Boosting combines weak hypotheses to create accurate predictions under bounded VC dimension.
problem How to combine weak hypotheses to achieve accurate predictions efficiently.
method Designing a novel boosting algorithm with complex aggregation rules for bounded VC dimension classes.
result The new boosting algorithm requires fewer weak hypotheses than classical lower bounds, provided they belong to a bounded VC class.
Machine Learning benefits from prior information and computational power for better performance and understanding.
problem Improper use of Machine Learning methods leads to lack of understanding and performance issues.
method Employing prior information and computational power to solve learning problems, emphasizing interpretability and performance.
result Combining prior information and computational power can lead to better understanding and performance in Machine Learning.
Paper develops a consistent model selection framework for learning Hypotheses Space from data.
problem Avoiding overfitting in complex spaces with limited data.
method Develops a model selection framework based on Learning Spaces, selecting a Hypotheses Space from data.
result The method converges with probability one to a target Hypotheses Space, providing a consistent framework for model selection.
Paper studies statistical tests on infinite random graphs.
problem Testing hypotheses on infinite random graphs.
method Formalism for stationarity, generalized time series results.
result Criterion for consistent test existence.
Proposes PHD to measure domain discrepancy for complex models.
problem Insufficient domain discrepancy measures for complex models.
method Introduces PHD, a novel discrepancy measure for complex models.
result PHD is computationally efficient and applicable to multi-class classification.
Optimal private tests for simple hypotheses are characterized.
problem Private testing of simple hypotheses under differential privacy constraints.
method Characterization of sample complexity and optimal tests using log-likelihood ratio tests.
result Optimal sample complexity achieved by a specific randomized and clamped variant of the log-likelihood ratio test.
The paper analyzes adversarial robustness for linear models and neural networks using Rademacher complexity.
problem Understanding adversarial robustness of linear models and neural networks.
method The paper uses Rademacher complexity to provide upper and lower bounds for adversarial robustness of linear hypotheses and neural networks.
result The paper provides bounds on adversarial Rademacher complexity for linear hypotheses and neural networks, offering a finer analysis of input dimensionality.
We prove Aubin's "Hypothese fondamentale" concerning the existence of Moser-Trudinger type inequalities on any integral compact Kähler manifold X. In the case of the anti-canonical class on a Fano manifold the constants in the inequalities are shown to only depend on the dimension of X (but there are counterexamples to…
Optimal observation selection for complex hidden hypotheses.
problem Diagnosis of complex hidden hypotheses using limited observations.
method Active diagnosis through selection of most informative observations based on past results.
result An implication model that predicts future outcomes based on past observations, selecting the most informative next observation.
Holomorphic residue formula for complex supermanifolds.
problem Residue localization on complex supermanifolds.
method Holomorphic residue localization formula for odd vector fields.
result Explicit local residue formula under isolated non-degeneracy hypotheses.
The paper introduces a data-adaptive method for high-dimensional hypothesis testing.
problem Simultaneous testing of thousands of null hypotheses in high-dimensional settings.
method Data mining techniques to screen covariates, create average ranks, and reduce the set of hypotheses.
result Valid statistical inference achieved without specifying which hypotheses will be tested.
Unified method for MMD variance estimation improves accuracy and computational efficiency.
problem Variance estimation for MMD in nonparametric testing.
method Unified finite-sample characterization of MMD variance through U-statistic and Hoeffding decomposition; exact acceleration method for univariate case.
result Unified estimators improve accuracy and computational efficiency for MMD variance.
We information-theoretically reformulate two measures of capacity from statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. We show these capacity measures count the number of hypotheses about a dataset that a learning algorithm falsifies when it finds the classifier in its repertoire …
We consider the fundamental question of learnability of a hypotheses class in the supervised learning setting and in the general learning setting introduced by Vladimir Vapnik. We survey classic results characterizing learnability in term of suitable notions of complexity, as well as more recent results that establish …
New framework for valid hypothesis testing in complex data settings.
problem Challenges in classical hypothesis testing frameworks.
method Add and subtract external noise to partition data, orthogonalize, and test hypotheses.
result Valid hypothesis tests can be conducted under minimal assumptions.
This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for determining a binary-valued function through a sequence of strategically selected q…
We show that a homotopy equivalence between manifolds induces a correspondence between their spin^c-structures, even in the presence of 2-torsion. This is proved by generalizing spin^c-structures to Poincare complexes. A procedure is given for explicitly computing the correspondence under reasonable hypotheses.
