New algorithm solves online resource allocation problems efficiently.
problem Dynamic resource allocation in operations research.
method Minimal Selection Principle and MSoE algorithm.
result Ensures optimal cumulative regret bounds in dynamic resource allocation.
PASTIS selects minimal models from stochastic dynamics data.
problem Overfitting in model selection for stochastic dynamics.
method Combining likelihood-estimation statistics with extreme value theory.
result PASTIS reliably identifies minimal models, even with low sampling rates or error.
We tackle the problem of penalty selection of regularization on the basis of the minimum description length (MDL) principle. In particular, we consider that the design space of the penalty function is high-dimensional. In this situation, the luckiness-normalized-maximum-likelihood(LNML)-minimization approach is favorab…
A new principle minimizes residual and introduces momentum to improve PDE solution dynamics.
problem Ill-conditioning in Dirac-Frenkel residual minimization leads to non-unique parameter dynamics.
method Introduces a history variable (momentum) to select better-conditioned parameter velocities, preserving residual minimization while promoting smooth parameter evolutions.
result The approach leads to increased robustness in singular and near-singular PDE solution regimes.
When applying the support vector machine (SVM) to high-dimensional classification problems, we often impose a sparse structure in the SVM to eliminate the influences of the irrelevant predictors. The lasso and other variable selection techniques have been successfully used in the SVM to perform automatic variable selec…
Minimal Morse functions on Poincaré dodecahedral space are selected via spectral properties.
problem Identifying minimal Morse functions on the Poincaré dodecahedral space.
method Spectral selection property P, obstruction principle, conformal variations, finite dimensional reduction.
result Restoration of minimal Morse selection on the Poincaré dodecahedral space via spectral mechanisms.
Stability is an important aspect of a classification procedure because unstable predictions can potentially reduce users' trust in a classification system and also harm the reproducibility of scientific conclusions. The major goal of our work is to introduce a novel concept of classification instability, i.e., decision…
New framework minimizes interference and selection bias in network A/B testing.
problem Interference and selection bias in network A/B testing.
method Proposes a principled framework that jointly minimizes interference and selection bias using edge spillover probability and cluster matching.
result Significantly lower error in causal effect estimation compared to existing solutions.
Minimizes indecisions in selective classification to control misclassification rates.
problem Controlling misclassification rates in high-risk scenarios.
method Using indecisions to control misclassification rates, even below Bayes optimal.
result Control of misclassification rates to any user-specified level, even below Bayes optimal.
We solve the paradox of score-based methods by minimizing path variance.
problem Score-based methods are path-dependent, leading to inaccurate and unstable estimators.
method Propose MVP Principle to minimize path variance, derive closed-form expression, and use flexible Kumaraswamy Mixture Model.
result Establishes new state-of-the-art results on challenging benchmarks.
In this paper we extend the results of "A strong minimax property of nondegenerate minimal submanifolds" by White, where it is proved that any smooth, compact submanifold, which is a strictly stable critical point for an elliptic parametric functional, is the unique minimizer in a certain geodesic tubular neighbourhood…
Bayesian approach optimizes in-context learning for state space models.
problem Optimizing in-context learning for state space models.
method Bayesian optimal sequential prediction over latent sequence tasks.
result Bayesian optimal predictor converges to posterior predictive mean.
Proves a principle for one-phase Bernoulli problem minimizers.
problem One-phase Bernoulli problem minimizers.
method Strong maximum principle, Alt-Caffarelli functional, Hardt-Simon-type foliation.
result Constructs a foliation for global minimizers.
Paper explores two methods for optimal portfolio selection in financial markets.
problem Optimal portfolio selection for financial markets with jumps.
method Maximum principle and dynamic programming approach.
result Relationship between two methods and their adjoint processes.
