In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitable hypotheses, we are able to characterize the Riemannian manifold which admits a stable solution. Furthermore, under the non-negativity of …
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48 results for “stable hypotheses”
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.
The paper explains knowledge distillation by analyzing visual concepts in DNNs.
problem Understanding how knowledge distillation affects the learning of visual concepts in deep neural networks.
method The paper proposes three hypotheses and designs mathematical metrics to evaluate feature representations of DNNs.
result The hypotheses were verified through experiments on various DNNs.
We give two structural conditions on a codimension integral -varifold with first variation locally summable to an exponent that imply the following: whenever each orientable portion of the -embedded part of the varifold (which is non-empty by the Allard regularity theory) is stationarity and the $C^…
The moduli space of tropical -weighted stable curves of volume is naturally identified with the dual complex of the divisor of singular curves in Hassett's spaces of -weighted stable curves. If at least two of the weights are , we prove that is homotopic to a wedge sum of spheres, possi…
Local minimality proven for stable free-boundary minimal hypersurfaces.
problem Proving local minimality for stable free-boundary minimal hypersurfaces.
method Using relative current setting and strict stability, proving local minimality among relative cycles.
result Local minimality of stable free-boundary minimal hypersurfaces in a small tubular neighborhood.
New algorithm learns regression models privately under growth condition.
problem Private learning of nonparametric regression models.
method Novel filtering procedure to output stable hypotheses for nonparametric function classes.
result Established first nonparametric private learnability guarantee for diverging fat shattering dimensions.
Gated recurrent units (GRUs) are specialized memory elements for building recurrent neural networks. Despite their incredible success on various tasks, including extracting dynamics underlying neural data, little is understood about the specific dynamics representable in a GRU network. As a result, it is both difficult…
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.
New methods for estimating causal effects with limited overlap, using Stable Probability Weighting.
problem Estimating causal effects with limited overlap in multivalued treatments.
method Stable Probability Weighting (SPW) and Finite-Sample Stable Probability Weighting (FPW) methods.
result SPW and FPW provide practical solutions for estimating and inferring causal effects with limited overlap.
We study the isoperimetric structure of asymptotically flat Riemannian 3-manifolds (M,g) that are C^0-asymptotic to Schwarzschild of mass m>0. Refining an argument due to H. Bray we obtain an effective volume comparison theorem in Schwarzschild. We use it to show that isoperimetric regions exist in (M, g) for all suffi…
We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in terms of modules over a stack of parametrized spectra and in terms of diagrams o…
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.
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.
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.
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.
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.
Investment strategies in financial markets can lead to instability due to market impacts.
problem Market impacts make it impossible for investors to accurately optimize their strategies.
method Built an agent-based model with technical analysis strategy agents to investigate optimization instability.
result Investment strategies' parameters never converged but continued to change, leading to unstable market price evolution.
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.
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 …
In this paper, we diagnose deep neural networks for 3D point cloud processing to explore utilities of different intermediate-layer network architectures. We propose a number of hypotheses on the effects of specific intermediate-layer network architectures on the representation capacity of DNNs. In order to prove the hy…
We propose a method to generate multiple diverse and valid human pose hypotheses in 3D all consistent with the 2D detection of joints in a monocular RGB image. We use a novel generative model uniform (unbiased) in the space of anatomically plausible 3D poses. Our model is compositional (produces a pose by combining par…
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.
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian motion model. It is formally equivalent to a model describing the stochastic dyn…
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.
There is a significant literature on methods for incorporating knowledge into multiple testing procedures so as to improve their power and precision. Some common forms of prior knowledge include (a) beliefs about which hypotheses are null, modeled by non-uniform prior weights; (b) differing importances of hypotheses, m…
Attention-based encoder decoder network uses a left-to-right beam search algorithm in the inference step. The current beam search expands hypotheses and traverses the expanded hypotheses at the next time step. This traversal is implemented using a for-loop program in general, and it leads to speed down of the recogniti…
Structured Radial Basis Function Network: Modelling Diversity for Multiple Hypotheses Predictioncs.LG
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.