Transformers prefer simpler explanations in hierarchical tasks.
problem Navigating tasks with varying complexity levels.
method Well-controlled testbeds based on Markov chains and linear regression.
result Transformers favor the least complex sufficient explanation when presented with simpler data.
The paper introduces stability of learning algorithms and bounds their generalization error.
problem Understanding and bounding the generalization error of learning algorithms.
method Introduces argument stability and uses martingale inequalities in Banach spaces.
result Bounds the generalization error of learning algorithms in terms of their argument stability.
The abstract discusses topological censorship with five hypotheses.
problem Proving topological censorship in spacetimes.
method Presented five hypotheses to prove a theorem.
result Proof of a topological censorship theorem.
Paper tackles efficient learning of non-convex hypotheses in metric spaces.
problem Efficiently find consistent hypotheses for non-convex hypotheses composed of possibly several disconnected regions.
method Proposes a general domain-independent algorithm for finding consistent weakly convex hypotheses and proves sufficient conditions for its efficiency.
result Shows that consistent hypothesis finding problem can be solved in polynomial time for a broad class of weakly convex hypotheses over metric spaces.
We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line b…
The article introduces gamma-Psi-dimensions for margin multi-category classifiers.
problem Margin multi-category classifiers' generalization performance under minimal learnability hypotheses.
method Derives gamma-Psi-dimensions, handles capacity measures, and establishes upper bounds on metric entropies and Rademacher complexity.
result Gamma-Psi-dimensions improve over fat-shattering dimension and offer a promising alternative for multi-class to binary transitions.
Stable planes are locally isomorphic to classical projective planes.
problem Characterizing stable planes that are locally isomorphic to classical projective planes.
method Analyzing properties of stable planes and comparing them to classical projective planes over specific fields.
result Simply connected stable planes with connected lines are isomorphic to open subplanes of classical projective planes.
DivDis learns diverse hypotheses from underspecified data to improve robustness.
problem Learning from underspecified datasets leads to multiple equally viable solutions, causing out-of-distribution issues.
method DivDis framework: 1) learns diverse hypotheses using unlabeled test data, 2) selects one hypothesis with minimal additional supervision.
result DivDis finds robust features in image and natural language processing problems.
New algorithms for multitask learning with long-term memory.
problem Learning from tasks partitioned into unknown segments with associated hypotheses.
method Online multitask learning algorithms exploiting segmentation and hypothesis association.
result Regret bounds and efficient algorithms for various hypothesis classes.
New method uses LLMs to generate detailed scientific hypotheses.
problem Generating detailed, actionable scientific hypotheses from coarse initial directions.
method Hierarchical search method that incrementally adds details to hypotheses.
result Hierarchical search method consistently outperforms strong baselines on expert-annotated hypotheses.
In many practical applications of multiple hypothesis testing using the False Discovery Rate (FDR), the given hypotheses can be naturally partitioned into groups, and one may not only want to control the number of false discoveries (wrongly rejected null hypotheses), but also the number of falsely discovered groups of …
Sequential tests for nonparametric hypotheses using supermartingales.
problem Designing valid sequential tests for nonparametric null hypotheses.
method Using elicitable and identifiable functionals, nonnegative supermartingales, and Online Convex Optimization.
result Rigorous guarantees on asymptotic power for a wide range of alternative hypotheses.
This paper speeds up speech recognition by vectorizing hypotheses and speech.
problem Slowness in beam search during speech recognition.
method Vectorization of hypotheses and speech, parallelism, batch processing, shallow fusion.
result 3.7x speedup achieved by vectorizing hypotheses, 10.5x by GPU.
Study examines how network architecture handles increasing data complexity.
problem Understanding how network architecture affects performance with complex data.
method Empirical study comparing various network architectures on an image classification task with increasing class numbers.
result Modern architectures show better generalization performance with increasing data complexity.
Hypothesis testing in singular models is fundamentally about identifiable vs. non-identifiable parameters.
problem Testing in singular models is inherently problematic due to non-identifiability and degeneracy of Fisher information.
method Formalized the overlap obstruction and showed that hypotheses over non-identifiable parameters are untestable, while those over identifiable parameters reduce to classical testing.
result Hypotheses over non-identifiable parameters are untestable, while those over identifiable parameters reduce to classical testing.
