We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our construction is naturally invariant to translations and reflections, but it decouples th…
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48 results for “Poisson point process”
Deep Neyman-Scott Processesstat.ML
A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.
problem Efficient inference in complex hierarchical point processes.
method Developed an efficient posterior sampling via Markov chain Monte Carlo for likelihood-based inference.
result More hidden Poisson processes improve likelihood fitting and event prediction.
Study on critical faces convergence in a Poisson point process.
problem Convergence of point processes associated with critical faces in a Čech filtration.
method Established convergence in -topology for critical faces above vanishing threshold.
result Obtained limit theorems for positive and negative critical faces.
A bandit problem with filtered Poisson process data.
problem Maximizing points revealed from a continuum action space.
method Upper confidence bound algorithm with data-adaptive discretisation.
result Regret bound of O(T^(2/3)) under Lipschitz assumption.
SNEPPPs use squared neural networks to efficiently model Poisson point processes.
problem Efficiently modeling Poisson point processes with flexibility.
method Parameterizing intensity function with squared norm of a two-layer neural network.
result Closed-form integration of intensity function for quadratic time computation.
The paper develops methods to create private synthetic spatial point patterns.
problem Generating private synthetic spatial point patterns.
method Developed differentially private Poisson and Cox point synthesizers.
result The synthesizers effectively maintain privacy and utility of synthetic data.
The logistic regression model is known to converge to a Poisson point process model if the binary response tends to infinitely imbalanced. In this paper, it is shown that this phenomenon is universal in a wide class of link functions on binomial regression. The proof relies on the extreme value theory. For the logit, p…
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity or . The changes of direction are governed by an homogeneous Poisso…
Adaptive importance sampling for estimating point process statistics.
problem Estimating the expected value of a statistic of a locally stable point process.
method Adaptive importance sampling with Poisson point processes and cross-entropy minimization.
result The proposed estimator converges to the target value almost surely and is asymptotically normal.
Study of lengths of cycles in large genus random maps converging to Poisson process.
problem Understanding the distribution of cycle lengths in large genus random maps.
method Teichmüller theory approach for uniformly random metric maps (ribbon graphs).
result The length spectrum converges to a Poisson point process with an explicit intensity as genus tends to infinity.
This work tackles fitting Hawkes processes to interval-censored data.
problem Fitting Hawkes processes to aggregated event counts without exact times.
method Developed MBPP, IC-LL, exogenous functions, and approximation methods.
result Connected Hawkes Intensity Process (HIP) to MBPP.
Study on length spectrum of random hyperbolic 3-manifolds.
problem Understanding the length spectrum of random hyperbolic 3-manifolds.
method Modeling random hyperbolic 3-manifolds using truncated tetrahedra and analyzing their length spectrum as volume tends to infinity.
result The length spectrum converges in distribution to a Poisson point process with a computable intensity λ as volume increases.
New method calculates Ricci curvature from distances between weighted volumes.
problem Calculating Ricci curvature for weighted Riemannian manifolds.
method Asymptotic retrieval of generalized Ricci tensor from scaled metric derivatives of Wasserstein 1-distances.
result Limiting coarse curvature of random graphs converges to generalized Ricci tensor.
Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to identify absence of fit through finding a classification rule that can efficientl…
Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity functions exist, especially when observed points lie in a high-dimensional space.…
This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…
We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but their use is hindered by the computational cost of existing inference schemes. Ou…
We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The measures used include normalised generalised Gamma processes that demonstrate power …
Bayesian approach for inhomogeneous Poisson process intensity estimation.
problem Intractable integral in likelihood of Gaussian Cox process.
method Joint modeling of intensity and cumulative intensity as transformed Gaussian process; exact MCMC sampler.
result Exact posterior inference without approximations.
We derive Gaussian approximations for random forest predictions using region-based stabilization.
problem Improving the accuracy of random forest predictions for Poisson process data.
method Region-based stabilization and Malliavin-Stein method for multivariate Gaussian approximation.
result Established Gaussian approximation bounds for random forest predictions under Poisson process.
Intensity Dot Product Graphsstat.ML
IDPGs extend RDPGs with a Poisson process for random latent positions.
problem Modeling randomness in latent positions for graph structure.
method Introduce IDPGs using Poisson point processes on latent Euclidean space.
result Continuous analogues of adjacency matrices link latent structure to observed graphs.
A new Poisson bracket defined on Poisson structures with applications to fixed points and cohomology.
problem Defining a Poisson bracket on the space of Poisson structures.
method Constructing a Poisson bracket on depending on a volume form, and defining invariant of Poisson structures.
result Invariant of Poisson structures detects unimodularity and related Poisson bracket for symplectic structures.
Poisson likelihood models have been prevalently used in imaging, social networks, and time series analysis. We propose fast, simple, theoretically-grounded, and versatile, optimization algorithms for Poisson likelihood modeling. The Poisson log-likelihood is concave but not Lipschitz-continuous. Since almost all gradie…
The Poisson equation on manifolds plays an fundamental role in many applications. Recently, we proposed a novel numerical method called the Point Integral method (PIM) to solve the Poisson equations on manifolds from point clouds. In this paper, we prove the convergence of the point integral method for solving the Pois…
In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing models that scale cubically and have a squared memory requirement in the number of da…
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers via a Poisson point process with mean measure on the power set of . Each $E\in\cate$ has a least monotone cover in $\catf$, the collection of monotone subsets of $\cate$, an…
We propose an efficient method for estimating covariate effects in doubly-stochastic spatial models.
problem Computational demands and restrictive assumptions in existing doubly-stochastic spatial models.
method Penalized regression method for estimating covariate effects in doubly-stochastic point processes.
result Consistency and asymptotic normality of the covariate effect estimates achieved despite model misspecification.
