Stability result for a popular algorithm in optimal transport.
problem Stability of the Iterative Proportional Fitting Procedure in time and metric.
method Uniform stability analysis in the 1-Wasserstein metric.
result Quantitative stability result for entropy-regularized Optimal Transport and Schrödinger bridges.
In this paper we present a geometric control law for position and line-of-sight stabilization of the nonholonomic spherical robot actuated by three independent actuators. A simple configuration error function with an appropriately defined transport map is proposed to extract feedforward and proportional-derivative cont…
Study examines how cluster number affects short-text clustering, introducing a stability metric.
problem Challenges in finding meaningful clusters in short-text data.
method Introduces a stability metric to determine cluster robustness and visualizes cluster subdivisions.
result Choosing a cluster number involves balancing informativeness and complexity, not seeking a single 'optimal' solution.
A note on utility maximization with costs, proving trading strategies.
problem Utility maximization with proportional transaction costs and stability of optimal portfolios.
method Proof of a limit theorem using a dual approach.
result Established a uniqueness result for optimal trading strategies.
Unified formula for arbitrary liquidity operations in weighted AMMs
problem Decentralized resource allocation in intelligent transportation systems
method Weighted invariant adapted from Balancer-type AMMs
result Unified formula for four resource allocation operations
Resampling outperforms reweighting for correcting biased data in machine learning models.
problem Correcting sampling bias in machine learning models trained on biased data sets.
method Compared resampling and reweighting techniques, focusing on their performance with stochastic gradient algorithms.
result Resampling outperforms reweighting when combined with stochastic gradient algorithms.
Analyzes how many people can receive stable income in a pooled annuity fund.
problem Quantifying the trade-off between income stability and the number of members in a pooled annuity fund.
method Investment returns held constant, systematic longevity risk omitted. Derived an analytical expression for income stability.
result The number of fund members who receive stable income is independent of the mortality model.
We examine the problem of dynamic reserving for risk in multiple currencies under a general coherent risk measure. The reserver requires to hedge risk in a time-consistent manner by trading in baskets of currencies. We show that reserving portfolios in multiple currencies V are time-consistent when (and only…
Improved Lasso estimator speeds up variable selection.
problem Efficient variable selection in high-dimensional data.
method Stability principle-based generalized debiased Lasso.
result Significantly reduces computational cost of resampling-based methods.
SGD noise helps select flat minima by concentrating in sharp directions and being proportional to loss value.
problem Understanding the implicit regularization of SGD and selecting flat minima in over-parameterized models.
method Relating SGD's linear stability to the Frobenius norm of the Hessian and analyzing the alignment property of SGD noise.
result Flat minima are linearly stable for SGD, and their sharpness is bounded independently of model size and sample size.
CoxSE combines deep learning with self-explaining neural networks for survival analysis.
problem Improving predictive power of Cox Proportional Hazards model while maintaining explainability.
method Proposes CoxSE, a locally explainable Cox proportional hazards model using SENN, and CoxSENAM, a hybrid model with NAM.
result CoxSE provides more stable and consistent explanations while maintaining predictive power.
Market activity scales near a constant of 0.632 in intrinsic time.
problem Understanding the stability of market scaling laws.
method Modeling market directional changes as a memoryless exponential hazard process and identifying the intrinsic time scaling constant.
result The intrinsic time scaling constant is 1−1/e=0.632. Stable GFlowNets prevent loss spikes and mode collapse in training.
problem Unstable training of GFlowNets leading to loss spikes and mode collapse.
method Assessed sensitivity of GFlowNet objectives, derived loss-to-TV bounds, and proposed Stable GFlowNets.
result Stable GFlowNets improve training behavior and distributional fidelity.
The stability of statistical analysis is an important indicator for reproducibility, which is one main principle of scientific method. It entails that similar statistical conclusions can be reached based on independent samples from the same underlying population. In this paper, we introduce a general measure of classif…
Using elementary arguments, we show how to derive Lp-error bounds for the approximation of frictionless wealth process in markets with proportional transaction costs. For utilities with bounded risk aversion, these estimates yield lower bounds for the frictional value function, which pave the way for its as…
The paper studies stability of mean-field variational inference for log-concave distributions.
problem Stability of mean-field variational inference for log-concave distributions.
method Novel approach via linearized optimal transport, lifting non-convex problem to convex optimization over transport maps.
result Dimension-free Lipschitz continuity of the MFVI optimizer with respect to the target distribution, measured in 2-Wasserstein distance.
