New method relaxes TV distance for two-sample testing without distributional assumptions.
problem Challenges in certifying equality or providing tight bounds on TV distance for two distributions.
method Examined blurred total variation distance, a relaxation of TV distance.
result Provided theoretical guarantees for upper and lower bounds on blurred TV distance.
Unified theoretical guarantees for distribution-free changepoint detection and testing.
problem Distribution-free changepoint inference with finite-sample validity and consistency.
method Distribution-free changepoint localization using conformal p-values with theoretical guarantees.
result Unified distribution-free guarantees for changepoint detection, localization, and testing.
New tests for binary classification regression functions without distribution assumptions.
problem Testing regression functions in binary classification without distributional assumptions.
method Conditional kernel mean embeddings and resampling-based framework.
result Distribution-free hypothesis tests with exact type I error control.
The paper develops distribution-free methods for ordinal classification.
problem Constructing valid prediction sets for ordinal classification problems.
method Leveraging conformal prediction and multiple testing with FWER control.
result The proposed methods achieve satisfactory levels of marginal and class-specific conditional coverages.
The paper reviews exchangeability and its implications for conformal prediction and rank tests.
problem Ensuring distribution-free predictive inference in machine learning and statistics.
method Explains exchangeability and its role in conformal prediction and rank tests.
result Discovers similarities between conformal prediction and rank tests based on exchangeability.
This paper offers a distribution-free method for post-detection changepoint localization.
problem Locating the exact time of a change in distribution after a sequential detection procedure.
method A distribution-free framework using conformal test martingales for sequential change detection and post-detection inference.
result Valid post-detection coverage guarantees and non-asymptotic bounds on confidence set size.
Study on continuous sequence classification with distribution uncertainty.
problem Classifying continuous sequences with varying distribution uncertainty.
method Proposes distribution-free tests for three test designs: fixed-length, sequential, and two-phase tests.
result Error probabilities decay exponentially fast for all test designs.
We review the main "omnibus procedures" for goodness-of-fit testing for copulas: tests based on the empirical copula process, on probability integral transformations, on Kendall's dependence function, etc, and some corresponding reductions of dimension techniques. The problems of finding asymptotic distribution-free te…
High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to possess various desirable properties along with a characteristic exploratory fl…
Improved change point detection using matched filters for non-parametric tests.
problem False positives and localization ambiguity in non-parametric two-sample tests.
method Derived and applied matched filters for various two-sample tests.
result Matched filters reduce false positives and improve test precision.
FactTest assesses LLM factuality with Type I error control.
problem Lack of rigorous factuality verification for LLMs.
method Formulates factuality testing as hypothesis testing, ensuring Type I and II error control.
result Improves model accuracy by over 40% in abstaining from unknown questions.
Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has not been fully investigated by means of statistical procedures. In this work a di…
We provide a distribution-free test that can be used to determine whether any two joint distributions p and q are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we rely on joint kernel distribution embedding to extend the kernel two-sample test…
This paper develops methods for obtaining distribution-free prediction regions for invariant representations.
problem Distributional shifts in machine learning models.
method Invariant risk minimization and weighted conformity scores.
result Proves the effectiveness of adaptive conformal intervals for uncertainty estimation.
Book teaches conformal prediction for complex machine learning systems.
problem Formal guarantees for machine learning prediction sets.
method Permutation tests and exchangeability for distribution-free inference.
result Provides formal, finite-sample guarantees for machine learning.
Study three types of uncertainty quantification for binary classification without distributional assumptions.
problem Uncertainty quantification for binary classification in a distribution-free setting.
method Established theorems connecting calibration, confidence intervals, and prediction sets for score-based classifiers.
result Distribution-free calibration is only possible using scoring functions that partition feature space into countably many sets.
The paper explores how over-parameterized linear regression models generalize without violating learning theory principles.
problem Understanding how over-parameterized linear regression models generalize without violating learning theory principles.
method The paper uses the predictive normalized maximum likelihood (pNML) learner to investigate the minimum norm solution of over-parameterized linear regression models.
result The model generalizes well when the test sample lies in a subspace spanned by eigenvectors associated with large eigenvalues of the training data.
