In this report, we derive a non-negative series expansion for the Jensen-Shannon divergence (JSD) between two probability distributions. This series expansion is shown to be useful for numerical calculations of the JSD, when the probability distributions are nearly equal, and for which, consequently, small numerical er…
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arXiv research
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.
169,051 papers · 148 categories
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48 results for “non-negative probabilities”
VAE enhances NMF for probabilistic non-negative matrix factorisation.
problem Non-negative matrix factorisation with probabilistic coefficients.
method Design a VAE network with non-negative weights and non-negative Weibull distribution.
result Effective probabilistic NMF for generating new data and linking latent and input variables.
Improved score matching for non-negative data models.
problem Estimating parameters of non-negative probability density functions.
method Generalized score matching method for non-negative data.
result Improved estimation efficiency and theoretical guarantees.
New gradient flows for non-negative and probability measures combining optimal transport and interaction forces.
problem Optimizing non-negative and probability measures using interaction forces and optimal transport.
method Interaction-Force Transport (IFT) gradient flows and their spherical variant, developed via infimal convolution of Wasserstein and spherical MMD tensors, with a particle-based optimization algorithm.
result The spherical IFT gradient flow provides global exponential convergence guarantees for both MMD and KL energy.
SOS programming verifies MTW tensor non-negativity for optimal transport maps.
problem Verifying MTW tensor non-negativity for general cost functions is difficult.
method Sum-of-Squares (SOS) programming for verifying and approximating MTW non-negativity.
result SOS programming provides certificates and approximations of MTW non-negativity.
A new method for decomposing non-negative tensors using energy-based modeling.
problem Challenges in traditional tensor decomposition methods, especially global optimization and rank selection.
method Energy-based modeling of tensors, considering interactions between modes for global optimization.
result Demonstrates effectiveness in tensor completion and approximation, revealing a relationship between many-body and low-rank approximations.
Graphs with non-negative curvature have improved heat semigroup estimates.
problem Estimating heat semigroup norms on graphs with curvature.
method Proved a reverse Poincaré inequality for graphs with non-negative Ollivier curvature.
result Heat semigroup norm estimates lead to Buser inequality, Liouville property, and eigenvalue estimates.
Efficiently reduces tensor ranks using mean-field approximation.
problem Low-rank approximation of non-negative tensors.
method Mean-field approximation of tensor rank reduction.
result Our algorithm achieves faster and competitive tensor rank reduction.
Model predicts traffic flow dynamics from sparse data.
problem Predict traffic flow from limited data.
method Mesoscopic model using factor graphs and message passing.
result Efficiently estimates traffic conditions with low probe vehicle penetration.
The paper improves SVR with linear constraints for better model properties.
problem Improving Support Vector Regression with linear constraints.
method Generalized SMO algorithm for solving optimization with linear constraints.
result The proposed method shows better practical performance on various datasets.
The abstract reviews models for analyzing count data.
problem Challenges in analyzing count data with standard methods.
method Review of generalized linear models and multinomial models.
result Fundamental connections between multinomial and count models.
The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex neural networks use -regularization with the non-negative constraint. However…
PSD models simplify probability density estimation.
problem Effective modeling of probability densities for inference.
method Positive semi-definite (PSD) models for non-negative functions.
result PSD models efficiently support product and sum rules.
A multi-task GP model tracks time-varying transition probabilities between two states.
problem Tracking time-varying transition probabilities between 'moves' and 'pauses' states.
method Kernel-based multi-task Gaussian Process model with time-variability and constraints.
result Enforces constraints while learning transition probabilities.
Generative source separation methods such as non-negative matrix factorization (NMF) or auto-encoders, rely on the assumption of an output probability density. Generative Adversarial Networks (GANs) can learn data distributions without needing a parametric assumption on the output density. We show on a speech source se…
We consider an insurance company in the case when the premium rate is a bounded non-negative random function $c_\zs{t}$ and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return and volatility . If we find exact the as…
DeepMP improves non-negative sparse recovery performance.
problem Recovering non-negative sparse signals with high coherence.
method Reformulated non-negative matching pursuit as a deep neural network.
result DeepMP yields significant improvement in exact recovery performance.
Study shows non-negative curvature on 4-manifolds with torus symmetry.
problem Classifying 4-manifolds with torus symmetry under non-negative curvature.
method Investigated invariant metrics on 4-manifolds with circle and torus actions.
result Found that almost non-negative curvature implies non-negative curvature for 4-manifolds with torus symmetry.
