Neuroimaging research has predominantly drawn conclusions based on classical statistics, including null-hypothesis testing, t-tests, and ANOVA. Throughout recent years, statistical learning methods enjoy increasing popularity, including cross-validation, pattern classification, and sparsity-inducing regression. These t…
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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48 results for “classical statistics”
Paper compares neural networks and classical statistics for dementia prediction, highlighting interpretability of classical methods.
problem Tackles the challenge of interpreting risk factors for dementia prediction.
method Compares neural networks and classical statistics for dementia prediction.
result Classical statistics provide clearer interpretation of risk factors compared to neural networks.
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.
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.
The paper explores quantum statistical manifolds and their autoparallelity, providing estimation-theoretical characterizations.
problem Quantum statistical manifolds and their geometric properties.
method Study of autoparallelity w.r.t. the e-connection, using quantum estimation theory.
result Characterizations of e-autoparallel submanifolds as statistical models with efficient estimators.
Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of embedded samples produced by classical multidimensional scaling. This lays the foundati…
We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore we obtain some conditions for a lightlike submanifold of indefinite…
The Yukawa term in statistical mechanics quantifies information generation.
problem Understanding information generation in statistical mechanics.
method Defining a statistical product and Yukawa term to quantify information generation.
result The Yukawa term diverges in the quantum case, indicating Bose-Einstein condensation.
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.
SAR evaluates ML-based linear regression models for statistical significance.
problem Lack of formal statistical significance in ML-based regression models.
method Statistical Agnostic Regression (SAR) using concentration inequalities and worst-case scenario analysis.
result SAR provides a threshold for statistical significance without assuming underlying assumptions.
Improved estimator reduces bias in statistical learning models.
problem Asymptotic bias in classic WDRO estimator.
method Adjusted Wasserstein distributionally robust estimator.
result Asymptotic unbiased estimator with smaller MSE.
Semi-Supervised U-statisticsmath.ST
Enhances U-statistics for semi-supervised datasets using unlabeled data.
problem Efficiently utilizing unlabeled data in semi-supervised settings.
method Semi-supervised U-statistics enhanced by unlabeled data.
result Proposed method is asymptotically Normal and more efficient than classical U-statistics.
New flexible confidence sequences for robust statistical inference.
problem Creating robust statistical inference methods that work under mild assumptions.
method Proposed a new class of asymptotic time-uniform confidence sequences.
result Sharp asymptotic time-uniform confidence sequences achieved under mild assumptions.
Improved MoM estimator enhances classical shadows protocol for quantum measurements.
problem Efficient estimation of expectation values with reduced measurement shots.
method Modified median-of-means estimator with optimal constants and U-statistics.
result Improved performance of modified estimator for Clifford measurements.
Paper tightens statistical aggregation results using local complexity.
problem Combining predictors to achieve nearly optimal predictions.
method Replacing global complexity with local complexity, using PAC-Bayes localization.
result Localized versions of classical aggregation bounds proven, improving previous results.
Modern ML methods show unexpected behaviors that contradict classical statistics.
problem Modern machine learning methods exhibit behaviors at odds with classical statistical intuitions.
method Comparison between fixed and random design settings in ML and statistics.
result Moving from fixed to random designs reveals new insights into bias-variance tradeoffs and overfitting.
Quantum learning complexity reviewed using information theory.
problem Learning properties of quantum systems or processing data via quantum computing.
method Information-theoretic techniques focusing on data, copy, and model complexity.
result Copy complexity due to irreversible quantum measurements limits information extraction.
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.
We introduce RSE to measure robustness in estimation problems.
problem Estimating statistical models from observed data.
method Developed theory for spectral functions of measures to compute RSE.
result RSE reveals a reciprocal relationship with problem complexity.
Global EQG sums boundary states over manifold diffeomorphism classes.
problem Summing boundary states over manifold diffeomorphism classes.
method Formulated as classical statistical physics, weights determined by general principles.
result Hartle-Hawking state as a probability measure.
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for financial market than the classical one. A part of our analysis is devoted to study t…
Simple methods combine statistical tests for out-of-distribution detection.
problem Detecting data points not following the training distribution.
method Combining classical parametric tests (Rao's score test) and a typicality test.
result Combining Fisher's method of test statistics improves out-of-distribution detection accuracy.
This paper develops dimension-agnostic inference methods for high-dimensional data.
problem Understanding how classical inference methods behave in high-dimensional settings.
method Using variational representations, sample splitting, and self-normalization to create a refined test statistic.
result The resulting statistic has a Gaussian limiting distribution regardless of how dimensionality scales with sample size.
Sketched Ridge Regression: Optimization Perspective, Statistical Perspective, and Model Averagingstat.ML
We address the statistical and optimization impacts of the classical sketch and Hessian sketch used to approximately solve the Matrix Ridge Regression (MRR) problem. Prior research has quantified the effects of classical sketch on the strictly simpler least squares regression (LSR) problem. We establish that classical …
Statistical Estimation in the Spiked Tensor Model via the Quantum Approximate Optimization Algorithmquant-ph
QAOA matches classical tensor power iteration in spiked tensor model recovery.
problem Statistical estimation in spiked tensor model with computational gap.
method Analysis of QAOA performance on spiked tensor model.
result QAOA weak recovery threshold matches tensor power iteration.
A Frequentist Statistical Introduction to Variational Inference, Autoencoders, and Diffusion Modelsstat.ML
This paper bridges statistical and machine learning approaches to variational inference.
problem Statisticians struggle to understand variational inference from a Frequentist perspective.
method Explains VI, VAEs, and DDMs from a Frequentist viewpoint, starting with EM.
result VI emerges as a scalable solution for intractable E-steps in VAEs and DDMs.
