New statistics are introduced that maintain the Fisher metric structure closely, akin to sufficient statistics.
problem Maintaining the Fisher metric structure in statistical models.
method Characterizing statistics that maintain the Fisher metric structure bi-Lipschitz equivalently.
result Characterized statistics that preserve the Fisher metric structure closely.
Paper discusses the Fisher metric and differentiability in statistical models.
problem Understanding the relationship between Fisher metric and differentiability in statistical models.
method Comparison of different concepts and models in Information Geometry, mathematical statistics, and measure theory.
result Discussion of various models and their differentiability properties.
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.
Machine learning improves official statistics but needs rigorous validation.
problem Lack of methodological robustness in machine learning for official statistics.
method Total Machine Learning Error (TMLE) framework to validate ML models.
result TMLE addresses representativeness and measurement errors in ML models.
This work uses statistical mechanics to explain AI learning.
problem Understanding the statistical principles behind AI learning.
method Starting from sample concentration behaviors, the study applies statistical mechanics principles to AI and machine learning.
result Exponential families and statistical quantities are key in AI and machine learning.
Quantum statistical models with singularities are studied for state estimation and model selection.
problem Understanding statistical properties of quantum singular models.
method Classical singular learning theory extended to quantum state estimation and model selection using algebraic geometrical methods.
result Asymptotically unbiased estimator (QWAIC) for quantum generalization loss constructed.
Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of summary statistic, but outside of special cases where the optimal summary statis…
Statistical arbitrageurs have inelastic demand, contrary to classical models.
problem Understanding the demand elasticity of statistical arbitrageurs.
method Thirteen models from the literature and a quantitative equilibrium model.
result Aggregate demand remains inelastic even with statistical arbitrageurs.
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the criterion for passing from one model to another without loss of information. Thi…
Triangular flows ensure statistical consistency and fast rates in generative modeling.
problem Ensuring statistical consistency and fast rates in generative models.
method Statistical guarantees and sample complexity bounds for triangular flow models using empirical process theory.
result Established statistical consistency and finite sample convergence rates for Kullback-Leibler estimator of Knöthe-Rosenblatt measure coupling.
A method uses neural networks to approximate sampling distributions of test statistics.
problem Accurate modeling of p-value functions or cdfs for correct confidence set coverage.
method Uses neural networks to model the cdf of test statistics, approximating sampling distributions.
result Neural network approximations of sampling distributions are effective and simple.
Efficiently transforms samples from various statistical models.
problem Approximately transforming samples from one statistical model to another without knowing the source model's parameters.
method Constructs computationally efficient procedures to reduce uniform, Erlang, and Laplace models to general target families.
result Establishes nonasymptotic reductions between canonical high-dimensional problems, such as mixtures of experts, phase retrieval, and signal denoising.
We seek to utilize the nonextensive statistics to the microscopic modeling of the interacting many-investor dynamics that drive the price changes in a market. The statistics of price changes are known to be fit well by the Students-T and power-law distributions of the nonextensive statistics. We therefore derive models…
The Ising model replicates financial asset statistical features.
problem Replicating statistical characteristics of financial markets.
method Employed the Ising model and Monte Carlo simulations.
result The Ising model can replicate most financial asset statistical features.
Optimized Franz-Parisi criterion matches SQ lower bounds for various statistical models.
problem Understanding computational hardness in statistical inference.
method Proposed and refined Franz-Parisi criterion, established equivalence with SQ lower bounds.
result Optimized Franz-Parisi criterion is equivalent to Statistical Query (SQ) lower bounds.
Investigates transfer learning in spatial statistics.
problem Applying transfer learning to spatial statistics.
method Simple MLP models for spatial data.
result Potential of transfer learning in spatial statistics.