This paper discusses the numéraire-based utility maximization problem in markets with proportional transaction costs. In particular, the investor is required to liquidate all her position in stock at the terminal time. We first observe the stability of the primal and dual value functions as well as the convergence of t…
EGMU optimizes portfolios using KL divergence, ensuring positive solutions.
problem Constructing multi-factor target-exposure portfolios efficiently and accurately.
method Convex optimization framework minimizing KL divergence, with explicit solvers.
result Established feasibility and uniqueness of strictly positive solutions under convex-hull conditions.
Background: Recent developments have made it possible to accelerate neural networks training significantly using large batch sizes and data parallelism. Training in an asynchronous fashion, where delay occurs, can make training even more scalable. However, asynchronous training has its pitfalls, mainly a degradation in…
The paper studies stability of generative models trained on mixed data.
problem Training generative models on mixed datasets (real and synthetic data).
method Developed a framework to rigorously study stability under specific conditions.
result Proved the stability of iterative training under certain conditions.
Study shows resampling can drastically alter PCA results.
problem Stability and sensitivity of PCA under data resampling.
method Analyzed resampling sensitivity of high-dimensional PCA.
result PCA's principal components become asymptotically orthogonal when resampling is significant.
Study geometric properties of log Calabi-Yau manifolds, focusing on Fano manifolds with smooth or two proportional components.
problem Geometric properties of log Calabi-Yau manifolds in two specific cases.
method Analysis of various geometric properties, focusing on Bochner principle, local triviality, polystability, and compactifiability of universal cover.
result The universal cover of X∖D is a Calabi-Yau manifold of infinite topological type when D has two components. Batching stabilizes risk in high-dimensional linear regression models.
problem Stability and risk behavior in high-dimensional overparameterized linear regression.
method Minimum-norm overparameterized linear regression model with batch-partitioning.
result Optimal batch size is inversely proportional to noise level and overparametrization ratio, leading to stable risk behavior.
Unified framework for stability and generalization of Push-Sum in decentralized learning over directed graphs.
problem Understanding stability and generalization of Push-Sum in decentralized learning over directed networks.
method Developed a unified uniform-stability framework for SGP algorithm, incorporating imbalance-aware consistency bounds.
result Established finite-iteration stability and optimization guarantees for convex and non-convex objectives.
New methods improve stability of Sinkhorn algorithm in machine learning.
problem Stability of Sinkhorn semigroups in high-dimensional settings.
method Semigroup analysis based on contraction coefficients and Lyapunov-type operator-theoretic techniques.
result Unified and simplified arguments in Sinkhorn algorithm stability.
Equivalent characterizations of multiportfolio time consistency are deduced for closed convex and coherent set-valued risk measures on Lp(Ω,F,P;Rd) with image space in the power set of Lp(Ω,Ft,P;Rd). In the convex case, multiportfolio time consistency is equivalent to a cocycle condition on…
Paper proposes a method to estimate true positive proportion without knowing it.
problem Bias in binary classifier performance due to different positive item proportions.
method Maximum likelihood estimator for true proportion of positives.
result Method accurately estimates true positive proportion in data sets.
Stable algebraic filters improve neural network performance.
problem Improving neural network stability to deformations.
method Analyzed stability of algebraic filters and neural networks under deformations of the homomorphism.
result Stable algebraic filters have frequency responses whose derivative is inversely proportional to frequency.
Paper improves deep learning for instance-level classification from label proportions.
problem Dealing with noisy pseudo-labeling and high-entropy class distributions in LLP.
method Introducing a two-stage training approach with constrained optimization and mixup strategy.
result Significant performance improvement in instance-level classification.
Learning from Label Proportions (LLP) is a learning setting, where the training data is provided in groups, or "bags", and only the proportion of each class in each bag is known. The task is to learn a model to predict the class labels of the individual instances. LLP has broad applications in political science, market…
Develops a method to estimate average hazard under non-proportional hazards without relying on proportional hazards assumption.
problem Estimation of treatment effects when hazards are non-proportional, leading to unstable hazard ratios.
method Semiparametric, doubly robust framework for covariate-adjusted average hazard estimation.
result Valid sqrt{n} inference with small bias and near-nominal confidence-interval coverage across proportional and non-proportional hazards settings.
Bagging stabilizes linear interpolators, improving their generalization performance.
problem Unstable linear interpolators fail on noisy data.
method Introduced multiplier-bootstrap-based bagged least square estimator.
result Bagging effectively mitigates variance, leading to bounded prediction risk.
