Bayesian inference reconstructs external potentials in DFT for many-particle systems.
problem Reconstructing external potentials in classical density-functional theory (DFT) for many-particle systems.
method Combines Bayesian inference with classical DFT to probabilistically reconstruct external potentials.
result Accurately infers external potentials and density profiles with uncertainty quantification.
Develops method to compute Chern-Simons potentials from higher-dimensional Pontryagin densities.
problem Computing Chern-Simons potentials from higher-dimensional Pontryagin densities.
method Systematic approach using a generic affine connection with non-vanishing torsion and non-metricity.
result Algorithm and code for determining Chern-Simons potential from Pontryagin density in arbitrary even dimensions.
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
Develops methods to learn correlation potentials for time-dependent Kohn-Sham systems.
problem Learning the correlation potential for time-dependent Kohn-Sham systems.
method Optimizing a least-squares objective subject to the TDKS equation using adjoints.
result Learned correlation potential models match ground truth electron densities and can have memory.
New method for modeling densities on Riemannian manifolds with symmetries.
problem Modeling densities on Riemannian manifolds with known symmetry groups.
method Combining implicit neural layers and optimal transport theory to propose IRCPMs.
result IRCPMs are simpler to incorporate symmetries and less expensive than ODE-flows.
We propose a procedure for supervised classification that is based on potential functions. The potential of a class is defined as a kernel density estimate multiplied by the class's prior probability. The method transforms the data to a potential-potential (pot-pot) plot, where each data point is mapped to a vector of …
Paper proves integrability and entropy compactness for Kähler potentials with uniform log-log threshold.
problem Integrability and entropy compactness for Kähler potentials with specific density.
method Skoda-Zeriahi type integrability theorem and log-log threshold detection.
result Positivity of integrability threshold and entropy compactness for uniform log-log threshold.
A novel density-based approach QC detects outliers in data with high precision.
problem Detecting outliers in data with high precision and sensitivity.
method Quantum Clustering (QC) approach based on the density of data points.
result QC effectively finds hidden outliers and subtle outliers with parameter adjustment.
DenSNet learns electron densities for molecular dynamics, enabling accurate spectroscopic predictions.
problem Lack of accurate electronic observables in MLIPs for molecular dynamics.
method DenSNet uses SE(3)-equivariant neural networks to predict electron densities and total energy.
result DenSNet predicts infrared spectra with excellent agreement to experimental data.
Framework learns inter-electronic potential for molecular dynamics.
problem Predicting time-dependent Hartree-Fock dynamics from electron density.
method Developed three models using four-index tensors, preserving symmetries.
result Model with eight-fold symmetry performs best across metrics.
Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also considered, including the estimation of a class of fields having nonzero vorticity.
A new method avoids partition function computation for Gibbs density estimation.
problem Estimating Gibbs density functions without partition function computation.
method Maximum Recovery MAP (MR-MAP) and least-action type potential.
result MR-MAP estimators solve optimization problem quickly using neural network.
We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target distribution, and therefore does not perform its full power on truncated distribu…
Quantum model captures rare financial events not seen by Gaussian statistics.
problem Underestimation of rare financial events by Gaussian statistics.
method Quantum Bohmian Mechanics applied to multifractal random walk (MRW) models.
result Rare financial events generate a potential barrier in quantum potentials.
Study non-semisimple TQFT for Burau representation density and unitarity.
problem Density and unitarity of the Burau representation from a non-semisimple TQFT perspective.
method TQFT construction of Squier's Hermitian form on the Burau representation.
result Density of the image of braid group in unitary representations.
Proposes SD-KDE for density estimation using debiased kernel density with score-based adjustments.
problem Density estimation with bias in kernel density estimation.
method Adjusts data points by taking a step along the estimated score function, then applies standard KDE with modified bandwidth.
result Significantly reduces mean integrated squared error compared to standard Silverman KDE, especially with noisy score function estimates.
