Paper uses optimal transport-based statistics for change point detection.
problem Change point detection in multivariate data.
method Soft rank energy and entropically regularized optimal transport.
result Soft rank energy performs better in real datasets with strong continuity and convergence properties.
New ABC method uses energy statistic for data comparison.
problem Handling intractable likelihood functions in Bayesian analysis.
method Importance Sampling ABC (IS-ABC) using two-sample energy statistic.
result Energy statistic-based ABC yields consistent pseudo-posterior distributions.
Author presents the second variational formula for statistical biharmonic maps.
problem Developing a formula for statistical biharmonic maps.
method Introduced the second variational formula for the statistical bi-energy functional.
result The second variational formula can be represented using Hessian curvature in Hessian manifolds.
Study smooth linear statistics on random covers of hyperbolic surfaces, showing central limit and variance results.
problem Analyzing fluctuations and energy variance of random covers of compact hyperbolic surfaces.
method Examining fluctuations in a small energy window around a fixed energy level, considering the variance of a typical surface, using a double limit where n and L go to infinity. result Distribution of fluctuations tends to a Gaussian with variance of GOE/GUE, and energy variance of a typical random n-cover is that of GOE/GUE. Study shows energy levels on hyperbolic surfaces follow GOE fluctuations.
problem Understanding energy level fluctuations on hyperbolic surfaces.
method Analysis of Laplace eigenvalues on hyperbolic surfaces, using GOE random matrix theory.
result Energy variance on typical hyperbolic surfaces closely matches GOE fluctuations.
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproduc…
Paper connects free-energy and low-degree hardness in high-dimensional statistics.
problem High-dimensional statistical inference problems are computationally hard.
method Defines a free-energy criterion and connects it to low-degree hardness.
result Establishes connection between free-energy and low-degree hardness for Gaussian models.
mAIS improves free energy evaluation efficiency.
problem Computational infeasibility of exact free energy evaluation.
method mAIS, a marginalized version of AIS.
result mAIS is more efficient under certain conditions.
Deep learning depends on tuning layers near critical points.
problem Understanding how deep learning architectures depend on tuning parameters.
method Random energy approach to analyze statistical dependence in deep belief networks.
result Statistical dependence can propagate only if layers are tuned near critical points.
Statistical learning theory connects to spin glass models via Rademacher complexity and replica theory.
problem Bounding generalization gap in statistical learning theory.
method Linking Rademacher complexity in statistical learning to synthetic models in statistical physics.
result Rademacher complexity is closely related to ground state energy in spin glass models.
GOE statistics emerge from surface moduli space averages.
problem Understanding spectral statistics on hyperbolic surfaces.
method Defined a smooth linear statistic, averaged over moduli space, and analyzed variance.
result GOE statistics are recovered in the large genus and high energy limits.
Contrastive learning simplifies statistical inference for complex models.
problem Computational intractability of likelihood functions for certain models.
method Contrastive learning as an alternative for parameter estimation and inference.
result Contrastive learning enables practical methods for diverse statistical problems.
Improved generative models using overparametrized shallow neural networks.
problem Improving generative models for data with hidden low-dimensional structure.
method Using energy-based models with overparametrized shallow neural networks as approximators.
result Models trained in the 'active' regime outperform those in the 'lazy' or kernel regime, leading to better adaptivity to hidden structure.
We investigate relationship between annual electric power consumption per capita and gross domestic production (GDP) per capita for 131 countries. We found that the relationship can be fitted with a power-law function. We examine the relationship for 47 prefectures in Japan. Furthermore, we investigate values of annual…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as establ…
This work optimizes statistical inference with neural networks for high-energy physics data.
problem Optimal dimensionality reduction with minimal loss of information in the presence of systematic uncertainties.
method Neural network optimization based on binned Poisson likelihoods with nuisance parameters.
result Estimates of parameters of interest close to optimal.
Energy trees handle complex data structures with multiple variable types.
problem Handling intricate data structures with various types of covariates.
method Energy trees, a regression and classification model, use energy statistics to accommodate structured covariates of different types.
result Energy trees maintain statistical foundations, interpretability, and robustness to overfitting.
