" of …

S2P2 model improves predictive likelihoods for MTPPs.

An adversarial detector identifies anomalous sequences in sequential data.

Disk and sphere graphs embed quasi-isometrically in R^2.

Proves Grothendieck-Teichmüller group acts on specific mapping class groups.

We study body-and-hinge and panel-and-hinge chains in R^d, with two marked points: one on the first body, the other on the last. For a general chain, the squared distance between the marked points gives a Morse-Bott function on a torus configuration space. Maximal configurations, when the distance between the two marke…

The paper tackles robust control for insurance contracts under uncertain transition rates.

New MTPP model offers interpretable predictions with state-of-the-art performance.

Exact asymptotic solutions found for nonlinear Hawkes processes.

The study finds rational points on specific types of hypersurfaces.

Survey on modeling event sequences through temporal processes.

User engagement in online social networking depends critically on the level of social activity in the corresponding platform--the number of online actions, such as posts, shares or replies, taken by their users. Can we design data-driven algorithms to increase social activity? At a user level, such algorithms may incre…

We introduce a new model for describing the fluctuations of a tick-by-tick single asset price. Our model is based on Markov renewal processes. We consider a point process associated to the timestamps of the price jumps, and marks associated to price increments. By modeling the marks with a suitable Markov chain, we can…

Study cohomology of surfaces with punctures and boundaries, proving bounds on rational cohomology.

We show that the mapping class group of a handlebody of genus at least 2 (with any number of marked points or spots) is exponentially distorted in the mapping class group of its boundary surface. The same holds true for solid tori with at least two marked points or spots.

It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence o…

Three elements generate balanced superelliptic mapping class groups.

Quantum duality map extended to general marked surfaces and its compatibility with skein algebras proven.

The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is given. The semi-stable and unstable cases are new, and it is shown that the flow …

Study Farrell cohomology for non-orientable surfaces, classifying subgroup conjugacy.

Estimates the rational homological dimension of Riemann surfaces with boundary and marked points.

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent Pólya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's Gaussian process prior. The augmented posterior allows for efficient inference by Gi…