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.
This work investigates a mixture of LMC and RMHMC with MMALA for geometric ergodicity.
Study classifies mappings of bivariate normal densities, revealing three types with distinct geometric and statistical properties.
In this paper, we examine a geometrical projection algorithm for statistical inference. The algorithm is based on Pythagorean relation and it is derivative-free as well as representation-free that is useful in nonparametric cases. We derive a bound of learning rate to guarantee local convergence. In special cases of m-…
We present two different approaches for parameter learning in several mixture models in one dimension. Our first approach uses complex-analytic methods and applies to Gaussian mixtures with shared variance, binomial mixtures with shared success probability, and Poisson mixtures, among others. An example result is that …
We will establish that the VC dimension of the class of d-dimensional ellipsoids is (d^2+3d)/2, and that maximum likelihood estimate with N-component d-dimensional Gaussian mixture models induces a geometric class having VC dimension at least N(d^2+3d)/2. Keywords: VC dimension; finite dimensional ellipsoid; Gaussian m…
New method extracts hidden phases in binary mixtures using tubular tilings.
New approach to control diffusion processes with soft constraints.
Introduces q-paths for generalizing geometric annealing paths in machine learning.
Paper solves a geometric problem involving mixtures of area and curvature measures.
Improved sample complexity for Gaussian Mixture Models using Pair Correlation Factor.
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric and on a family o…
Paper proposes MWDE for estimating finite location-scale mixtures.
Enhanced 3D shape analysis using information geometry.
Exponential families and mixture families are parametric probability models that can be geometrically studied as smooth statistical manifolds with respect to any statistical divergence like the Kullback-Leibler (KL) divergence or the Hellinger divergence. When equipping a statistical manifold with the KL divergence, th…
The total variation distance is a core statistical distance between probability measures that satisfies the metric axioms, with value always falling in . This distance plays a fundamental role in machine learning and signal processing: It is a member of the broader class of -divergences, and it is related to …
Understanding separation effects on parameter estimation in finite Gaussian mixtures
Gradient method converges locally linearly for overparameterized Gaussian mixtures.
Paper proposes a method to efficiently cluster stretched mixtures.
A new method for anomaly detection using random subspaces and Gaussian mixture models.
A new probabilistic polygonal curve representation using Gaussian Mixture Models.
We give several new criteria to judge whether a simple convex polytope in a Euclidean space is combinatorially equivalent to a product of simplices. These criteria are mixtures of combinatorial, geometrical and topological conditions that are inspired by the ideas from toric topology.
New slicing methods speed up Gaussian mixture Wasserstein distance computations.
New methods combine model predictions to avoid linear mixtures' limitations.
A novel method compares 3D point clouds using information geometry.
This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an arbitrary metric space into the l2 space, while preserving their pairwise distance distr…
Generative model on manifolds reduces divergence computation and improves scalability.
New accelerators for EM improve convergence speed in complex mixture models.
Given a set of mixtures, blind source separation attempts to retrieve the source signals without or with very little information of the the mixing process. We present a geometric approach for blind separation of nonnegative linear mixtures termed {\em facet component analysis} (FCA). The approach is based on facet iden…
A new method identifies sub-populations in unlabelled heterogeneous data by accounting for co-features.
The Expectation-Maximization (EM) algorithm is a widely used method for maximum likelihood estimation in models with latent variables. For estimating mixtures of Gaussians, its iteration can be viewed as a soft version of the k-means clustering algorithm. Despite its wide use and applications, there are essentially no …
An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian Motion Model with optimal weighting factors selected by goodness of fit tests, sub…
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and the related Fisher Information metric. We explain how this apparatus can be used…
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…
Gradient EM converges globally for over-parameterized Gaussian mixtures.
Extends likelihood ratio exponential families to analyze various optimization methods.
We introduce a new homological machine for the study of secondary geometric invariants. The objects, called spark complexes, occur in many areas of mathematics. The theory is applied here to establish the equivalence of a large family of spark complexes which appear naturally in geometry, topology and physics. These co…
This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed process can match exactly the risk-neutral distributions implied by both spot va…
Universal model for soft tissue mechanics under shock waves.
We introduce a multivariate diffusion model that is able to price derivative securities featuring multiple underlying assets. Each asset volatility smile is modeled according to a density-mixture dynamical model while the same property holds for the multivariate process of all assets, whose density is a mixture of mult…
Generative models improve angular variable simulation in high dimensions.
A new clustering method estimates non-linear boundaries and automatically selects the number of clusters.
Latent MoS learns multiple symmetries for efficient dynamic learning.
Unified perspective on natural gradient methods for GMMs, improving variational inference.
A line of recent work has analyzed the behavior of the Expectation-Maximization (EM) algorithm in the well-specified setting, in which the population likelihood is locally strongly concave around its maximizing argument. Examples include suitably separated Gaussian mixture models and mixtures of linear regressions. We …
Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution ena…
Geometric tempering improves sampling from distributions, with exponential convergence rates.
Study calculates tail risk for various mixture distributions.
Enhances mixture models with classifier-defined weights.