Sharp inequality in spaces with non-negative Ricci curvature.
problem Proving a sharp isoperimetric inequality in metric measure spaces.
method Using volume entropy in non-compact metric measure spaces with non-negative synthetic Ricci curvature.
result Proved a sharp dimension-free isoperimetric inequality.
Odd GKM-manifolds with non-negative curvature split cohomology.
problem Understanding cohomology of odd-dimensional GKM-manifolds.
method Proving cohomology splitting for specific manifolds.
result Cohomology splits for GKM manifolds of non-negative curvature.
We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the no-arbitrage condition characterization and the existence of an optimal portfolio i…
Non-negative curvature affects Markov chains' mixing and expansion properties.
problem Understanding the behavior of Markov chains with non-negative curvature.
method Analyzing conductance, displacement, and cutoff phenomenon in sparse Markov chains.
result Non-negatively curved Markov chains exhibit specific, non-standard behavior in terms of mixing and expansion.
Graphs with non-negative Ollivier curvature have constant bounded harmonic functions.
problem Liouville property for graphs with non-negative Ollivier curvature.
method Proving Liouville property and improving concentration results.
result Every bounded harmonic function on graphs with non-negative Ollivier curvature is constant.
Formal manifolds with non-negative Ricci curvature have formal covers.
problem Formality of manifolds with non-negative Ricci curvature.
method Study of universal covers and formal properties.
result Closed non-orientable manifolds with non-negative Ricci curvature are formal.
In this paper we study non-negatively curved and rationally elliptic GKM manifolds and orbifolds. We show that their rational cohomology rings are isomorphic to the rational cohomology of certain model orbifolds. These models are quotients of isometric actions of finite groups on non-negatively curved torus orbifol…
Study Kähler metrics on complex tori with almost non-negative scalar curvature.
problem Stability of Kähler metrics on complex tori.
method Proved convergence of non-collapsing subsequence of Kähler metrics to flat torus.
result Kähler metrics with almost non-negative scalar curvature on complex tori converge to flat torus.
Sharp inequality for submanifolds in manifolds with non-negative Ricci curvature.
problem Establishing a Fenchel-Willmore inequality for submanifolds in manifolds with non-negative Ricci curvature.
method Analyzing submanifolds in manifolds with non-negative intermediate Ricci curvature and Euclidean volume growth.
result Sharp Fenchel-Willmore inequality for submanifolds in manifolds with non-negative intermediate Ricci curvature.
The paper proves conjectures and classifies metrics on 3D manifolds.
problem Proving conjectures and classifying metrics on 3D manifolds with specific curvature conditions.
method Analytical proofs and classification theorems.
result Critical metrics on 3D manifolds are isometric to geodesic balls in space forms.
The study examines symmetries in spaces with positive or non-negative curvature.
problem Understanding symmetries in spaces with curvature constraints.
method Survey of existing results for Riemannian manifolds with specified curvature properties and symmetries.
result Results on symmetries in spaces with curvature bounds.
Non-negative constraints improve neural network defenses.
problem Effective defenses against adversarial attacks in neural networks.
method Non-negative weight constraints applied to binary and non-binary classification problems.
result Non-negative constraints can improve resistance to adversarial attacks, especially in binary classification with asymmetric costs.
Survey on rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.
problem Rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.
method Survey and observation on Cheeger-Yau inequality on RCD spaces.
result Observations on the Cheeger-Yau inequality and its applications.
We study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sectional curvature on closed and open manifolds. We construct, in particular, the first classes of manifolds for which these moduli spaces have non-trivial rational homotopy, homology and cohomology groups. We also show tha…
Study on rigidity with non-negative intermediate curvature on low-dimensional manifolds.
problem Extending non-existence theorem of positive scalar curvature to product manifolds.
method Introduced intermediate curvature and studied rigidity conditions.
result Rigidity when intermediate curvature is non-negative in low dimensions.
Lower bound on minimum vertex degree for non-negative Lin-Lu-Yau curvature on graphs.
problem Determining the minimum vertex degree for non-negative Lin-Lu-Yau curvature.
method Investigation of Ollivier-Ricci curvature and Lin-Lu-Yau modification on locally finite graphs.
result Lower bound on minimum vertex degree ensuring non-negative Lin-Lu-Yau curvature.