We introduce a new principle for model selection in regression and classification. Many regression models are controlled by some smoothness or flexibility or complexity parameter c, e.g. the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with polyno…
Directed graphical models provide a useful framework for modeling causal or directional relationships for multivariate data. Prior work has largely focused on identifiability and search algorithms for directed acyclic graphical (DAG) models. In many applications, feedback naturally arises and directed graphical models …
Hasse principle applied to area-minimizing submanifolds across different homology types.
problem Understanding the behavior of area-minimizing submanifolds in various homology contexts.
method Extending the Hasse principle from number theory to geometric variational problems.
result Recovering information about area-minimizing submanifolds in integral homology from those in real and mod n homology. Active inference minimizes expected free energy for optimal behavior.
problem Understanding and optimizing behavior in complex systems.
method Combines Bayesian decision theory, optimal Bayesian design, and the free energy principle.
result Active inference emerges as a unified framework for information-seeking, utility maximization, and goal-directed behavior.
New margin-based regularization and selective sampling improve deep neural network performance.
problem Improving deep neural network performance on various classification tasks.
method Multi-margin regularization (MMR) and minimal margin score (MMS) for selective sampling.
result Improved results on multiple classification tasks across domains.
Study shows strong min-max principle for phase transitions.
problem Understanding nodal sets near minimal hypersurfaces.
method Analogous to White's principle, applies to Allen-Cahn energy.
result Strong min-max principle for phase transitions.
Unified approach for selecting summary statistics in ABC.
problem Efficient inference from large datasets in likelihood-free methods.
method Characterizing and unifying three classes of summary statistics, minimizing expected posterior entropy.
result EPE-minimizing summaries lead to competitive posterior inference.
The study proves a strong parametric h-principle for minimal surfaces.
problem Proving a parametric h-principle for minimal surfaces.
method Using a parametric h-principle due to Forstneric and Larusson.
result The space of complete nonflat conformal minimal immersions has the same homotopy type as the space of continuous maps.
The paper proves the law of one price in a continuous-time setting without friction.
problem Identifying conditions under which the law of one price holds in a continuous-time setting without frictions.
method Formulating a new mechanism for LOP failure and proving a novel variant of the uniform boundedness principle.
result Establishes the equivalence of the economic concept of LOP with the probabilistic property of the existence of a local $\scr{E}$-martingale state price density.
The thesis optimizes quantum state exploration using bandit algorithms.
problem Maximizing reward in online learning of quantum state properties.
method Multi-armed bandit approach to select observables, minimizing regret.
result Optimal strategies with matching upper and lower bounds for regret.
Improves Gaussian process regression without bias.
problem Bias in Gaussian process regression estimates.
method Adaptive computation selection to minimize bias.
result Guaranteed small bias in log marginal likelihood estimates.
A new method for selective classification trades off accuracy for coverage.
problem Selective classification allows a classifier to abstain from predicting some instances.
method Optimizes a collection of class-wise decoupled one-sided empirical risks.
result The method achieves near-optimal coverage in high target accuracy regimes.
Study finds volume minimization principle for conical Calabi-Yau structures on horospherical cones.
problem Existence and classification of conical Calabi-Yau structures on horospherical cones.
method Variational approach to establish equivalence between volume minimization and existence of conical Calabi-Yau structures.
result Existence of many irregular horospherical cones with mild singularities.
A new strategy selects k in k-NN regression without hold-out data.
problem Choosing optimal k in k-NN regression without hold-out data.
method Iterative procedure over k, minimum discrepancy principle.
result Minimax-optimal over smoothness function classes.
Bayesian principles improve neural additive models for better feature selection and uncertainty.
problem Lack of calibrated uncertainties and feature selection in neural additive models.
method Augmenting NAMs with Bayesian principles to provide credible intervals, feature selection, and interaction ranking.
result Improved performance on tabular datasets and real-world medical tasks.
Minimal surfaces reflect across spheres, proving annulus uniqueness.
problem Uniqueness of free boundary minimal annuli in balls.
method Reflection principle applied to minimal surfaces meeting spheres at 90 degrees.
result Every embedded free boundary minimal annulus in a ball is the critical catenoid.
Hutter (2007) recently introduced the loss rank principle (LoRP) as a generalpurpose principle for model selection. The LoRP enjoys many attractive properties and deserves further investigations. The LoRP has been well-studied for regression framework in Hutter and Tran (2010). In this paper, we study the LoRP for clas…
Study compares nodal sets of solutions to the Allen-Cahn equation.
problem Comparing nodal sets of solutions to the Allen-Cahn equation with conical asymptotics.
method Maximum principle for linearized operator on unbounded domains.
result Positive phase uniquely determines the solution and enforces global ordering.
