The study examines statistical inference with gradient ascent in multi-modal likelihood functions.
problem Statistical inference with multiple initializations in multi-modal likelihood functions.
method Derives population quantity, studies asymptotic normality, bootstrap, and likelihood ratio tests.
result Coverage deficiency and differences in CIs due to finite number of initializations.
Generalizing the theorem of Green--Lazarsfeld and Gromov, we classify Kaehler groups of deficiency at least two. As a consequence we see that there are no Kaehler groups of even and strictly positive deficiency. With the same arguments we prove that Kaehler groups that are non-Abelian and are limit groups in the sense …
Let L be a lattice in a connected Lie group. We show that besides a few exceptional cases, the deficiency of L is nonpositive.
The study shows subgroup separability conditions for specific groups.
problem Conditions for subgroup separability in free-by-cyclic and deficiency 1 groups.
method Analyzes polynomially growing monodromy and asymptotic probability of random groups.
result Random deficiency 1 groups are not subgroup separable with positive probability.
The study calculates the Smith-Thom deficiency of Hilbert squares and provides conditions for maximality.
problem Calculating the Smith-Thom deficiency of Hilbert squares and conditions for maximality.
method Using Mayer-Vietoris mapping and rank calculations.
result Established necessary and sufficient conditions for maximality of Hilbert squares in projective complete intersections.
Contextual bandit methods fail with deficient support data.
problem Learning from support-deficient data in contextual bandits.
method Three approaches to IPS-based learning: action space restriction, reward extrapolation, and policy space restriction.
result Systematic analysis and empirical evaluation of approaches to IPS-based learning.
The paper addresses flaws in fixed point assertions for digital images.
problem Deficiencies in previously published works on fixed point assertions for digital images.
method Continues a series of studies to identify and rectify issues in fixed point assertions.
result Identifies and corrects flaws in fixed point assertions for digital images.
The paper calculates the number of oriented rational links with a given deficiency.
problem Counting oriented rational links with a specific deficiency.
method Derived precise formulas for the number of oriented rational links with crossing number n and deficiency d.
result Precise formulas for the number of oriented rational links with crossing number n and deficiency d.
Analyzes the structure and rank of neural network Hessians.
problem Understanding redundancy in overparameterized neural networks.
method Theoretical tools to analyze Hessian map range and rank deficiency.
result Exact formulas and tight upper bounds for Hessian rank of deep linear networks.
We examine certain symmetries in the deficiencies of a rational surgery on a knot in S3 by comparing the Spinc-structures on the rational surgery with those on a related integral surgery. We then provide an application of these symmetries in the form of a theorem that obstructs Dehn surgeries in S3. Thi…
Specialists tolerate defects to gain flexibility, which can be removed when needed.
problem The economic benefits and limitations of deliberately tolerating defects in decision-making.
method Analyzes the conditions under which defects can be kept and removed, using economic models and structural analysis.
result A defect is profitably removable if certain conditions are met, and the premium is the support function of the class's ROC set.
Specialists tolerate defects to gain flexibility, which can be removed when needed.
problem The economic benefits and limits of deliberately tolerating defects in decision-making.
method Analyzes the economic position of keeping and removing defects, using a coupling lemma and structural economic models.
result A defect is profitably removable if the detector-relevant distinction survives a restriction and the advantage condition holds.
Study uses DHS to classify anemia types using CBC indices.
problem Anemia classification for medical purposes.
method Dynamic Harmony Search (DHS) applied to CBC indices.
result DHS outperforms other models in anemia classification.
Proves one-relator groups are fundamental groups of Sasakian manifolds.
problem Characterizing groups that can be fundamental groups of Sasakian manifolds.
method Analyzes one-relator groups and classifies groups of deficiency at least two.
result Proves sufficient and necessary conditions for one-relator groups to be fundamental groups of Sasakian manifolds.
Framework disentangles deep feature uncertainty for efficient inference.
problem Inference-time uncertainty estimation for reliable decision-making.
method Uncertainty-Guided Inference-Time Selection framework.
result Significantly tighter prediction intervals and 60% compute reduction.
"Deep Learning" methods attempt to learn generic features in an unsupervised fashion from a large unlabelled data set. These generic features should perform as well as the best hand crafted features for any learning problem that makes use of this data. We provide a definition of generic features, characterize when it i…
A new algorithm solves constrained optimization problems with stochastic gradients.
problem Nonlinear equality constrained optimization with rank-deficient Jacobians.
method Step decomposition strategy combining normal and tangential steps.
result Convergence guarantees in rank-deficient Jacobian cases.