Upper bounds on Laplacian eigenvalues on manifolds with non-negative curvature.
problem Bounding Laplacian eigenvalues on manifolds with non-negative scalar curvature.
method Investigation of invariant spectrum on compact Riemannian manifolds with large isometry groups.
result Upper bounds for eigenvalues of the invariant spectrum assuming non-negative scalar curvature.
Optimal diameter estimates for 3D spaces with non-negative Ricci curvature.
problem Estimating the diameter of 3D spaces with non-negative Ricci curvature.
method Proving positive scalar curvature passes to Ricci limit spaces of non-negative curvature.
result Optimal Bonnet-Myers upper bound for 3D spaces.
New Bochner technique for foliations with non-negative Ricci curvature.
problem Analyzing foliations with non-negative transverse Ricci curvature.
method Generalizing Bochner technique to foliations with non-negative transverse Ricci curvature.
result Obtained a new vanishing theorem for basic cohomology.
Paper proves edge-connectivity equals minimum degree for graphs with non-negative curvature.
problem Edge-connectivity vs. minimum degree in graphs with non-negative curvature.
method Analyzes finite connected graphs with non-negative Lin-Lu-Yau curvature.
result Edge-connectivity equals minimum degree for graphs with non-negative curvature.
nUDEs use neural networks to model biology without negative values.
problem Unrealistic negative values in hybrid models of biology.
method Developed non-negative UDEs (nUDEs) with regularization techniques.
result nUDEs provide realistic solutions for biological models.
Non-negative -approximating polynomials for Gaussian distributions are proven for certain classes of sets.
problem Existence of non-negative -approximating polynomials for Gaussian distributions.
method Proving the existence of degree- non-negative polynomials that approximate indicator functions of sets with Gaussian surface area in -norm.
result Proves the existence of non-negative -approximating polynomials for certain classes of sets with Gaussian surface area.
NCL improves interpretability of deep features by enforcing non-negativity.
problem Lack of interpretability in deep representations.
method Non-negative Contrastive Learning (NCL) using non-negativity constraints.
result NCL outperforms standard contrastive learning in feature disentanglement and selection.
Compact Kähler orbifolds with non-negative Ricci curvature are simply connected.
problem Understanding the topology of Kähler orbifolds with non-negative Ricci curvature.
method Proved orbifold versions of Kobayashi's theorem.
result Compact Kähler orbifolds with non-negative Ricci curvature are simply connected under certain conditions.
Vanishing theorem on CR manifolds with non-negative curvature.
problem Vanishing theorem for Betti numbers on CR manifolds.
method Application of Bochner technique to CR manifolds with non-negative curvature.
result Proof of vanishing theorem for Betti numbers.
New findings on stable commutator lengths in recursively presented groups.
problem Understanding stable commutator lengths in recursively presented groups.
method Analyzing recursively presented groups and infinitely presented small cancellation groups.
result All non-negative algebraic or computable numbers are in the set of stable commutator lengths.
Place Cells as Multi-Scale Position Embeddings: Random Walk Transition Kernels for Path Planningq-bio.NC
Model place cells as spatial embeddings for efficient path planning and cognitive map construction.
problem Encoding spatial navigation in the hippocampus.
method Model place cells using spectral decomposition of multi-step random walk transition kernels, inducing sparsity and adjacency.
result Place cells encode spatial information through non-negativity and inner-product structure, forming a cognitive map.
Estimates on Einstein manifolds improve Brownian motion behavior and curvature limits.
problem Improving estimates on Einstein manifolds for Brownian motion behavior.
method Generalizing Benjamini-Pemantle-Peres estimate to manifolds with Ricci curvature bounds.
result Sharp estimates for Brownian motion on high curvature parts of Ricci-flat manifolds.
Study on Kähler manifolds with non-negative mixed curvature, proving splitting and structure theorems.
problem Investigating properties of Kähler manifolds with specific curvature conditions.
method Conformal perturbation method.
result Established structure and splitting theorems for Kähler manifolds with non-negative mixed curvature.
Paper generalizes bipolar theorems for non-negative random variables.
problem Problems with existing bipolar theorems under stronger assumptions.
method Generalizes existing theorems in a robust probabilistic framework.
result Provides necessary and sufficient conditions for bipolar representation.