We prove a reflection principle for minimal surfaces in smooth (non necessarily analytic) three manifolds and we give an explicit application when the ambient space is just a smooth manifold.
We give a proof of the classical Schwarz reflection principle for Jenkins-Serrin type minimal surfaces in the homogeneous three manifolds E(κ,τ) for κ⩽0 and τ⩾0. In our previous paper we proved a reflection principle in Riemannian manifolds. The statements and techniques in the two papers are d…
The h-principle helps solve complex geometric problems.
problem Solving complex geometric problems using the h-principle.
method Developed from the Oka-Grauert principle and Gromov's theory, the h-principle is applied to Oka manifolds and maps.
result Recent developments and applications of the h-principle in complex analysis and geometry.
A new active learning method considers both uncertainty and diversity to minimize labeling and decision costs.
problem Classical AL approaches fail to capture data distribution in unlabeled data, leading to mislabeling of outliers.
method CBAL considers classification uncertainty and instance diversity, using a min-max approach to minimize labeling and decision costs.
result Extensive experiments show CBAL outperforms state-of-the-art AL approaches.
A new principle for optimizer selection improves training speed and performance.
problem Finding the best optimizer hyperparameters for faster training.
method Formulate optimizer selection as maximizing the expected drop rate in loss, treating gradients and updates as signals and an optimizer as a causal filter.
result Greedy optimizer selection yields stable and effective momentum rules.
We establish a boundary maximum principle for free boundary minimal submanifolds in a Riemannian manifold with boundary, in any dimension and codimension. Our result holds more generally in the context of varifolds.
The paper proves a nonholonomic version of Maupertuis-Jacobi principle and shows that nonholonomic trajectories minimize length.
problem Nonholonomic dynamics and their length minimization.
method Contact bundle formulation and geometric equivalence between problems.
result Regular solutions of nonholonomic mechanical problems are reparametrizations of geodesics with minimized Riemannian length.
BoostTransformer uses boosting to improve transformer efficiency and accuracy.
problem Heavy computational resources and hyperparameter tuning in transformer architectures.
method Augments transformers with boosting principles through subgrid token selection and importance-weighted sampling, incorporating a least square boosting objective directly into the pipeline.
result BoostTransformer demonstrates faster convergence and higher accuracy compared to standard transformers.
The choice of activation function can significantly influence the performance of neural networks. The lack of guiding principles for the selection of activation function is lamentable. We try to address this issue by introducing our variational neural networks, where the activation function is represented as a linear c…
Eliashberg simplifies singularities in geometry.
problem Complex singularities in geometric structures.
method Philosophy of the h-principle and simplification techniques.
result Simplified understanding of singularities in geometry.
Extends Smale's principle to produce minimal graphs with singularities.
problem Creating minimal graphs with isolated singularities in higher dimensions.
method Extends Smale's singular bridge principle to arbitrary codimension and applies it to specific minimal cones.
result Produces a minimal graph in 7D with any number of isolated singularities.
Based on works by Hopf, Weinberger, Hamilton and Evans, we state and prove the strong elliptic maximum principle for smooth sections in vector bundles over Riemannian manifolds and give some applications in Differential Geometry. Moreover, we use this maximum principle to obtain various rigidity theorems and Bernstein …
We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has recently turned out that they are in fact robust against various types of model un…
The paper explains how data augmentation can improve domain generalization by weakening spurious correlations.
problem Machine learning models trained with observational data fail to generalize to unseen domains due to spurious correlations.
method Developed a causal perspective to explain the success of data augmentation and derived an algorithm to select effective augmentation techniques.
result Data augmentation can be used to simulate interventional data, leading to better domain generalization.
A framework for efficient multi-objective optimization using entropy search.
problem Optimizing expensive black-box functions with multiple objectives.
method Output space entropy search (OSE) to minimize resource cost.
result Improves efficiency and accuracy in multi-objective optimization.
We provide a probabilistic approach to studying minimal surfaces in three-dimensional Euclidean space. Following a discussion of the basic relationship between Brownian motion on a surface and minimality of the surface, we introduce a way of coupling Brownian motions on two minimal surfaces. This coupling is then used …