Improved computational complexity in statistical models using second-order information.
problem Polynomial convergence of gradient descent in singular statistical models.
method Normalized Gradient Descent (NormGD) algorithm with second-order information.
result NormGD reaches final statistical radius in logarithmic iterations of n. Proposes an exponentially increasing step-size for faster parameter estimation in statistical models.
problem Slow convergence of gradient descent in locally convex loss functions.
method Exponentially increasing step-size in gradient descent algorithm.
result Converges linearly to optimal solution under homogeneous assumptions.
The paper extends statistical inference methods for black-box generative models.
problem Understanding and validating black-box generative models without access to their internal data.
method Develops model-level statistical inference tasks using generative model representations.
result Model-level representations are effective for multiple inference tasks.
FNNs can be made more interpretable with statistical methods.
problem FNNs lack interpretability and are often used as black-box models.
method Supplement FNNs with statistical inference and covariate-effect visualizations.
result FNNs can be made more like traditional statistical models.
We have developed a statistical technique to test the model assumption of binary regime switching extension of the geometric Brownian motion (GBM) model by proposing a new discriminating statistics. Given a time series data, we have identified an admissible class of the regime switching candidate models for the statist…
Breiman discusses two statistical cultures, advocating for more research on 'before' and 'after' the black box.
problem Statistical modeling lacks exploration of processes before and after the 'black box'.
method Analyzes Breiman's visual metaphor of two statistical cultures.
result Promotes the importance of studying the 'before' and 'after' of data transformations.
Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity. An alternative approach, mainly studied in the statistical physics literature, is the study of generalization in simple synthetic-data models. Here we discuss the c…
Noise Sensitivity Exponent controls statistical-computational gaps in learning.
problem Understanding when learning is statistically possible yet computationally hard in high-dimensional statistics.
method Investigating statistical-computational gaps in single- and multi-index models using Noise Sensitivity Exponent.
result Noise Sensitivity Exponent governs statistical-computational gaps in high-dimensional learning.
A quantum circuit designed for efficient statistical model preparation and training.
problem Challenges in preparing and learning statistical models on quantum processors.
method Utilizes the maximum entropy principle to design a statistics-informed parameterized quantum circuit (SI-PQC).
result Improves trainability and interpretability for learning quantum states and classical model parameters.
Research aims to bridge statistical learning to causal models in AI.
problem Challenges in machine learning and AI related to causality.
method Transition from statistical learning to causal models.
result Progress in AI may require advances in causal modeling.
Efficiently learns Ising model parameters with limited statistics.
problem Learning Ising model parameters with limited sample configurations.
method Examines trade-offs between computation and observation, using Ising model as example.
result Reconstructs model parameters with statistics up to order O(γ) for ℓ1 width γ. Bayesian approach controls FDR in high-dimensional models.
problem High-dimensional variable selection and inference.
method Adapted Mirror Statistic to Bayesian framework for FDR control.
result Effective FDR control without data splitting.
Statistical methods remain relevant for ODE inverse problems, especially with sparse data.
problem The relevance of statistical methods in the era of deep learning for ODE inverse problems.
method Employed physics-informed neural networks (PINN) and manifold-constrained Gaussian process inference (MAGI) to compare statistical and deep learning approaches.
result Statistically principled methods outperform deep learning models in tasks like parameter inference and trajectory reconstruction.
Survey of statistical queries and their applications.
problem Understanding statistical queries and their applications.
method Exploration of statistical queries model, definitions, and connections to learnability.
result Connections to learnability and applications in optimization, evolvability, and differential privacy.
This guide explains statistical distances for evaluating generative models.
problem Evaluating the quality of samples from generative models.
method Four statistical distances: SW, C2ST, MMD, FID.
result Different distances can yield varying results on similar data.
We define and study the statistical models in exponential family form whose sufficient statistics are the degree distributions and the bi-degree distributions of undirected labelled simple graphs. Graphs that are constrained by the joint degree distributions are called dK-graphs in the computer science literature and…
Paper uses SLT to improve model selection for SHM.
problem Model selection for SHM using data-based systems.
method Utilizes Statistical Learning Theory to rigorously estimate generalisation.
result Incorporating domain knowledge improves model generalisation.