For every N > 0 there exists a group of deficiency less than -N that arises as the fundamental group of a smooth homology 4-sphere and also as the fundamental group of the complement of a compact contractible submanifold of the 4-sphere. A group is the fundamental group of the complement of a contractible submanifold o…
We address two fundamental and well-known problems of Gromov and Lyndon: \demo{Problem A} (Gromov, see [5]). Consider a category Mn of closed manifolds of dimension n with nonzero-degree ways as morphisms. Study a partial order M≥N⇔Mor(M,N)=φ. For which N the degrees of maps $f: M \t…
Study on Neumann eigenvalues controlled by domain isoperimetric ratio.
problem Control the number of Neumann eigenvalues no greater than the first Dirichlet eigenvalue.
method Combination of analytical and numerical results, related to Yau's conjecture.
result Neumann eigenvalues are controlled by the isoperimetric ratio of the domain.
A new method combines online and offline learning to tackle contextual bandits with missing action support.
problem Learning optimal policies with logged data when the logging policy has deficient support.
method Hybrid approach using online exploration to exploit supported actions and offline learning to avoid unnecessary explorations.
result Determines an optimal policy with theoretical guarantees using minimal online explorations.
We study "how far away" a finite index subgroup G of SL(2,Z) is from being a congruence group. For this we define its deficiency of being a congruence group. We show that the index of the image of G in SL(2,Z/nZ) is biggest, if n is the general Wohlfahrt level. We furthermore show that the Veech groups of origamis (or …
New method uses label-weighted conformal prediction for macro-coverage guarantees in classification.
problem Finding a balance between class-conditional and marginal coverage in long-tailed datasets.
method Label-weighted conformal prediction for macro-coverage guarantees.
result Validated prediction sets with macro-coverage guarantees on large-scale image datasets.
Study on confidence intervals for Sliced Wasserstein distance, with optimal risk bounds.
problem Statistical inference for the Sliced Wasserstein distance.
method Construct minimax confidence intervals with adaptive lengths.
result Minimax optimal confidence intervals for the Sliced Wasserstein distance.
Algorithm balances learning and coverage for multi-robots over unknown fields.
problem Balancing learning and coverage for multi-robots over unknown, nonuniform sensory fields.
method DSLC algorithm that schedules learning and coverage epochs, using Gaussian Process modeling and coverage regret analysis.
result Upper bound on expected cumulative coverage regret provided for DSLC.
Improved conformal prediction for better conditional coverage of classifier predictions.
problem Achieving exact conditional coverage in finite samples for prediction sets.
method Developed a variant of conformal prediction targeting coverage conditional on confidence and trust score.
result Empirically improved conditional coverage properties compared to standard conformal prediction.
Adaptive coverage policies improve conformal prediction accuracy.
problem Fixed coverage levels in traditional conformal prediction lead to uninformative predictions.
method Optimizes adaptive coverage policy using a neural network trained on leave-one-out calibration.
result Adaptive coverage policies produce more informative and flexible prediction sets.
Bayesian model predicts iron deficiency from multi-source multi-way molecular data.
problem Predicting iron deficiency in rhesus monkeys from multi-source multi-way molecular data.
method Developed a Bayesian approach with a linear model incorporating multi-way dependence and varying signal sizes across sources.
result Model accurately classifies iron deficiency in monkeys and outperforms simpler models.
New metrics improve understanding of predictive system reliability.
problem Evaluating conditional coverage of predictive systems.
method Casting conditional coverage estimation as a classification problem, using excess risk of the target coverage (ERT) metrics.
result Modern classifiers provide higher statistical power for estimating conditional coverage.
Kandinsky conformal prediction expands conditional coverage guarantees.
problem Disparities in coverage guarantees across different subpopulations.
method Flexible handling of overlapping and fractional group memberships.
result Minimax-optimal high-probability conditional coverage bound.
ST-BCP narrows the coverage gap in BCP by transforming nonconformity scores.
problem The looseness in BCP's coverage guarantee due to Markov's inequality.
method Introduces a data-dependent transformation of nonconformity scores.
result Reduces the average coverage gap from 4.20% to 1.12% on benchmarks.
Improves conditional coverage of regression models using conformal prediction.
problem Lack of conditional coverage guarantees in conformal prediction methods.
method Proposes a novel algorithm to train a regression function to improve conditional coverage after split conformal prediction.
result Establishes an upper bound for miscoverage gap and proposes an end-to-end algorithm to control it.