Novel connections between Neyman-Scott processes and Bayesian nonparametric mixture models enable scalable inference.
problem Efficiently modeling and detecting clusters in spatiotemporal data.
method Adapting collapsed Gibbs sampling for Neyman-Scott processes via connections to mixture of finite mixture models.
result Demonstrated scalability and effectiveness on neural spike trains and document streams.
Single linear solve combines surface reconstruction and uncertainty quantification.
problem Reconstructing surfaces from partial point clouds with uncertainty.
method Geometric Gaussian processes for stochastic surface reconstruction.
result Single linear solve for surface reconstruction with probabilistic capabilities.
A Riemannian symmetric space is a Riemannian manifold in which it is possible to reflect all geodesics through a point by an isometry of the space. On such spaces, we introduce the notion of a distributional lattice, generalizing the notion of lattice. Distributional lattices exist in any Riemannian symmetric space: th…
Spherical Poisson Point Process Intensity Function Modeling and Estimation with Measure Transportstat.ME
New method models intensity functions on spheres using normalizing flows.
problem Modeling non-homogeneous Poisson process intensity functions on the sphere.
method Flexible bijective map using normalizing flows to transform intensity functions.
result Normalizing flows provide a flexible way to model intensity functions on spheres.
Proposes a framework for modeling RTB auctions using point processes.
problem Modeling and optimizing repeated auctions in the RTB ecosystem.
method Develops a stochastic framework using point processes to model and optimize RTB auctions.
result The proposed framework can be approximated to a Poisson point process, enabling the use of established properties.
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…
The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poiss…
We study the stability of singular points for smooth Poisson structures as well as general Lie algebroids. We give sufficient conditions for stability lying on the first (not necessarily linear) approximation of the given Poisson structure or Lie algebroid at a singular point. The main tools used here are the classical…
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infi…
V1 cortex reconstructs images as Poisson equation solutions with varying weights.
problem Reconstructing images from V1 cortical cell receptive profiles.
method Solves a heterogeneous Poisson equation with varying weights representing neural connectivity.
result Reconstructions converge to homogeneous solutions using homogenization techniques.
We compute the formal Poisson cohomology of a broken Lefschetz fibration by calculating it at fold and Lefschetz singularities. Near a fold singularity the computation reduces to that for a point singularity in 3 dimensions. For the Poisson cohomology around singular points we adapt techniques developed for the Sklyani…
Study of Poisson homeomorphisms and rigidity of coisotropic submanifolds.
problem Rigidity and non-rigidity phenomena in Poisson geometry.
method Study of Poisson homeomorphisms, use of clean intersection points, and analysis of characteristic partitions.
result Poisson homeomorphisms preserve symplectic foliations and coisotropic submanifolds are flexible.
The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we prove that such repulsive sampling schemes lowers the variance of the gradient est…
We propose the point process model as the Poissonian-like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on NYSE. The proposed scaled stochastic differential equation provides the universal description of the trad…
Paper proposes a new method for estimating conditional densities using logistic regressions.
problem Estimating conditional densities for complex distributions.
method Parametric conditional density estimation via weighted logistic regressions.
result Maximum likelihood estimates can be obtained efficiently via a block-wise alternating maximization scheme and local case-control sampling.
The paper defines and explores Poisson-Nijenhuis structures on Lie groupoids.
problem Defining and understanding Poisson-Nijenhuis structures on Lie groupoids.
method Introducing and studying right-invariant Poisson-Nijenhuis structures on Lie groupoids and their infinitesimal counterparts.
result A mutual correspondence between structures on Lie algebroids and Poisson-Nijenhuis structures on Lie groupoids.
Study on geodesics and eigenvalues on random hyperbolic surfaces with cusps.
problem Counting short geodesics and small eigenvalues on random hyperbolic surfaces.
method Rescaling and convergence to a Poisson point process.
result The probability of having at least arbitrarily small eigenvalues tends to 1 as .
Study shows convergence rates for BSDEs approximated by compound Poisson processes.
problem Analyzing convergence rates of BSDEs driven by Lévy processes.
method Approximating Lévy processes by compound Poisson processes and studying BSDEs.
result Optimal convergence rates derived for BSDEs in -norm and Wasserstein distance.
We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time 1 value satisfies a specific constraint. This construction allows us to show the existence of Glosten-Milgrom equilibrium and its as…
We show that the fixed point set of a proper action of a Lie group on a Poisson manifold by Poisson automorphisms has a natural induced Poisson structure and we give several applications.
Applications of Nijenhuis geometry: Nondegenerate singular points of Poisson-Nijenhuis structuresmath.DG
We study and completely describe pairs of compatible Poisson structures near singular points of the recursion operator satisfying natural non-degeneracy condition.