We briefly review statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the agents in payment for goods and services. We focus on conceptual foundations for this …
Improved language models by incorporating statistical discriminators.
problem Distinguishing model-generated text from real text reliably.
method Energy-Based Model framework to incorporate discriminators.
result Improves language model performance in perplexity and human evaluation.
A statistical model or a learning machine is called regular if the map taking a parameter to a probability distribution is one-to-one and if its Fisher information matrix is always positive definite. If otherwise, it is called singular. In regular statistical models, the Bayes free energy, which is defined by the minus…
New method improves wind and solar energy forecasts by 48 hours.
problem Volatility of wind and solar energy makes accurate forecasts difficult.
method Two-step machine learning approach to calibrate ensemble forecasts.
result Statistical post-processing improves forecast skill by at least 48 hours.
In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \emph{Energy Landscape Maps} (ELMs) which characterize and visualize an energy function with a tree structure, in which each leaf node re…
Stochastic Gradient Descent finds wide but shallow minima due to undersampling, akin to energy-entropy competition.
problem The empirical effectiveness of Stochastic Gradient Descent in machine learning.
method Deriving a correspondence between parameter inference and free energy minimisation in statistical physics, where the degree of undersampling plays the role of temperature.
result Stochasticity in Stochastic Gradient Descent biases it towards wide minima, explaining its empirical effectiveness.
Bayesian inference learns free energy landscapes from experimental data.
problem Characterize the free energy landscape of classical many-body systems from experimental data.
method Combines non-parametric Bayesian inference with physically-motivated constraints to automate the construction of approximate free energy functionals.
result Inference algorithms yield a probability distribution over free energy functionals, leading to highly accurate analytic expressions.
Machine learning in high-energy physics faces challenges from nuisance parameters, which are reviewed and techniques to mitigate their impact are discussed.
problem Impact of nuisance parameters on machine learning performance in high-energy physics.
method Review and discussion of techniques including nuisance-parameterized models, modified or adversary losses, semi-supervised learning, and inference-aware techniques.
result Various methods to reduce the impact of nuisance parameters and improve model performance in high-energy physics.
Kernel k-Groups uses Hartigan's method for clustering in metric spaces of negative type.
problem Clustering in metric spaces of negative type.
method Weighted energy statistics, quadratically constrained quadratic program, kernel k-groups, Hartigan's method.
result Improved performance in higher dimensions compared to spectral clustering and kernel k-means.
Paper explores sustainable machine learning with energy harvesting.
problem Energy-efficient distributed machine learning in resource-constrained devices.
method Developed a practical learning framework with theoretical guarantees for distributed learning over energy-harvesting devices.
result Demonstrated significant performance improvement over non-harvesting benchmarks.
New image restoration method using localized patches and external databases.
problem Image restoration challenges.
method Localized structured prediction and non-linear multi-task learning for optimizing a penalized energy function.
result Strong statistical guarantees and practical effectiveness demonstrated on various image restoration problems.
Method converts sparse systems to dense ones for statistical mechanics problems.
problem Statistical mechanics on sparse graphs
method Extracts a Feedback Vertex Set, learns variational distribution, estimates free energy.
result More accurate and faster than existing methods for sparse systems.
Develops a statistical arbitrage strategy with stop-loss and leverage for energy markets.
problem Optimizing trading strategies in high-frequency energy markets with stop-loss and leverage.
method Analytical approach using mean-reverting processes and optimal trading strategies.
result Analytical expressions for expected First-Exit-Times and long-run returns of the strategy.
This research improves calorimeter simulations by creating a faster model.
problem Efficiently simulating detailed calorimeter data for high-energy physics.
method Developed a conditional normalizing flow model for superresolution.
result The model successfully reproduces reference distributions.
Study normal tempered stable processes for energy derivative pricing.
problem Pricing energy derivatives with spot price models.
method Specified statistical properties, derived non-arbitrage conditions, developed efficient algorithm for trajectory generation.
result Validated pricing models for various energy contracts.