Enhances scenario approach for certifying design properties post-design.
problem Certifying additional useful properties in designs not considered during the design phase.
method Two-level framework of appropriateness: baseline and post-design. Distribution-free upper bounds on risk derived.
result Distribution-free upper bounds on the risk of failing to meet post-design appropriateness.
The paper develops robust tests for detecting independence in synchronous stochastic systems with finite sample guarantees.
problem Detecting independence in synchronous stochastic systems with finite sample guarantees.
method Combines confidence region estimates with permutation tests and dependence measures to detect nonlinear dependence.
result Consistent hypothesis tests for detecting independence under mild assumptions.
Paper proposes a new framework for combining investment strategies without market-specific assumptions.
problem Lack of a distribution-free and consistent preference framework for decision-making in combining investment strategies.
method Introduces a novel framework for decision-making in combining strategies, free from market conditions and statistical assumptions.
result Proposed strategies outperform individual component strategies in long-term wealth accumulation, with small tradeoffs in Sharpe ratios.
E-values enhance conformal prediction methods.
problem Distribution-free uncertainty quantification.
method Reformulation of conformal prediction using e-values.
result E-values offer new theoretical and practical capabilities.
We revisit the Kolmogorov-Smirnov and Cramér-von Mises goodness-of-fit (GoF) tests and propose a generalisation to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the "effective" number of independent observations. The generalised GoF tests are not…
Locus scores predictions for risk, reducing large-loss events.
problem Deployment cost from inaccurate predictions, especially large losses.
method Distribution-free loss-scale reliability score using any predictive distribution.
result Reduces large-loss frequency compared to standard heuristics.
Characterizes distribution-free rates in unbalanced classification problems.
problem Minimizing error under two different distributions in unbalanced settings.
method Characterizes minimax rates over all pairs of distributions using a geometric condition.
result Identifies a dichotomy between hard and easy classes based on a three-points-separation condition.
The paper proposes a method for distribution-free prediction sets that adapt to unknown temporal changes.
problem Distribution-free prediction sets require reliable calibration data, which is often unavailable in real-world settings with temporal changes.
method The method selects an adaptive window to construct prediction sets, optimizing a bias-variance tradeoff.
result The method provides sharp coverage guarantees and is shown to be adaptive to temporal drift through numerical experiments.
This work examines fundamental limits in model falsification without assuming specific distributions.
problem Establishing lower bounds on model class risk in distribution-free settings.
method Model-agnostic fundamental hardness result for constructing lower bounds on test error.
result No positive lower bound on model class risk is possible in certain settings.
This paper develops a method for estimating animal motion submanifolds using distribution-free learning.
problem Estimating submanifold models of animal motion supported on a configuration manifold.
method Formulates a novel method based on distribution-free learning over the manifold of measurements.
result Derives approximations of the unknown mapping that converge with rates dependent on sample size and dimensionality.
The paper tackles uncertainty quantification for classification under label shift without assuming i.i.d. data.
problem Uncertainty quantification for classification under label shift in non-i.i.d. settings.
method The paper uses conformal prediction and post-hoc binning for distribution-free UQ, and reweights these methods for label shift.
result The reweighted methods improve UQ performance under label shift, preserving coverage and calibration.
Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being intelligently desi…
A new test method improves goodness-of-fit tests for copulas.
problem Developing robust tests for copula goodness-of-fit.
method Binary Expansion Approximation of UniformiTY (BEAUTY) and Binary Expansion Adaptive Symmetry Test (BEAST).
result The BEAST method improves empirical power against various alternatives.
The paper provides high-probability bounds on false discovery proportions in conformal inference.
problem Existing methods fail to provide high-probability bounds on the realized false discovery proportion.
method Constructing a high-probability envelope for the empirical distribution function of null conformal p-values by sampling from their joint distribution.
result Establishes finite-sample, distribution-free upper bounds on the FDP that hold simultaneously over all possible rejection thresholds.
FedFaiREE addresses fairness in decentralized learning with small samples.
problem Ensuring fairness in decentralized federated learning with limited data.
method FedFaiREE is a post-processing algorithm for distribution-free fair learning in decentralized settings with small samples.
result FedFaiREE provides theoretical guarantees for both fairness and accuracy in decentralized environments.