Algorithm aligns 3D density maps using Wasserstein distance.
problem Aligning 3D density maps in cryogenic electron microscopy.
method Minimizing 1-Wasserstein distance after rigid transformation using Bayesian optimization.
result Improved accuracy and efficiency in protein molecule alignment.
We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems transforms the search for a probability density into the solution of a differential…
iEFM trains CNF models from unnormalized densities efficiently.
problem Training generators from energy functions or unnormalized densities.
method Iterated energy-based flow matching (iEFM) with simulation-free objective.
result iEFM outperforms existing methods in probabilistic modeling.
Quantum computers outperform classical methods in density modeling.
problem Density modeling with quantum computers.
method Quantum-classical separation for density modeling.
result Quantum computers offer a super-polynomial advantage over classical algorithms for density modeling.
This paper proposes a new method for automatically selecting the optimal kernel bandwidth in density estimation.
problem The challenge of selecting the optimal kernel bandwidth in unsupervised density estimation.
method The approach uses a topology-based loss function for automated bandwidth selection.
result Demonstrates the potential of the topology-based approach across different dimensions.
The paper improves boundary detection and density estimation on noisy data.
problem Detecting boundary points and estimating density on noisy data from compact manifolds.
method Doubly stochastic scaling of the Gaussian heat kernel via Sinkhorn iterations.
result The new estimates of boundary points and density outperform standard methods, especially under noise.
M-flows learn data manifolds and densities, improving manifold learning and inference.
problem Representing datasets with manifold structure more faithfully.
method Combining normalizing flows, GANs, autoencoders, and energy-based models, with a new training algorithm.
result M-flows learn data manifolds better than standard flows and provide handles for dimensionality reduction.
NFs improve on HEP's complex data, tested on increasing dimensions.
problem Leveraging NFs for high-dimensional data in HEP.
method Tested various NF types on toy datasets with varying dimensions.
result NFs robustness increases with higher dimensions.
We show how effective-potential path-integrals methods, stemming on a simple and nice idea originally due to Feynman and successfully employed in Physics for a variety of quantum thermodynamics applications, can be used to develop an accurate and easy-to-compute semi-analytical approximation of transition probabilities…
Density sketches summarize data distributions for accurate sampling and estimation.
problem Accurately estimating and sampling from complex data distributions.
method Online algorithm generating additive density sketches.
result Density sketches provide statistically sound estimators and sampling capabilities.
A model-free framework extracts risk-neutral densities from short-dated options.
problem Arbitrage and bid-ask spread issues in short-dated options.
method Develops ARIES for filtering static arbitrage and SEDEx for density extraction.
result Robust density extraction across various market conditions and volatility smiles construction.
Machine learning predicts liquid water properties from cluster data.
problem Accuracy of bulk properties from machine-learned potentials is limited by training data.
method Local, atom-centred descriptors enable prediction of bulk properties from cluster data.
result Excellent agreement with experimental and theoretical counterparts of liquid water properties.
Study finds optimal martingale coupling between two distributions with minimal entropy.
problem Finding the optimal martingale coupling between two distributions with minimal relative entropy.
method Solving a dual problem to find the log-density of the optimal coupling, which represents the marginal and martingale constraints.
result The log-density of the optimal coupling is given by a triplet of real functions representing the marginal and martingale constraints.
The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more accurately detect small erroneous deviations in reconstructed density matrices, which c…
A new tensor ring mixture model improves density estimation efficiency.
problem Efficient probability density estimation in statistical machine learning.
method Tensor ring decomposition with mixture model for adaptive weights.
result Enhanced expressive capability and flexibility in density estimation.
This work uses neural density estimation to analyze laser-induced breakdown spectroscopy data, enabling accurate predictions and uncertainty quantification.
problem Inference of probability densities in high-dimensional spectral data is often intractable.
method Normalizing flows on structured spectral latent spaces for density estimation and uncertainty quantification.
result The approach enables generation of realistic spectral samples and accurate prediction of state vectors with well-calibrated uncertainties.
