Proposes a more robust rating scale for banks.
problem Inconsistent rating scale validation leading to higher capital requirements.
method Develops a new rating scale that is statistically distinguishable and robust.
result Reduces the calibration probability of default, saving capital requirements.
Neural networks have achieved dramatic improvements in recent years and depict the state-of-the-art methods for many real-world tasks nowadays. One drawback is, however, that many of these models are overparameterized, which makes them both computationally and memory intensive. Furthermore, overparameterization can als…
Mathematical foundation for phylogenetic tree uncertainty quantification.
problem Uncertainty in evolutionary relationships between species.
method Introducing the Wald space as a subset of symmetric positive definite matrices, studying its topology and structure, and proposing a new numerical method for geodesics and curvature.
result Wald space has a topology of disjoint open cubes, is contractible, and is a Whitney stratified space of type (A).
Proves conditions for Cauchy horizons in low-regularity spacetimes.
problem Conditions for the existence of Cauchy horizons in spacetimes with low regularity.
method Analyzes the relationship between complete Cauchy hypersurfaces, almost closed causal curves, and points at infinity.
result Wald's conjecture reformulated as a PDE problem about Cauchy horizons.
Proposes a new phylogenetic tree space with biologically principled geometry.
problem Developing a space for statistical analysis of phylogenies with biologically informed assumptions.
method Introduces wald space, a new phylogenetic tree space, and two related geometries based on Fisher information and Gaussian processes.
result Geodesics in wald space are similar to those in the Fisher information geometry, but the two geometries are distinct.
Proposes a new test for validating multivariate dynamic regression models.
problem Inadequate exogeneity conditions for conventional model specification tests in dynamic systems.
method Develops a generalized Durbin estimator for multiple-equation systems with dynamic dependencies, and constructs Wald tests.
result Bootstrap-based Wald tests improve finite-sample size control and validate the null hypothesis in multifactor models.
Study GLS estimator properties in multivariate regression with heteroskedastic and autocorrelated errors.
problem Asymptotic properties of GLS estimator in multivariate regression with specific error structures.
method Derive Wald statistics for linear restrictions and assess their performance.
result Wald statistics remain robust to heteroskedasticity and autocorrelation.
This paper introduces a novel clustering algorithm for heteroscedastic Gaussian data without needing to know the number of clusters.
problem Clustering heteroscedastic Gaussian data without prior knowledge of the number of clusters.
method Introduces a novel cost function and fixed-point analysis to estimate centroids, introduces Wald kernel for measurement plausibility, and derives CENTRE-X algorithm.
result CENTRE-X algorithm can estimate centroids without prior knowledge of the number of clusters and performs comparably to standard algorithms K-means and Mean-Shift.
New private algorithm for sequential hypothesis testing with privacy and error rate guarantees.
problem Privacy protection in sequential hypothesis testing for sensitive data.
method Renyi differential privacy, Wald's Sequential Probability Ratio Test (SPRT).
result Private algorithm with strong privacy guarantees and theoretical performance analysis.
Bayesian UQ matches frequentist UQ for adaptively collected data.
problem Uncertainty quantification for adaptive data collection.
method Extends Bernstein-von Mises theorem to adaptively collected data.
result Bayesian UQ asymptotically matches Wald-type frequentist UQ.
Two tests identify heterogeneous components in distributed learning.
problem Identifying parameter heterogeneity in distributed learning with minimal data transmission.
method Two tests: Wald and Extreme Contrast (ECT).
result ECT avoids bias accumulation and is robust to varying levels of sparsity.
The paper develops a method for self-normalized inference in adaptive experiments.
problem Adaptive experiments require a fixed horizon for ATE estimation, but propensities can change.
method The method uses self-normalized martingale limit theory to estimate ATE.
result The Studentized statistic is asymptotically N(0,1) at the prespecified horizon.
We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons in Minkowski space.
Optimism stabilizes Thompson Sampling for adaptive inference in multi-armed bandits.
problem Subtle inferential properties of Thompson Sampling under adaptive data collection.
method Introduced optimism as a key mechanism to restore stability and validity of inference.
result Suitably implemented optimism stabilizes Thompson Sampling and enables asymptotically valid Wald inference.
