Deep learning used for parameter estimation in hard-to-infer models.
problem Parameter estimation in intractable models like max-stable processes.
method Train deep neural networks on simulated data to estimate parameters.
result Deep learning provides accurate and faster parameter estimation.
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.
EFI automates statistical inference for big data.
problem Statistical inference for model parameters based on observations.
method EFI uses stochastic gradient Markov chain Monte Carlo and sparse deep neural networks.
result EFI provides higher fidelity in parameter estimation and automates the inference process.
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for long time horizons, however, averages over the time-dependent parameters. To model…
Proposes a new measure to evaluate stability of statistical parameters under distributional shifts.
problem Difficulty in transferring knowledge across data sets due to distributional changes.
method Introduces a measure of instability quantifying sensitivity of statistical parameters to Kullback-Leibler divergence and directional shifts.
result The proposed measure can elucidate the type of shifts a parameter is sensitive to and improve estimation accuracy under shifted distributions.
Develops methods for estimating constrained function-valued parameters in infinite-dimensional models.
problem Estimating function-valued parameters with structural constraints in complex models.
method Characterizes constrained solutions as minimizers of penalized population risk, using a Lagrange-type formulation and path through unconstrained space.
result Proposes estimators that achieve optimal risk and constraint satisfaction, applicable across various statistical learning approaches.
Responds to critiques on tests for causal parameter confidence intervals.
problem Testing nominal confidence interval coverage for causal parameters estimated by machine learning.
method Rejoinder to critiques on nearly assumption-free tests.
result Clarifies and supports the original research's approach.
KIPLMC methods improve statistical inference in latent variable models.
problem Statistical inference in latent variable models.
method Joint diffusion process in parameter and latent variable spaces, with two explicit discretizations.
result KIPLMC methods achieve accelerated convergence rates in Wasserstein-2 distance.
Extends JKO scheme for iterative algorithms with unknown parameters.
problem Computational and statistical analysis of iterative algorithms with unknown parameters.
method Develops statistical methods to estimate unknown parameters and adapts JKO scheme.
result Establishes asymptotic theory for the statistical JKO scheme.
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.
A new Weyl prior is proposed for Bayesian statistics, offering a more canonical choice for parameter α.
problem Choosing a prior distribution for Bayesian inference.
method Proposed a new Weyl prior based on the Weyl structure on a statistical manifold.
result The Weyl prior is a special case of the α-parallel prior with α = -n, where n is the dimension of the statistical manifold.
Method estimates parameters for disease spread models robustly.
problem Estimating parameters for disease spread models.
method Statistical Learning applied to Approximate Bayesian Computation.
result Qualitative properties of disease evolution can be assessed.
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. Develops black-box methods to estimate parameters of complex models.
problem Lack of efficient methods to produce simulations for complex statistical models.
method Pre-training deep neural networks on extensive simulated databases for well-structured likelihoods. Iterative algorithm for other complex dependencies.
result Successfully estimates and quantifies uncertainty of parameters from non-Gaussian models.
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…
The paper provides a statistical decision-theoretical derivation of the Two-Stage approach for parameter estimation.
problem Theoretical justification for the Two-Stage approach in situations where likelihood is difficult to evaluate.
method Statistical decision-theoretical derivation leading to Bayesian and Minimax estimators.
result The Two-Stage approach is justified theoretically and applied to independent and identically distributed samples.
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.
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…
Develops a new asymptotic efficiency theory for non-Euclidean parameter spaces.
problem Lack of a unified efficiency theory for non-Euclidean parameter spaces.
method Introduces a new theory for Riemannian manifolds with regularity conditions.
result Establishes efficiency bounds for non-Euclidean parameter spaces.
The paper proposes using Autoencoders to learn summary statistics for Bayesian inference.
problem Approximating posterior distributions for models with intractable likelihood functions.
method Using Autoencoders to extract summary statistics that retain parameter information and cancel noise.
result The approach effectively learns summary statistics that improve posterior approximation.
Dual Bayesian Affine Estimators for Wiener-type state-space models
problem Estimating parameters in Wiener-type state-space models
method Fixed-point architecture combining two affine estimators
result Dual basis-parameter estimator achieves comparable parameter MSE to purely affine estimator
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.
New formulae identify discrete probability laws without needing normalization constants.
problem Characterizing non-normalized discrete probability distributions.
method Derive explicit formulae for mass functions using Stein's method.
result Developed tools for solving statistical problems without normalization constants.
Paper analyzes consistency of Bayesian and machine learning methods for hierarchical parameter estimation.
problem Learning hierarchical parameters in complex and real-world problems.
method Empirical Bayes and Kernel Flow approaches.
result Consistency results for Matérn-like model on the torus, and comparison of algorithms.
Paper studies PSGD for constrained optimization problems and its statistical properties.
problem Online inference for constrained optimization problems.
method Stochastic gradient descent with projection (PSGD) for constrained optimization.
result Limiting distribution of PSGD-based estimates under linear-equality constraints.
Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying uncertainty, called predictive-matching Generative Parameter Sampler (GPS). This procedure …
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.
Transformer improves parameter estimation without needing closed-form solutions.
problem Parameter estimation in statistics, especially for complex distributions.
method Transformer-based approach for parameter estimation without closed-form solutions or derivations.
result Transformer-based approach achieves similar or better accuracy than maximum likelihood estimation.
Flexible multi-task learning framework using summary statistics.
problem Data-sharing constraints in healthcare settings.
method Proposes a flexible multi-task learning framework utilizing summary statistics and adaptive parameter selection.
result Systematic non-asymptotic analysis and simulations demonstrate the method's performance.
Complex computer simulations are commonly required for accurate data modelling in many scientific disciplines, making statistical inference challenging due to the intractability of the likelihood evaluation for the observed data. Furthermore, sometimes one is interested on inference drawn over a subset of the generativ…
Paper proposes a statistical test for transfer learning in linear regression.
problem Theoretical framework for parameter transfer in linear regression.
method Developed a statistical test to predict transfer quality.
result The test can predict if a fine-tuned model has lower prediction risk.
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from…
Paper introduces a new gradient statistic to improve deep learning convergence.
problem Fluctuation effect of gradient updates between iterations.
method Introduces an unbiased stratified statistic \(\bar{G}_{mst}\) and a new algorithm MSSG.
result MSSG algorithm outperforms other sgd-like algorithms in training deep models.
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estima…
New method estimates model parameters from incomplete data.
problem Estimating model parameters from incomplete data.
method Variational Gibbs Inference (VGI)
result Competitive or better performance compared to existing methods.
Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov regularisation parameter from noisy data. In this work, we improve their results and ext…
A new framework bridges classical and machine learning methods for reliable inference from complex models.
problem Intractable likelihood functions in complex systems make classical statistics ineffective for likelihood-free inference.
method Likelihood-Free Frequentist Inference (LF2I) framework that combines classical statistics and machine learning.
result Valid confidence sets with near finite-sample validity can be constructed for any parameter value.
New findings challenge the traditional U-shaped curve of model complexity and error, revealing a second descent in error as model size increases.
problem The traditional U-shaped curve of model complexity and prediction error is incomplete, with recent work suggesting a second descent in error as model size increases.
method Careful consideration of multiple complexity axes and a nonparametric statistics perspective were used to interpret the observed double descent curves.
result The observed double descent curves in classical statistical machine learning methods fold back into traditional convex shapes, resolving tensions with statistical intuition.
New quantum states capture more information, enabling advanced processing tasks.
problem Quantum information processing challenges with limited statistical information.
method Introducing Random-Coefficient Pure States (RCPS) and exploiting their higher-order statistics.
result RCPS provide richer information than density operators, enabling new quantum tasks.
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.
The paper introduces a method to incorporate expert opinion on observable quantities into statistical models.
problem Tackling the challenge of integrating expert knowledge on observable quantities into statistical models.
method The approach involves updating a prior belief using a loss function that reflects expert opinion on observable quantities.
result The method allows for a flexible specification of expert opinion and is straightforward to implement.
We investigate a generic problem of learning pairwise exponential family graphical models with pairwise sufficient statistics defined by a global mapping function, e.g., Mercer kernels. This subclass of pairwise graphical models allow us to flexibly capture complex interactions among variables beyond pairwise product. …
Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their asymmetric generalizations. Properties of these estimators depend on the choice of pena…
The paper improves asymmetric causality tests by addressing inefficiencies and statistical significance issues.
problem Inefficiencies and statistical significance issues in asymmetric causality tests.
method Improved asymmetric causality tests via partial cumulative sums for positive and negative components, explicitly testing differences between causal parameters.
result Efficiently tested hypotheses on asymmetric causal interaction between financial markets.
Method detects effects of synthesis parameters on plutonium oxide microstructure.
problem Detecting effects of synthesis parameters on material microstructure.
method Copula theory, high dimensional distribution distances, and permutational statistics.
result Effects of strike order and oxalic acid feed on plutonium oxide microstructure detected.
New framework recovers reward and rationality parameters from game behavior.
problem Statistical ambiguity in identifying reward and rationality parameters in competitive games.
method Blind Inverse Game Theory (Blind-IGT) using entropy-regularized Quantal Response Equilibrium and Normalized Least Squares (NLS) estimator.
result Optimal convergence rate of O(N−1/2) for joint parameter recovery. Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such as time series into a few informative, low-dimensional summary statistics. The qu…
Estimates matrix trace optimization with statistical learning theory.
problem Optimizing trace of parameter-dependent matrices.
method Monte Carlo estimator with bounds derived from epsilon nets and generic chaining.
result Predicts small sampling amount for matrices with small off-diagonal mass.