A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New Gamma-Poisson model improves topic selection for short text.
Two approaches improve parameter learning in various mixture models.
This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main algorithm. In explaining the main algorithm, first, fitting a mixture of two distribu…
Developed shrinkage methods for Poisson regression models with experts to handle multicollinearity.
A model for the phenomenological description of tick-by-tick share prices in a stock exchange is introduced. It is based on mixtures of compound Poisson processes. Preliminary results based on Monte Carlo simulation show that this model can reproduce various stylized facts.
The paper improves Fisher-Pitman tests for Poisson mixtures, detecting autism-related genes.
Flexible models cluster RNA sequencing data.
Blind source separation (BSS) aims at recovering signals from mixtures. This problem has been extensively studied in cases where the mixtures are contaminated with additive Gaussian noise. However, it is not well suited to describe data that are corrupted with Poisson measurements such as in low photon count optics or …
Paper develops a consistent estimator for discrete mixture models.
Paper optimizes clustering for multi-layer networks and discrete mixtures.
We investigate the class of -stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs which encompasses most of the the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, Pitman-Yor p…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process f…
Novel connections between Neyman-Scott processes and Bayesian nonparametric mixture models enable scalable inference.
In this paper we show that very large mixtures of Gaussians are efficiently learnable in high dimension. More precisely, we prove that a mixture with known identical covariance matrices whose number of components is a polynomial of any fixed degree in the dimension n is polynomially learnable as long as a certain non-d…
Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.
This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. …
Efficient algorithms for sparse parameter recovery in mixture models.
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statis…
Analyzing the underlying structure of multiple time-sequences provides insights into the understanding of social networks and human activities. In this work, we present the \emph{Bayesian nonparametric Poisson process allocation} (BaNPPA), a latent-function model for time-sequences, which automatically infers the numbe…
Parallel recordings of neural spike counts have revealed the existence of context-dependent noise correlations in neural populations. Theories of population coding have also shown that such correlations can impact the information encoded by neural populations about external stimuli. Although studies have shown that the…
New algorithm improves mixing in Bayesian mixture models.
A drone-based MOT algorithm tracks vehicles using neural network detections and TPMBM filter.
We present a general framework, the coupled compound Poisson factorization (CCPF), to capture the missing-data mechanism in extremely sparse data sets by coupling a hierarchical Poisson factorization with an arbitrary data-generating model. We derive a stochastic variational inference algorithm for the resulting model …
Count data, for example the number of observed cases of a disease in a city, often arise in the fields of healthcare analytics and epidemiology. In this paper, we consider performing regression on multivariate data in which our outcome is a count. Specifically, we derive log-likelihood functions for finite mixtures of …
The paper extends sequences while preserving statistical properties using a mixture model.
Method proposed for pricing insurance products covering both foreseeable and unforeseeable risks.
Modeling trading volume curves using hierarchical Poisson processes.
Local minimax analysis for Poisson deconvolution of discrete signals.
The problem of Poisson denoising appears in various imaging applications, such as low-light photography, medical imaging and microscopy. In cases of high SNR, several transformations exist so as to convert the Poisson noise into an additive i.i.d. Gaussian noise, for which many effective algorithms are available. Howev…
Data of the form of event times arise in various applications. A simple model for such data is a non-homogeneous Poisson process (NHPP) which is specified by a rate function that depends on time. We consider the problem of having access to multiple independent observations of event time data, observed on a common inter…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let be an arbitrary distribution over an interval which is -close (in total variation distance) to an unknown probability distribution $…
The goal of data clustering is to partition data points into groups to minimize a given objective function. While most existing clustering algorithms treat each data point as vector, in many applications each datum is not a vector but a point pattern or a set of points. Moreover, many existing clustering methods requir…
The claim experience of the past is a very important information to calculate the fair price of an insurance contract. In a lot of European countries for instance the prices for motor car insurance depend on the number of claims the driver has reported to the insurance company during the last years. Classically these p…
Advocates for MLE in regression and forecasting for better inductive biases and post-hoc optimization.
Modeling price clustering in financial markets using discrete distributions.
Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case basis; examples include robust linear regression, robust mixture models, and bur…
New sampling method uses gradient-free IPS with RKHS velocity field.
New insights into empirical Bayes and compound decision problems with improved regret bounds.
Geometrically proves twisted Poincaré duality for orientable Poisson manifolds.
We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson generalization of the reduction of symplectic manifolds with symmetry. Having as basic tools the equivariant momentum maps of Poisson actions, the double group of a Poisson-Lie group and the reduction of Poisson manifold…
New Poisson structures on algebras linked to derivatives.
New Lie groups found for Poisson diffeomorphisms.
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributions, Negative binomial regression, Poisson-Gamma hierarchical models, …
We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant connection, and the …
We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices…
The paper establishes a Poisson Poincaré-Dulac theorem for Poisson-flat connections.
The first cohomology of Poisson algebras is described and conditions for its vanishing are established.
The paper normalizes Poisson saturation of coregular submanifolds.