The paper uses RL to verify hypotheses, overcoming existing limitations.
problem Verifying hypotheses using reinforcement learning.
method Formulated hypothesis verification as an RL problem, exploiting hypothesis structure.
result RL agents can successfully verify hypotheses, even those not factorizable.
Analyzes the complexity of linear hypothesis sets using Rademacher complexity.
problem Understanding the complexity of linear hypothesis sets for various norms.
method Tight analysis of empirical Rademacher complexity for linear hypothesis classes with bounded weights.
result Improved bounds on Rademacher complexity for linear hypothesis sets, matching or improving existing results.
Method generates multiple 3D poses from 2D joint detections, addressing ambiguity and uncertainty.
problem Ambiguity and uncertainty in 3D human pose estimation from 2D joint detections.
method Generative model, compositional, anatomical constraints, removing model bias.
result Generates multiple valid 3D poses consistent with 2D joint detections.
The paper analyzes different neural network architectures for 3D point cloud processing.
problem Understanding the effects of specific intermediate-layer network architectures on 3D point cloud processing.
method Designing five metrics to diagnose various types of DNNs and conducting comparative studies.
result The hypotheses on the effects of specific intermediate-layer network architectures on the representation capacity of DNNs are verified.
The paper proves vanishing theorems for complex line bundles using a new adiabatic limit approach.
problem Vanishing theorems for complex line bundles under specific conditions.
method Generalizes adiabatic limit construction to connections on complex line bundles, proving vanishing theorems.
result Proves vanishing theorems for D′′-cohomology groups under certain conditions. s-RBFN integrates multiple hypotheses for efficient and diverse prediction.
problem Integrating multiple hypotheses into learning models for regression.
method Structured Radial Basis Function Network (s-RBFN) using Voronoi tessellations and least-squares training.
result s-RBFN achieves superior generalization and efficiency compared to other models.
DP-SPRT improves privacy in sequential tests with near-optimal error rates.
problem Privacy constraints in sequential probability ratio tests.
method A wrapper for SPRT that uses a private mechanism to determine when to stop based on predefined intervals.
result DP-SPRT achieves near-optimal error rates and privacy guarantees.
It was proved in 1998 by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same…
Uniformizes compact complex manifolds via Anosov representations.
problem Uniformization of compact complex manifolds.
method Anosov homomorphisms with small limit sets.
result Local homeomorphism of character variety to Teichmüller space.
Near-optimal private tests for simple and MLR hypotheses developed under Gaussian differential privacy.
problem Developing private tests for simple and MLR hypotheses under Gaussian differential privacy.
method A private mean estimator with data-driven clamping bounds, constructing private test statistics.
result Private tests achieve the same asymptotic relative efficiency as non-private most powerful tests.
Crowdsourcing generated useful hypotheses for predicting residential energy usage.
problem Predicting residential electric energy usage using crowdsourced data.
method Crowdsourced questions and answers were used to build a predictive model of monthly electric energy consumption.
result The crowd can generate useful hypotheses for predicting energy usage, even with sparse data.
Novel method models dynamic brain graphs from time series data.
problem Generating hypotheses for dynamic brain states.
method Conditionally weighted superposition of static graphs.
result Improves f1-scores by 22-28% on average over baselines.
Unified algorithm for incorporating various prior knowledge in multiple testing.
problem Improving power and precision in multiple testing procedures with prior knowledge.
method p-filter algorithm that incorporates four types of prior knowledge: null hypotheses, penalties, groups, and independence.
result Unified framework allows for recovery of various known algorithms.
Confirmation bias leads to biased estimates in noisy data analysis.
problem Confirmation bias affects scientific conclusions in noisy data environments.
method Investigation of confirmation bias in Gaussian mixture models using K-means and EM algorithms.
result Estimates from algorithms are biased and resemble initial hypotheses, not the noise.
Study finds solutions for complex problems on non-compact manifolds.
problem Solving fully nonlinear Yamabe-type problems on non-compact manifolds.
method Existence results for a class of problems, considering both positive and negative cases.
result Explicit examples of manifolds satisfying the hypotheses of the theorems.
The study shows that certain cubical presentations lead to aspherical spaces.
problem Understanding the asphericity of cubical presentations in 2D.
method Analyzing the second homotopy group of coned-off spaces associated with cubical presentations.
result The coned-off space is aspherical under specific conditions.