MCD reformulates conditional density estimation into binary classification.
problem Conditional density estimation in statistical and machine learning.
method Marginal Contrastive Discrimination, reformulating into marginal and ratio density functions for binary classification.
result Significantly outperforms existing methods on most density models and regression datasets.
Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is …
Develops a new density ratio estimator for causal inference.
problem Estimation of density ratio functions in statistics.
method Super learning approach with a novel loss function.
result Empirical validation of the density ratio super learner's performance.
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.
New model for density estimation using tensor trains.
problem Estimation of high-dimensional probability density functions.
method Tensor train-based density estimation (TTDE) with Riemannian optimization.
result TTDE outperforms competitors in training speed and performance.
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and highly accurate energies are achieved. Accurate {\em constrained optimal densitie…
New binary loss functions improve density ratio estimation accuracy.
problem Improving accuracy of density ratio estimators using binary classifiers.
method Characterized loss functions based on prescribed error measures in Bregman divergences.
result Novel loss functions prioritize accurate estimation of large density ratio values.
This work explores CS-RBFs as novel probability density functions.
problem Underexplored use of CS-RBFs in statistics and probability modeling.
method Derivation of statistical properties of CS-RBFs as univariate and conditional densities, analysis of mixture models, and introduction of an incremental learning algorithm.
result CS-RBF densities provide competitive results in likelihood and model complexity compared to Gaussian mixture models.
New deep neural network method improves change point detection.
problem Change point detection in data streams.
method Deep density ratio estimation using gradient descent objective functions.
result Deep neural network outperforms other methods on seizure detection.
The study applies spatial density models to mobile node movements using Möbius distributions.
problem Modeling the steady-state density of mobile nodes on a 2D terrain.
method Used mixture density networks with Möbius distributions to describe node density over a disk.
result Möbius distributions are more suitable for capturing radial changes in node density compared to Gaussian distributions.
Deep learning speeds spectral density estimation for large 2D/3D grids.
problem Computational challenges in estimating spectral densities for large grids.
method Deep learning neural network for spectral density estimation.
result Deep learning estimator is a universal approximator and faster than existing methods.
WDL models density curves using Wasserstein distance and flexible mixture models.
problem Modeling entire distribution and non-negativity constraints.
method Wasserstein distance, Semi-parametric Conditional Gaussian Mixture Models (SCGMM), Majorization-Minimization optimization.
result WDL better characterizes nonlinear dependence of conditional densities.
Deep learning improves OFDFT for molecular systems.
problem Limited accuracy of OFDFT for non-periodic molecular systems.
method M-OFDFT using deep learning to approximate kinetic energy density.
result Achieves comparable accuracy to Kohn-Sham DFT on large molecules.
Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on hyperparameters. We find universal features of the behavior in extreme limits, includi…
New method trains deep neural networks for non-interacting kinetic-energy functionals in DFT.
problem Lack of exact relationship between electron density and non-interacting kinetic energy.
method Variational principle to regularize machine-learned density functionals.
result Excellent results on kinetic-energy functionals for various systems.
Equivariant graph neural networks predict electron density for molecules, liquids, and solids.
problem Predicting electron density for molecules, liquids, and solids using machine learning.
method Equivariant graph neural networks for predicting electron density at query points.
result The model predicts electron density with accuracy beyond state of the art and significantly faster than traditional DFT methods.
Two new methods estimate quantum density matrices using machine learning.
problem Estimating the quantum density matrix for complex systems.
method Quantum Maximum Likelihood and Quantum Variational Inference with quantum flows.
result Improved estimation of quantum density matrices for mixed states.
LLMs learn probability density functions in-context, showing distinct learning trajectories.
problem Density estimation of time series data in LLMs.
method Intensive Principal Component Analysis (InPCA) to visualize and analyze LLMs' learning dynamics.
result LLMs follow similar learning trajectories in a low-dimensional InPCA space, distinct from traditional methods.
A new model estimates complex densities without explicit normalizing constants.
problem Accurately estimating the normalizing constant of high-dimensional energy functions.
method Autoregressive Energy Machine (AEM) learns an unnormalized density and an importance-sampling estimate of the normalizing constant.
result Achieves state-of-the-art performance on density-estimation tasks.
Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields, ranging from materials science to biochemistry to astrophysics. Machine learning holds the promise of learning the kinetic energy functional …
The paper analyzes how a known density function can be deviated by a mixture distribution as more data is collected.
problem Modeling the deviation of a known density function when more data is collected.
method A novel distinguishability notion is used to establish rates of convergence for maximum likelihood estimates of the deviated proportion and latent mixing measure.
result Rates of convergence for the maximum likelihood estimates of the deviated proportion and latent mixing measure are established under the Wasserstein metric.
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or O(n*log(n)) for constructing a classifier, where n is the number of sampling instances.…
This research improves demand forecasting by predicting complete probability density functions using machine learning.
problem Forecasting complete probability density functions for better operational decision making.
method Supervised machine learning method 'Cyclic Boosting' for explainable predictions.
result Predicted probability density functions are fully explainable and avoid 'black-box' models.
Machine learning is used to approximate the kinetic energy of one dimensional diatomics as a functional of the electron density. The functional can accurately dissociate a diatomic, and can be systematically improved with training. Highly accurate self-consistent densities and molecular forces are found, indicating the…
Bayesian optimization improves efficiency with semi-supervised learning.
problem Efficiently find global optima of expensive functions.
method Density ratio estimation combined with semi-supervised learning.
result Improved accuracy in identifying global optima with unlabeled data.