We develop an online learning method for prediction, which is important in problems with large and/or streaming data sets. We formulate the learning approach using a covariance-fitting methodology, and show that the resulting predictor has desirable computational and distribution-free properties: It is implemented onli…
Wide class of elliptically contoured distributions is a popular model of stock returns distribution. However the important question of adequacy of the model is open. There are some results which reject and approve such model. Such results are obtained by testing some properties of elliptical model for each pair of stoc…
Researchers define quantiles on Riemannian manifolds using optimal transport.
problem Defining quantiles on nonlinear manifolds.
method Measure-transportation-based approach.
result Theoretical and empirical properties of quantile functions on manifolds.
This research designs a data-driven partition to test independence between continuous variables.
problem Testing independence between continuous random variables.
method Empirical log-likelihood statistic and data-driven tree-structured partition.
result Strongly consistent test of independence over probability families.
Large language models can't efficiently reason conditionally in a distribution-free setting.
problem Impossibility of conditional PAC-efficient reasoning in large language models.
method Proof of impossibility in a distribution-free setting for non-atomic input spaces.
result Any algorithm achieving conditional PAC efficiency must defer to the expert model with high probability.
New GoF test improves change point detection in multivariate time series.
problem Detecting changes in multivariate time series data efficiently and robustly.
method Developed a novel multivariate rank-energy GoF test (sRE) for change point detection.
result sRE-based CPD outperforms existing methods in AUC and F1-score.
Valid p-value for bounded random variables without distributional assumptions.
problem Calibration of predictive algorithms in a distribution-free setting.
method Built a super-uniform p-value based on a concentration inequality.
result Super-uniform p-value is tighter than existing alternatives.
Study robustness of split conformal prediction under adversarial attacks.
problem Ensuring distribution-free coverage guarantees in CP under adversarial conditions.
method Theoretical analysis and extensive experiments on split conformal prediction robustness.
result Prediction coverage varies with calibration-time attack strength, enabling control over coverage under adversarial tests.
New algorithm for precise changepoint localization without assumptions.
problem Offline changepoint localization in arbitrary distributions.
method Distribution-free algorithm CONformal CHangepoint localization (CONCH) using exchangeability arguments.
result Derives principled score functions for informative and small confidence sets with normalized length shrinking to zero.
Study robust linear regression without distributional assumptions for heavy-tailed responses.
problem Linear regression with heavy-tailed responses and no distributional assumptions.
method Combining truncated least squares, median-of-means, and aggregation theory to construct a non-linear estimator.
result Achieves excess risk of order d/n with optimal sub-exponential tail. A new method reduces computational costs for testing RF variable importance measures.
problem Testing variable importance measures from random forests is computationally expensive and challenging.
method Sequential permutation testing and sequential p-value estimation to reduce computational costs.
result Theoretical properties of sequential tests are confirmed, maintaining type-I error and high power.
Validates network bootstraps for uncertainty quantification in network visualisation.
problem Quantifying uncertainty in network embeddings when only a single observation is available.
method Statistical indistinguishable embeddings using k-nearest neighbour smoothing, validated by an exchangeable network test.
result Proposes a principled, distribution-free network bootstrap that passes the exchangeable network test.
The paper offers a method to create prediction sets with uncertainty control.
problem Calibrating and communicating uncertainty in machine learning predictions.
method Distribution-free, risk-controlling prediction sets using a holdout set to calibrate set sizes.
result Explicit finite-sample guarantees for error control in various machine learning tasks.
New algorithm learns disjunctions faster than previous methods.
problem Learning Boolean disjunctions in the agnostic PAC model.
method Developed an agnostic learner with complexity 2ildeO(n1/3). result First separation between SQ and CSQ models in distribution-free agnostic learning.
Conformal prediction provides distribution-free uncertainty quantification for black-box models.
problem Uncertainty quantification for high-risk machine learning applications.
method Conformal prediction creates valid uncertainty sets without distributional assumptions.
result Sets contain the ground truth with a specified probability, e.g., 90%.
New test ensures quality of shared data in machine learning.
problem Ensuring quality of external data in machine learning tasks.
method Distribution-free two-sample testing procedures grounded in conformal outlier detection.
result Identifies valuable external data agents for model personalization.