The paper extends hypothesis testing to non-diagonalizable matrices, improving network statistics inference.
problem Testing on non-diagonalizable matrices for network statistics.
method Generalizes Wald and t-tests to non-symmetric matrices, controlling convergence rates.
result Improved inference on network statistics from directed networks.
New method predicts sets under unknown covariate shift with high confidence.
problem Adapting to unknown covariate shift in prediction sets.
method PredSet-1Step, a flexible distribution-free method.
result Achieves asymptotic probably approximately correct coverage.
Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less samples in average. For a binary detection problem, it is well known that for k…
The paper addresses uncertainty in demand prediction for dynamic pricing.
problem Uncertainty quantification in the demand function for dynamic pricing.
method Developed a debiased approach to construct accurate confidence intervals for the demand function.
result Asymptotic normality guarantee of the debiased estimator for the demand function.
For many causal effect parameters of interest, doubly robust machine learning (DRML) estimators ψ^1 are the state-of-the-art, incorporating the good prediction performance of machine learning; the decreased bias of doubly robust estimators; and the analytic tractability and bias reduction of sample splitting wi…
New method selects causal features from diverse data types.
problem Discovering causal relationships from non-continuous data types.
method Transformation-Model (TRAM) based Invariant Causal Prediction (TRAM-ICP) with TRAM-GCM and TRAM-Wald tests.
result Improved power and type I error control for diverse response types.
We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter family of initial data which has ordinary and scaled "point-particle" limits an…
Develops a method to estimate optimal policy value in online learning.
problem Challenges in evaluating ongoing policies in online learning environments.
method Doubly Robust Interval Estimation (DREAM) method.
result Valid inference on online conditional mean estimator with asymptotically normal distribution.
Unified framework for fair decision-making across diverse groups.
problem Statistical brittleness in fairness testing for small subgroups.
method Size-adaptive hypothesis testing framework.
result Validated approach for interpretable, statistically rigorous decisions.
This paper proposes a decorrelation-based approach to test hypotheses and construct confidence intervals for the low dimensional component of high dimensional proportional hazards models. Motivated by the geometric projection principle, we propose new decorrelated score, Wald and partial likelihood ratio statistics. Wi…
New KNN test improves association analysis of high-dimensional sequencing data.
problem Challenges in using neural networks for high-dimensional sequencing data analysis.
method Kernel-based neural network (KNN) test for complex association analysis.
result KNN test outperforms SKAT in detecting non-linear and interaction effects.
We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends one result of Friedrich, Rácz and Wald, which was limited to the interior of th…
A new algorithm reduces inference error in adaptive contextual bandits.
problem Challenges in statistical inference for adaptive contextual bandits.
method Proposes a regularized EXP4 algorithm that satisfies the Lai-Wei stability condition.
result Valid Wald-type confidence intervals for linear functionals can be achieved without the price of adaptivity.
Study revisits Bondi mass and discusses memory effect in polyhomogeneous spacetimes.
problem Analyzing the asymptotic behavior and memory effect in polyhomogeneous spacetimes.
method Revisits Bondi mass using Iyer-Wald formalism and discusses memory effect in vacuum polyhomogeneous spacetimes.
result The balance law remains unchanged in polyhomogeneous spacetimes with logarithmic terms.
We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function. We derive the population quantity that is the target of this estimator and study the properties of confidence intervals (CIs) constructed from asymptotic n…
Early stopping of iterative algorithms is an algorithmic regularization method to avoid over-fitting in estimation and classification. In this paper, we show that early stopping can also be applied to obtain the minimax optimal testing in a general non-parametric setup. Specifically, a Wald-type test statistic is obtai…
We describe a methodology for modeling the performance of decision-level data fusion between different sensor configurations, implemented as part of the JIEDDO Analytic Decision Engine (JADE). We first discuss a Bayesian network formulation of classical probabilistic data fusion, which allows elementary fusion structur…
Tests validity of DML estimators without assumptions.
problem Validating DML estimators without making assumptions.
method Develops tests to falsify assumptions for DML estimators.
result Falsifies assumptions for DML estimators with non-trivial power.