A Fourier transform approach optimizes clustering algorithms.
problem Optimizing clustering algorithms for accuracy and reliability.
method Fourier transform and Gaussian filtering to smooth density functions, detecting peaks as cluster centroids.
result Remarkable accuracy in finding cluster centroids, overcoming initialization problems.
New method learns models from data density and generates samples.
problem Learning models that estimate data density and generate samples.
method Denoising density estimators (DDEs) trained to minimize KL-divergence.
result Our method converges to correct solution without specific network architecture.
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.
LDDNN learns physical dynamics from data without exact solutions.
problem Learning physical dynamics from data without exact solutions.
method LDDNN topology that learns Lagrangian density from data.
result LDDNN can learn physical dynamics from data.
This work improves imitation learning and goal-conditioned RL by estimating value densities.
problem Effective solutions for imitation and goal-conditioned reinforcement learning require reliably reaching specified states or demonstrations.
method The approach uses recent advances in density estimation to learn value functions efficiently and without hindsight bias.
result The method achieves state-of-the-art demonstration sample-efficiency in imitation learning and is both efficient and bias-free in goal-conditioned reinforcement learning.
Given iid observations from an unknown absolute continuous distribution defined on some domain Ω, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function. Our density estimate is a piecewise constant function defined on a binary partition o…
New α-divergence loss function improves neural density ratio estimation.
problem Optimization challenges in existing DRE methods, especially overfitting and high sample requirements.
method Derived α-divergence loss function (α-Div) for neural density ratio estimation. result The α-divergence loss function (α-Div) offers stable and effective optimization for DRE. Optimizes kernel density ratios for better predictions and information measures.
problem Improving accuracy of kernel density estimates for density ratios.
method Derives an optimal weight function using calculus of variations.
result Reduces bias in kernel density estimates, leading to improved prediction posteriors and information-theoretic measures.
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.
Paper develops estimators for unbounded density ratios with applications in error control.
problem Estimating density ratios with unbounded domains and ranges.
method Least squares and logistic regression loss functions for density ratio estimation.
result Established upper bounds on estimation errors with optimal rates for unbounded density ratios.
A new method predicts electron density accurately from atom-centered models.
problem Predicting electron density accurately from atom-centered models.
method Gradient-based approach to minimize loss function in an optimized sparse feature space.
result Extremely accurate predictions of electron density and total energies.
Kernel Density Machines learn probability densities without structural assumptions.
problem Learning probability densities under minimal assumptions.
method Kernel-based framework, agnostic to structural requirements.
result Consistency and functional central limit theorem for sample estimator.
Researchers created an accurate kinetic energy functional for materials modeling.
problem Lack of accurate analytic kinetic energy functionals for large-scale ab initio materials modeling.
method Interpretative machine learning of crystal cell-averaged kinetic energy densities guided by a hybrid Gaussian process regression - neural network (GPR-NN) method.
result Constructed an analytic kinetic energy functional that reproduces Kohn-Sham DFT energy-volume curves with sufficient accuracy.
A new method improves density ratio estimation with fewer function evaluations.
problem Stable and accurate estimation of density ratios with high variance issues.
method Diffusion Secant Alignment for Score-Based Density Ratio Estimation (ISA-DRE)
result ISA-DRE achieves comparable or superior results with fewer function evaluations.
New method combines strengths of two PCL approaches without density ratio estimation.
problem Estimating causal functions in Proxy Causal Learning with unobserved confounders and proxies.
method Kernel-based doubly robust estimators combining treatment and outcome bridges, density ratio-free.
result Outperforms existing methods on PCL benchmarks, including a prior doubly robust method.
Generative models improve image probability estimation but lack interpretability.
problem Lack of interpretability in generative models for natural image distributions.
method Extracted explicit probability density estimates from GANs and analyzed latent representations.
result Natural image density functions are difficult to interpret.
New method estimates model discrepancy without sampling for unnormalized models.
problem Evaluating and training unnormalized density models efficiently.
method Estimate Stein discrepancy using neural network parameterized vector function.
result Method outperforms existing goodness-of-fit tests and training methods.
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.
Study on flow-based methods for capturing tail properties in densities.
problem Flow-based methods struggle with capturing non-Gaussian tails.
method Characterize and adapt triangular maps to capture tail properties.
result Flow models lack the ability to capture non-Gaussian tails.
By representing words with probability densities rather than point vectors, probabilistic word embeddings can capture rich and interpretable semantic information and uncertainty. The uncertainty information can be particularly meaningful in capturing entailment relationships -- whereby general words such as "entity" co…
GBHT uses gradient boosting for density estimation with theoretical guarantees.
problem Density estimation for unsupervised learning.
method Gradient Boosting Histogram Transform (GBHT) with Negative Log Likelihood loss.
result GBHT achieves faster convergence rates and better performance than base learners in density estimation.
New algorithm uses density ratios for efficient online reinforcement learning.
problem Challenges in collecting exploratory data for online reinforcement learning.
method Density ratio modeling for online exploration, combining truncation and optimism.
result Sample-efficient online exploration achieved with GLOW and HyGLOW.
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.