New scaling framework for MoE architectures ensures stability and optimal performance at scale.
problem Lack of principled understanding of how hyperparameters should scale in MoE architectures.
method Developed a novel Dynamical Mean Field Theory (DMFT) for three scaling regimes of MoE architectures.
result Derived Maximally Scale-Stable Parameterization (MSSP) for SGD and Adam, providing robust learning rate transfer and monotonic improvement with scale.
Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is ``interrupted'' by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the distribution contrasts with a lar…
Proposes a method for stable variable selection in high-dimensional data.
problem Challenges of variable selection in high-dimensional, correlated data.
method Resample-aggregate framework using diffusion models.
result Stable subset of predictors with calibrated stability scores.
New learning rules achieve optimal sample complexity for weakly supervised classification.
problem Learning from label proportions in weakly supervised settings.
method Debiased proportional square loss and EasyLLP learning rule.
result Achieves optimal sample complexity in both realizable and agnostic settings.
learn2mix trains neural nets faster by adjusting class proportions dynamically.
problem Training neural nets efficiently with limited resources and imbalanced classes.
method Adaptive class proportion adjustment during training.
result Neural nets trained with learn2mix converge faster than static methods.
Paper tackles model collapse in recursive generative models using a weighted training scheme.
problem Model collapse in recursive generative models trained on synthetic data.
method Iteratively trains models on real and synthetic data, evaluates weighted training schemes.
result Optimal weighting scheme for synthetic data follows a unified expression, revealing a trade-off with model performance.
We study the problem of learning with label proportions in which the training data is provided in groups and only the proportion of each class in each group is known. We propose a new method called proportion-SVM, or ∝SVM, which explicitly models the latent unknown instance labels together with the known group …
A reinsurance contract should address the conflicting interests of the insurer and reinsurer. Most of existing optimal reinsurance contracts only considers the interests of one party. This article combines the proportional and stop-loss reinsurance contracts and introduces a new reinsurance contract called proportional…
Study examines how insurance affects households prone to proportional losses, especially those near poverty.
problem Impact of insurance on households susceptible to proportional losses, focusing on poverty traps.
method Modelled proportional capital losses with insurance, derived closed formulae and non-local differential equations.
result New formulae and methods to calculate trapping probability, constraints on parameters to prevent certainty of trapping.
Paper proposes a new method for estimating mixture proportions without irreducibility assumption.
problem Estimating mixture proportions when component distributions are not irreducible.
method Developed a resampling-based meta-algorithm that adapts existing MPE algorithms to non-irreducible settings.
result Empirical results show improved estimation performance compared to baseline methods and regrouping-based algorithms.
Paper improves signal proportion estimation by accounting for variable dependence.
problem Traditional estimators assume independence, limiting applicability in real-world scenarios.
method Integrates arbitrary covariance dependence information using principal factor approximation.
result Method outperforms state-of-the-art estimators in accuracy and detection of weaker signals.
RLSbench benchmarks domain adaptation under label proportion shifts, revealing widespread failures and proposing a two-step meta-algorithm.
problem Domain adaptation under label proportion shifts is poorly understood and inconsistent across methods.
method RLSbench introduces a large-scale benchmark with 500 distribution shift pairs. It proposes a two-step meta-algorithm to improve domain adaptation methods under label proportion shifts.
result The two-step meta-algorithm improves domain adaptation methods by 2-10% accuracy points under large label proportion shifts.
Proportional transaction costs present difficult theoretical problems in trading algorithm design, on account of their lack of analytical tractability. The author derives a solution of DT-NT-DT form for an arbitrary model in which the the traded asset has diffusive dynamics described by one or more stochastic risk fact…
The paper explores learning from label proportions, showing differences in efficiency between LLP and PAC learning.
problem Learning from label proportions (LLP) in unlabeled data with given label proportions.
method Formal definition and computational complexity analysis of LLP learning.
result LLP learning is more restrictive than PAC learning for finite VC classes, and some classes are uncharacterizable.
Framework simplifies vision-based control and goal discovery.
problem Learning proportional control from visual data.
method Introduces NewtonianVAE for proportional control and goal discovery.
result Dramatic simplification and acceleration of vision-based controllers.
New framework for weakly supervised learning from label proportions.
problem Lack of consistent learning procedure and theoretical training criterion for LLP.
method Pose LLP as mutual contamination models (MCMs) and establish unbiased losses and generalization error bounds.
result Established novel technical results for MCMs and proposed a new experimental setting.