Reweighting improves GAN accuracy without sacrificing statistical power.
problem Improving the fidelity of generative models.
method Post-hoc reweighting function applied to generated examples.
result Weighted GAN examples significantly improve accuracy.
We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schrödinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models a…
FoG RF achieves high accuracy with low energy consumption.
problem Energy efficiency in ML algorithms for constrained systems.
method Field of Groves (FoG) implementation of random forests.
result FoG RF achieves comparable accuracy to CNNs and SVMs with significantly lower energy consumption.
Enhanced tabular benchmarks for energy-efficient neural architecture search.
problem Energy consumption in deep learning models.
method Introducing EC-NAS, an enhanced tabular benchmark with energy consumption data.
result EC-NAS reveals a balance between energy usage and accuracy in neural architecture search.
Paper proposes Gini distance statistics for estimating feature-label dependence.
problem Identifying statistical dependence between features and categorical labels.
method Generalized Gini distance in RKHS for feature-label dependence estimation.
result Gini distance statistics converge faster and have tighter error bounds than distance covariance.
Study shows increased renewables lead to more extreme price spikes in balancing markets.
problem Higher variability of renewable energy leads to increased ancillary service costs, especially extreme price spikes.
method Agent-based modeling to simulate fluctuations in load and renewable energy production, forecasting resulting energy prices and costs.
result The probability of extreme price events increases with an increased share of renewable energy sources.
The study uses statistical methods to analyze nuclear mass models.
problem Understanding the information content of nuclear masses from models.
method Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis.
result A dramatic parameter reduction can be achieved in both 4-parameter and 14-parameter models.
Proposes an energy-based sliced Wasserstein distance for improved probability measure comparison.
problem Inefficiencies and limitations in existing sliced Wasserstein distance approaches.
method Introduces an energy-based slicing distribution for better performance and stability.
result Demonstrates superior performance of the EBSW distance in various applications.
A thermodynamic theory explains EU election vote distributions.
problem Describing EU election vote distributions.
method Tracing parallels between system energies of coupled nonlinear oscillators and party vote fractions.
result The Rayleigh-Jeans (RJ) theory well depicts EU vote results and candidate vote dispersion.
Study on weather forecasting errors for solar energy forecasting.
problem Uncertainty in weather forecasting for solar PV generation.
method Comparison of forecasted and observed weather data, statistical metrics, and sensitivity test.
result Identified influential weather variables improving solar PV generation forecasting.
This paper presents an assessment of global economic energy potentials for all major natural energy resources. This work is based on both an extensive literature review and calculations using natural resource assessment data. Economic potentials are presented in the form of cost-supply curves, in terms of energy flows …
Boltzmann Generators use deep learning to efficiently sample complex systems.
problem Sampling equilibrium states in many-body systems like proteins is computationally challenging.
method Combining deep learning and statistical mechanics, Boltzmann Generators learn a coordinate transformation to generate unbiased samples.
result Boltzmann Generators can generate one-shot equilibrium samples of complex systems and proteins.
Proposes a new acquisition function for batched Bayesian optimization.
problem Intractability of acquisition functions for batched Bayesian optimization.
method Statistical physics inspired acquisition function for Gaussian processes.
result Demonstrates competitive performance on various problems.
This Chapter is written for the Festschrift celebrating the 70th birthday of the distinguished economist Duncan Foley from the New School for Social Research in New York. This Chapter reviews applications of statistical physics methods, such as the principle of entropy maximization, to the probability distributions of …
DEEN learns energy and score functions from complex data.
problem Challenges in density estimation for high-dimensional data.
method Inference-free hierarchical framework using score matching and multilayer perceptrons.
result DEEN successfully learns energy and score functions from synthetic and high-dimensional data.
Paper extends multivariate rank tests for robust subspace detection.
problem Testing distributional similarity in multivariate data.
method Soft and subspace robust multivariate rank tests based on entropy regularized optimal transport.
result Trade-off between detection power and false alarm rate via projections.