Geometry of hypersurfaces defined by the relation which generalizes classical formula for free energy in terms of microstates is studied. Induced metric, Riemann curvature tensor, Gauss-Kronecker curvature and associated entropy are calculated. Special class of ideal statistical hypersurfaces is analyzed in details. No…
Fundamentals of Regressionstat.ML
This chapter reviews classic regression methods and their evolution to physics-informed approaches.
problem Finding relationships between variables using regression.
method Introduces traditional and physics-informed regression methods, linking them to computational science.
result Regression methods have evolved from purely statistical to incorporating physical knowledge.
We study the fundamental tradeoffs between computational tractability and statistical accuracy for a general family of hypothesis testing problems with combinatorial structures. Based upon an oracle model of computation, which captures the interactions between algorithms and data, we establish a general lower bound tha…
New measures generalize existing ones, linking information and risk.
problem Linking information measures and risk in statistical decision problems.
method Introducing new families of divergence measures and deriving an information processing equality.
result Extension of variational -divergence representation to multiple distributions.
New method improves statistical inference using machine learning-imputed data.
problem Improving statistical inference with imputed data from machine learning.
method Two-phase sampling approach for Z-estimation with ML-imputed outcomes.
result Guaranteed efficiency matching or exceeding classical inference, regardless of prediction quality.
Develops a goodness-of-fit test for self-exciting processes.
problem Quantifying how well generative models capture self-exciting point processes.
method Connects to Quasi-maximum-likelihood estimator (QMLE) theory and develops a non-parametric self-normalizing statistic, the Generalized Score (GS) statistics.
result Validates the proposed GS test's good performance through numerical simulation and real-data experiments.
The paper tackles statistical and computational challenges in learning correlated reward models.
problem The Independence of Irrelevant Alternatives (IIA) assumption collapses human preferences into a universal utility function, leading to coarse approximations.
method The paper investigates the statistical and computational challenges of learning a correlated probit model using best-of-three preference data.
result Best-of-three preference data overcomes the limitations of pairwise preference data, allowing for more fine-grained modeling of human preferences.
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.
New statistical test for change-point detection using relative entropy.
problem Offline change-point detection using divergence metrics.
method Study of empirical relative entropy distributions, derivation of approximations, introduction of new Berry-Esseen bounds.
result Theoretical and practical validation of relative entropy for change-point detection.
New bandit algorithms focus on extreme values, outperforming existing methods.
problem Optimizing decisions based on extreme values rather than expected values.
method Robust statistics-based algorithms with vanishing extremal regret.
result The proposed algorithms achieve superior performance compared to existing methods.
Statistical boosting algorithms have triggered a lot of research during the last decade. They combine a powerful machine-learning approach with classical statistical modelling, offering various practical advantages like automated variable selection and implicit regularization of effect estimates. They are extremely fle…
The Cost of Privacy: Optimal Rates of Convergence for Parameter Estimation with Differential Privacystat.ML
Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between statistical accuracy and privacy in mean estimation and linear regression, under both the …
We present a novel method for frequentist statistical inference in -estimation problems, based on stochastic gradient descent (SGD) with a fixed step size: we demonstrate that the average of such SGD sequences can be used for statistical inference, after proper scaling. An intuitive analysis using the Ornstein-Uhlen…
Unified framework for singular statistical models using observable charts.
problem Non-identifiability and breakdown of classical asymptotic theory in singular models.
method Invariant framework based on observable charts to define local coordinate systems in model space.
result Observable order provides a lower bound on KL divergence vanishing rate in singular models.
Deep learning's success is puzzling from a statistical perspective.
problem Deep learning's success is puzzling from a statistical perspective.
method Physics-informed investigation of deep learning features and surprises.
result Neural scaling laws and their interplay with inductive biases.
Study minimax robustness in statistical estimation under Wasserstein contamination.
problem Adversarial perturbations in statistical data.
method Developed minimax theory for losses under Wasserstein- contaminations.
result Exact minimax risk identified for joint contaminations in location estimation and prediction in linear regression.
The paper uses statistics to improve the explainability of models.
problem Subjective human assessment of explanations and lack of theoretical guarantees.
method Leveraging statistical estimators for proper definition and evaluation of explanations.
result Statistical tools provide theoretical guarantees and evaluation metrics for explanations.
U-statistics improve gradient estimation in importance-weighted variational inference.
problem High variance in gradient estimation for importance-weighted variational inference.
method Use U-statistics to average base gradient estimators on overlapping batches of size m, achieving lower variance.
result U-statistic variance reduction leads to modest to significant improvements in inference performance.
Researchers study the geometric properties of a specific type of stable processes.
problem Understanding the information geometry of tempered stable processes.
method Derivation of α-divergence, Fisher information matrices, and α-connections.
result Obtained Fisher information matrices and α-connections for statistical manifolds.
The modal age of Statisticsstat.ME
Recently, a number of statistical problems have found an unexpected solution by inspecting them through a "modal point of view". These include classical tasks such as clustering or regression. This has led to a renewed interest in estimation and inference for the mode. This paper offers an extensive survey of the tradi…
Topology of Currencies: Persistent Homology for FX Co-movements: A Comparative Clustering Studystat.ML
TDA improves FX clustering quality over traditional methods.
problem Capturing complex currency co-movements in FX markets.
method Topological Data Analysis (TDA) compared to traditional statistical methods on monthly FX returns.
result TDA-based clustering yields more compact and well-separated clusters.
Information geometry offers new tools for statistical analysis.
problem Statistical analysis of probability distributions.
method Geometric perspective on statistical manifolds.
result New applications in radar sensing, signal processing, etc.