The bias potential model explains how generative models can generalize or memorize samples.
problem Understanding and achieving generalization in generative models like GANs.
method Introducing the bias potential model to analyze the behavior of generative models.
result Dimension-independent generalization accuracy can be achieved with early stopping in the bias potential model.
K-nearest neighbors (KNN) method is used in many supervised learning classification problems. Potential Energy (PE) method is also developed for classification problems based on its physical metaphor. The energy potential used in the experiments are Yukawa potential and Gaussian Potential. In this paper, I use both app…
We present a deep generative model, named Monge-Ampère flow, which builds on continuous-time gradient flow arising from the Monge-Ampère equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible…
In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means clustering. Mean Shift clustering is a generalization of the k-means clustering wh…
By introducing the concept of \emph{Kato control pairs} for a given Riemannian minimal heat kernel, we prove that on every Riemannian manifold (M,g) the Kato class K(M,g) has a subspace of the form Lq(M,dϱ), where ϱ has a continuous density with respect to the volume measure $μ_g…
The article derives some novel independence measures and contrast functions for Blind Source Separation (BSS) application. For the kth order differentiable multivariate functions with equal hyper-volumes (region bounded by hyper-surfaces) and with a constraint of bounded support for k>1, it proves that equality …
In this paper, we study the classical problem of the first passage hitting density of an Ornstein--Uhlenbeck process. We give two complementary (forward and backward) formulations of this problem and provide semi-analytical solutions for both. The corresponding problems are comparable in complexity. By using the method…
Direct Density Ratio Optimization aligns LLMs with human preferences without assuming specific models.
problem Statistical inconsistency in aligning LLMs with human preferences.
method Direct Density Ratio Optimization (DDRO) estimates density ratio directly.
result DDRO is statistically consistent, converging to true human preferences as data grows.
Estimates modes and ridges in mixed Euclidean and directional spaces.
problem Estimating local modes and density ridges in product spaces combining Euclidean and directional metrics.
method Extends mean shift algorithm to product spaces, addressing challenges in generalization.
result Established convergence of the proposed methods and demonstrated effectiveness on real-world datasets.
This study investigates the effects of Markov chain Monte Carlo (MCMC) sampling in unsupervised Maximum Likelihood (ML) learning. Our attention is restricted to the family of unnormalized probability densities for which the negative log density (or energy function) is a ConvNet. We find that many of the techniques used…
SympFormer accelerates attention blocks using inertial dynamics on density spaces.
problem Improving the efficiency of self-attention blocks in Transformers.
method Introduced accelerated attention blocks derived from inertial Nesterov dynamics on density spaces.
result Accelerated attention blocks converge faster than classical blocks while preserving oracle calls.
In the present paper, an expansion of the transition density of Hyperbolic Brownian motion with drift is given, which is potentially useful for pricing and hedging of options under stochastic volatility models. We work on a condition on the drift which dramatically simplifies the proof.
Research on manifold learning within a density ridge estimation framework has shown great potential in recent work for both estimation and de-noising of manifolds, building on the intuitive and well-defined notion of principal curves and surfaces. However, the problem of unwrapping or unfolding manifolds has received r…
New method preserves GCM spatial dependencies for better climate projections.
problem Systemic biases in GCM output and loss of spatial/temporal dependencies.
method SPECD approach using Vecchia approximation and semi-parametric quantile regression.
result SPECD preserves key marginal and joint distribution properties of precipitation and temperature.
We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS'. Subsequently, alloy-type perturbations of th…
InQMAD detects anomalies in streaming data using quantum measurements and density matrices.
problem Detecting anomalies in streaming data with challenges like conceptual drift and continuous learning.
method Incremental anomaly detection based on random Fourier features and quantum measurements.
result InQMAD outperforms 12 state-of-the-art methods in a systematic evaluation.