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…
Study finds nighttime lights correlate with Indian GDP growth.
problem Accurate forecasting of Indian economic growth.
method Examined relationship between GDP and nighttime lights using DMSP and VIIRS datasets.
result Nighttime lights correlate with Indian GDP growth.
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.
Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these hypotheses may concern a wide range of parameters, with complex and unknown depen…
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.
Simultaneous inference after model selection is of critical importance to address scientific hypotheses involving a set of parameters. In this paper, we consider high-dimensional linear regression model in which a regularization procedure such as LASSO is applied to yield a sparse model. To establish a simultaneous pos…
The paper proves weaker conditions for global smoothings of special Lagrangian submanifolds with conical singularities.
problem Conditions for global smoothings of special Lagrangian submanifolds with isolated conical singularities.
method Proof of weaker conditions for global smoothings.
result Global smoothings are possible under weaker hypotheses than previously known.
BERT fine-tuning is unstable due to optimization issues, not forgetting or dataset size.
problem Stability of fine-tuning BERT-based models across different random seeds.
method Analysis of BERT, RoBERTa, and ALBERT fine-tuned on GLUE datasets, identifying optimization difficulties as the cause of instability.
result Fine-tuning instability is due to optimization difficulties leading to vanishing gradients, not forgetting or dataset size.
Study identifies and analyzes spurious correlations in data-driven models.
problem Spurious correlations in data-driven models are unreliable and hard to detect.
method Collect and analyze synthetic datasets generated from causal graphs to investigate spurious correlations.
result Patterns connecting spurious correlation hypotheses and model design choices were observed.
Boosting algorithms produce a classifier by iteratively combining base hypotheses. It has been observed experimentally that the generalization error keeps improving even after achieving zero training error. One popular explanation attributes this to improvements in margins. A common goal in a long line of research, is …
We consider a distributed learning setup where a network of agents sequentially access realizations of a set of random variables with unknown distributions. The network objective is to find a parametrized distribution that best describes their joint observations in the sense of the Kullback-Leibler divergence. Apart fr…
We consider minimizing harmonic maps from into a closed Riemannian manifold and prove: (1) an extension to of Almgren and Lieb's linear law. That is, if the fundamental group of the target manifold is finite, we have \[ \mathcal{H}^{n-3}(\textrm{sing } …
Crowdsourcing has been successfully applied in many domains including astronomy, cryptography and biology. In order to test its potential for useful application in a Smart Grid context, this paper investigates the extent to which a crowd can contribute predictive hypotheses to a model of residential electric energy con…
This work bounds the generalization error of private algorithms for discrete data.
problem Bounding the generalization error of private algorithms for discrete data.
method Information-theoretic approach using relative entropy and the method of types.
result Explicit upper bounds on the generalization error of stable private algorithms for discrete data.
Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a criterion for the existence of a consistent test for complex hypotheses is presented,…
Context. Generative models open up the possibility to interrogate scientific data in a more data-driven way. Aims: We propose a method that uses generative models to explore hypotheses in astrophysics and other areas. We use a neural network to show how we can independently manipulate physical attributes by encoding ob…
New method uses geometric properties for better density estimation.
problem Uncertainty quantification in ambiguous tasks.
method Winner-takes-all training with centroidal Voronoi tessellations.
result Improved quantization and density estimation.
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.
Thinking LLMs struggle with stock prediction, especially as data complexity increases.
problem Evaluating the performance of 'thinking' LLMs in stock prediction, especially under varying levels of cross-sectional complexity.
method Rolling 48m/1m walk-forward evaluation, comparing direct LLMs, TLLMs, and classical learners on cross-sectional ranking loss, MSE, and backtests with transaction costs.
result TLLMs' ranking quality deteriorates as cross-sectional complexity grows, while direct LLMs remain stable.
LLM agents discover cryptocurrency factors under reproducible constraints.
problem Flexibility of LLM agents in empirical discovery leads to uncontrolled search.
method Sequential hypothesis search with fixed data splits and portfolio tests.
result Ridge-combined portfolio achieves 44.55% annualized return in out-of-sample period.