Study shows computational and statistical gaps in Gaussian Single-Index Models.
problem Statistical and computational trade-offs in high-dimensional regression problems.
method Analysis of SQ and LDP frameworks, partial-trace algorithm.
result Computational algorithms require significantly more samples than information-theoretic limits.
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are collected at an ever-growing scale, statistical machine learning faces some new cha…
DPpack offers R tools for private data analysis and machine learning.
problem Ensuring privacy in statistical analysis and machine learning.
method Differential privacy mechanisms (Laplace, Gaussian, exponential).
result User-friendly implementation of privacy-preserving models.
This paper mainly contributes to a classification of statistical Einstein manifolds, namely statistical manifolds at the same time are Einstein manifolds. A statistical manifold is a Riemannian manifold, each of whose points is a probability distribution. With the Fisher information metric as a Riemannian metric, infor…
Flexible framework for deep distributional regression models.
problem Learning conditional distributions from semi-structured data.
method Combines additive regression models with deep networks using TensorFlow.
result State-of-the-art predictive performance with interpretability.
Diffusion models learn simple statistics before complex ones, revealing a sample complexity exponent.
problem Understanding the learning dynamics of diffusion models.
method Empirical observations and theoretical analysis of diffusion models and denoisers.
result Diffusion models learn simple statistics (pair-wise correlations) at linear sample complexity, while higher-order statistics (e.g., fourth cumulant) require cubic sample complexity.
New DP EM algorithm with statistical guarantees for mixture models.
problem Preserving privacy in EM algorithms for mixture models.
method Proposed a DP EM algorithm with statistical guarantees.
result Near optimal estimation error for GMM in DP model.
Establishes statistical and computational bounds for influence diagnostics.
problem Identifying influential datapoints or subsets in machine learning models.
method Finite-sample statistical bounds and computational complexity for influence functions and approximate maximum influence perturbations.
result Established statistical and computational guarantees for influence diagnostics.
New statistical factors improve portfolio risk estimation.
problem Improving estimation of portfolio risk using new statistical factors.
method Matrix factor models and statistical methods (partial F test, double selection LASSO).
result New statistical factors add explanatory power in asset pricing.
The paper analyzes statistical guarantees for denoising reflected diffusion models.
problem The mismatch between theoretical design and implementation of diffusion models introduces issues in high-dimensional target data.
method The paper uses a reflected diffusion process as the driver of noise and establishes rates of convergence in total variation.
result The statistical guarantees for denoising reflected diffusion models match the minimax lower bound up to a polylogarithmic factor.
Generative models are reinterpreted in statistical terms, enabling better understanding and inference.
problem Insufficient interpretability of generative models in statistical terms.
method Flow matching and orthogonalization/cross-fitting in double/debiased machine learning.
result Generative models can be used to estimate nuisance components while maintaining inferential validity.
Statistical models outperform mechanistic models in short-term COVID-19 incidence forecasts.
problem Comparing accuracy of mechanistic vs statistical models for short-term COVID-19 incidence forecasts.
method Empirical comparison of forecasts from mechanistic and statistical models using daily incidence data from six US states.
result Statistical models are at least as accurate as mechanistic models and better capture volatility.
The paper evaluates variational auto-encoders using model criticism methods.
problem Evaluating the quality of variational auto-encoders (VAEs).
method Statistical model criticism, focusing on reproducing statistics of unknown data generating processes.
result The proposed framework offers possibilities for model selection beyond intrinsic metrics.
In this note we prove certain necessary and sufficient conditions for the existence of an embedding of statistical manifolds. In particular, we prove that any compact smooth (C1 resp.) statistical manifold can be embedded into the space of probability measures on a finite set. As a result, we get an answer to the La…
A new statistical model uses Orlicz-Sobolev spaces with Gaussian weight.
problem Statistical modeling of infinite-dimensional probability measures.
method Affine statistical bundle on Gaussian Orlicz-Sobolev space.
result Provides tools for solving infinite-dimensional evolution problems.