This study uses AI to analyze financial market coverage from YouTube videos.
problem Challenges in analyzing a large number of financial market videos.
method Used Whisper model to generate text from videos, applied natural language processing.
result Highlights dynamics of financial market coverage and identifies trending topics.
Two conformal methods create flexible conditional predictive bands without strong assumptions.
problem Achieving asymptotic conditional coverage without strong dependence assumptions.
method Flexible distribution-free conditional predictive bands using density estimators.
result Methods achieve better control of conditional coverage and smaller length than previous methods.
Study finds limited correlation between DNN coverage and robustness.
problem Limited correlation between DNN coverage and robustness.
method Empirical study using 100 DNN models and 25 metrics.
result Improving coverage does not improve robustness.
TQA improves prediction intervals for time series data by adjusting quantiles for both cross-sectional and longitudinal coverage.
problem Constructing reliable prediction intervals for cross-sectional time series data.
method Temporal Quantile Adjustment (TQA) method that adjusts the quantile in Conformal Prediction to account for both cross-sectional and longitudinal coverage.
result TQA improves longitudinal coverage while preserving cross-sectional coverage, as validated through extensive experimentation.
New conformal prediction methods for long-tailed classification problems.
problem Rare classes are systematically omitted in existing conformal prediction methods.
method Introduced a new conformal score function and a new interpolation procedure.
result Smoothly trade off set size and class-conditional coverage.
New coverage conditions improve sample efficiency in online reinforcement learning.
problem Improving sample efficiency in online reinforcement learning with function approximation.
method Identifying and studying new coverage conditions for online reinforcement learning.
result Improved regret bounds achieved with new coverage conditions.
We introduce the concept of coverage risk as an error measure for density ridge estimation. The coverage risk generalizes the mean integrated square error to set estimation. We propose two risk estimators for the coverage risk and we show that we can select tuning parameters by minimizing the estimated risk. We study t…
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 method improves conditional coverage of conformal prediction.
problem Improving conditional coverage in conformal prediction.
method Trainable transformation of conformity scores to improve conditional coverage.
result Highly adaptive to local data structure, outperforming existing methods.
Audited Conformal Prediction improves conditional coverage in pretrained models under distribution shift.
problem Uncertainty quantification for pretrained models under unknown distribution shift
method Leverages a small labeled dataset to train an audit model for marginal coverage, integrates outputs into conformal prediction framework
result Significantly higher conditional coverage than existing approaches
Equalized coverage method ensures fair prediction intervals across protected groups.
problem Ensuring fair use of data-driven recommendation systems by communicating their uncertainty.
method Operational methodology that forces unbiased prediction intervals across all protected groups, offering rigorous distribution-free coverage guarantees.
result Equalized coverage constructs unbiased prediction intervals, unlike competitive methods.
Pre-training improves model coverage, crucial for downstream performance.
problem Understanding why pre-training enhances model performance.
method Coverage principle, focusing on next-token prediction and model quality.
result Coverage generalizes faster than cross-entropy, improving downstream performance.
Adapts conformal prediction for missing data, ensuring valid coverage.
problem Uncertainty quantification with missing covariates.
method Proposes a reweighted conformal prediction procedure for handling missing values.
result Guaranteed Marginal Coverage and Mask-Conditional Validity for general missing data mechanisms.
Unified coverage analysis for linear off-policy evaluation in reinforcement learning.
problem Lack of a unified understanding of coverage parameters in linear off-policy evaluation.
method Developed a novel finite-sample analysis for LSTDQ algorithm, introducing feature-dynamics coverage.
result Unified understanding of coverage parameters in linear off-policy evaluation.
Study optimal policies under budget and coverage constraints.
problem Optimal policy learning with budget and coverage constraints.
method Combination of knapsack structure, affine threshold rule, linear programming relaxation, Greedy-Lagrangian (GLC), and rank-and-cut (RC) algorithms.
result GLC closely approximates the optimal solution and achieves near-optimal performance in finite samples; RC is approximately optimal under certain conditions.
Quantile regression undercovers true uncertainty, revealing a bias in high dimensions.
problem Under-coverage bias in uncertainty estimation by quantile regression.
method Theoretical study on coverage of uncertainty estimation algorithms in learning quantiles.
result Quantile regression undercovers true uncertainty, revealing a bias in high dimensions.