Study disproves a generalized numerical criterion for certain pairs.
problem Generalized numerical criterion for pairs
method Provided counterexamples
result Negative answer to the generalized numerical criterion problem
New polynomial criterion for periodic knots identified.
problem Identifying periodic knots efficiently.
method Examined HOMFLY-PT and Kauffman polynomials of periodic links.
result Criterion is stronger than existing methods.
New algorithms optimize a soft-robust criterion in reinforcement learning, reducing conservatism.
problem Computing robust policies for high-stakes decisions with limited data.
method Soft-robust criterion using risk measures, two algorithms for optimization.
result Our algorithms produce less conservative solutions than existing methods.
We introduce a new criterion to determine the order of an autoregressive model fitted to time series data. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information criterion. When the data is generated from a finite order autoregression, the Bay…
Modified Bakry-Émery criterion inequality for Tsallis entropy monotonicity.
problem Establishing improved logarithmic Sobolev inequalities and monotonicity of Tsallis entropy.
method Proving a one-parameter family of weighted Bakry-Émery Γ2 criterion inequalities and a modified inequality. result Yields a family of sharp Sobolev inequalities and monotonicity of Tsallis entropy.
A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an overestimating term of a widely applicable Bayesian information criterion. Adjustment of…
New criterion improves predictive evaluation in weighted inference scenarios.
problem Improving predictive evaluation in scenarios with different likelihoods for estimation and evaluation.
method Developed the posterior covariance information criterion (PCIC) to handle weighted likelihood inference.
result PCIC is asymptotically unbiased for quasi-Bayesian generalization error in weighted inference.
Criterion for stopping conjugacy class enumeration in triangle groups.
problem Enumerating all conjugacy classes in cocompact triangle groups.
method Encoding by P. Dehornoy and T. Pinsky; stopping criterion based on geometric length.
result Stopping criterion for the generation of conjugacy classes in cocompact triangle groups.
In [D.A. Fedoseev, V.O. Manturov, A sliceness criterion for odd free knots,arXiv:1707.04923], the authors proved a sliceness criterion for odd free knots: free knots with odd chords. In the present paper we give a similar criterion for stably odd free knots. Some additional results on knot sliceness and cobordism are g…
New criterion for solving inverse Hessian equations, including J-equation.
problem Existence of solutions to inverse Hessian equations, including J-equation.
method Stability of pairs in the sense of Paul, formulated in terms of GIT criterion.
result New numerical criterion for existence of solutions to inverse Hessian equations.
Criterion for nilpotent Lie groups to have nilsolitons.
problem Existence of nilsolitons in nilpotent Lie groups.
method Algebraic criterion for nilpotent Lie algebras, proving necessary and sufficient condition for nilsolitons.
result Criterion provides a necessary and sufficient condition for nilpotent Lie groups to admit nilsolitons.
Study proposes a stopping criterion for active learning based on error stability.
problem Improving predictive performance in active learning by adaptively annotating samples.
method Proposes a stopping criterion based on error stability for Bayesian active learning.
result Demonstrates the proposed criterion stops active learning at the appropriate timing for various models and datasets.
Clarifies boundary criterion for non-one-ended subgroups in cubulation theory.
problem Boundary criterion for relative cubulation in non-one-ended subgroups.
method Showed that if boundary criterion is satisfied for a relatively hyperbolic group, the group admits a relatively geometric action on a CAT(0) cube complex.
result The refinement of the boundary criterion is useful for constructing new relative cubulations.
Derives criteria for Kähler structures on holomorphic submersions.
problem Criteria for Kähler structures on holomorphic submersions.
method Derives a criterion for Kähler structures using holomorphic submersions.
result Proves Kähler structures for certain holomorphic submersions.
Partial answer to affineness of entire Grauert tubes, with Stein manifold criterion.
problem Affineness of entire Grauert tubes
method Generalized Demailly's criterion for Stein manifolds
result Complement of a codimension-one subset is affine
Optimizes recommendation models using skew normal distribution.
problem Improving personalized recommendation systems.
method Develops a new optimization criterion based on skew normal distribution.
result Significantly outperforms state-of-the-art models.