New RL algorithms show model-based methods are more efficient than model-free ones in complex decision processes.
problem Efficient reinforcement learning in contextual decision processes with strategic exploration.
method Design of new model-based RL algorithms with sample complexity governed by witness rank.
result Exponential separation between model-based and model-free RL in some rich-observation settings.
OMLE combines optimism and MLE for efficient sequential decision making.
problem Efficiently solving sequential decision making problems, especially in partially observable settings.
method Combines optimism for exploration and maximum likelihood estimation for model learning.
result OMLE learns near-optimal policies for a wide range of sequential decision making problems.
New approach for neural models to be transparent over structured data.
problem Training neural models to be transparent in a functional manner.
method Setup as a cooperative game between a predictor and witnesses, encouraging local agreement.
result The predictor remains globally powerful while agreeing locally with witnesses.
Geometric framework for signed multivariate tail-dependence compatibility at various thresholds.
problem Modeling and analyzing signed multivariate tail-dependence across different thresholds.
method Developed a geometric witness framework to represent and invert signed tail families, identifying nonnegative weights and normalized masses.
result Characterization and synthesis of signed multivariate tail-dependence at finite thresholds, preserving the complete signed tail family throughout.
Proximal Mediation Analysis with Hidden Recanting Witnesses
problem Identifying path-specific effects in mediation analysis when recanting witnesses are unknown
method Proximal causal inference and semiparametric inference framework
result Developed three novel identification strategies and a semiparametric inference framework
Gradient Descent with small random initialization solves rank-1 matrix completion efficiently.
problem Matrix completion for rank-1 symmetric matrices.
method Gradient Descent with small random initialization.
result Gradient Descent converges to the ground truth for rank-1 symmetric matrix completion.
New graphs show hierarchical hyperbolic properties, extending previous work.
problem Characterizing hierarchically hyperbolic properties of multiarc and curve graphs.
method Analyzing the geometric intersection number and using PMod(S) action.
result Multiarc and curve graphs are hierarchically hyperbolic.
Proposes a method to learn from multiple views with low-rank embeddings.
problem Learning from multiple views with varying correlations is challenging.
method Multi-view Locality Low-rank Embedding (MvL2E) method that uses low-rank representations and centroid-based scheme.
result MvL2E achieves comparable performance with previous methods on benchmark datasets.
A new method detects hidden driving forces in systems with multiple observables.
problem Hidden driving forces in systems with multiple observables cannot be detected by scalar statistics.
method Cross-spectral witness for hidden nonequilibrium.
result Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to scalar reductions.
USD algorithm transports distributions with or without mass conservation.
problem Transporting distributions with different masses.
method Particle descent algorithm using Sobolev-Fisher discrepancy.
result USD converges to target distribution in MMD sense.
A new witness two-sample test improves data efficiency and power.
problem Nonparametric two-sample testing.
method Optimizes kernel and defines weights and basis points using training data.
result The new test is consistent, has well-controlled type-I error, and has comparable or higher power.
Loxodromic elements are pseudo-Anosov on specific graphs.
problem Characterizing loxodromic elements in specific groups.
method Analyzing subgroups acting on multiarc and curve graphs, and the handlebody group on disk graphs.
result Loxodromic elements are pseudo-Anosov on witness graphs.
AutoML simplifies two-sample tests for detecting distribution shifts.
problem Detecting distribution shifts between datasets.
method Uses mean discrepancy of a witness function with squared loss minimization.
result AutoML simplifies and improves two-sample testing performance.
Robust high-dimensional data processing has witnessed an exciting development in recent years, as theoretical results have shown that it is possible using convex programming to optimize data fit to a low-rank component plus a sparse outlier component. This problem is also known as Robust PCA, and it has found applicati…
Survey of reinforcement learning guarantees with data constraints.
problem Guaranteeing near-optimal policies with limited data in reinforcement learning.
method Coverage-Structure-Objective (CSO) framework to decompose sample complexity results.
result Progress on PAC guarantees for reinforcement learning, covering various models and settings.
Link's sphere number equals its bridge number.
problem Determining the minimum number of generators for a link's fundamental group.
method Using meridional presentations with embedded two-spheres in fixed diagrams.
result The minimum number of generators equals the bridge number.
Proposes MvLPE for better multi-view representation learning.
problem Learning representations from multi-view data with varying correlations.
method Integrates multi-view data into a centroid view while maintaining low-rank reconstruction relations.
result MvLPE outperforms existing methods on benchmark datasets.
The past decade has witnessed a successful application of deep learning to solving many challenging problems in machine learning and artificial intelligence. However, the loss functions of deep neural networks (especially nonlinear networks) are still far from being well understood from a theoretical aspect. In this pa…
Study on deleting user data in linear regression models to maintain limited memory.
problem Deleting user data in a limited time frame for statistical models.
method Proposed FIFD-OLS and FIFD-Adaptive Ridge algorithms for low-dimensional and online settings.
result Demonstrated effectiveness of FIFD-Adaptive Ridge in maintaining statistical efficiency.
New parallel algorithms optimize on manifolds, reducing communication costs.
problem Optimization on non-Euclidean spaces like manifolds.
method Generalized parallel inference algorithms for optimization on manifolds.
result Communication-efficient and convergent algorithms for manifold optimization.
In this paper we show that certain generalizations of the C r C^r C r -Whitney topology, which include the Hölder-Whitney and Sobolev-Whitney topologies on smooth manifolds, satisfy the Baire property, to wit, the countable intersection of open and dense sets is dense.
A new method for analyzing adaptive experiments using kernel treatment effects.
problem Efficiently analyzing adaptive experiments that adjust treatment assignments based on outcomes.
method Kernel Treatment Effects (KTE) framework combining RKHS scores and witness functions.
result Effective for both mean shifts and higher-moment differences, outperforming adaptive baselines.
Example shows dense subgroup of SL5(Z) not finitely presented.
problem Finding dense subgroups of SL5(Z) that are not finitely presented.
method Discussing an example of a Zariski-dense finitely generated subgroup of SL5(Z).
result Example shows a subgroup that is dense but not finitely presented.
A new framework reduces RL sample complexity for complex MDPs.
problem Handling large state and action spaces in reinforcement learning.
method Unified model-based and model-free RL framework with ABC class, novel estimation function, and functional eluder dimension.
result OPERA algorithm achieves sample-efficient regret bounds for various MDP models.
A new test detects differences between two distributions without flow.
problem Detecting differences between two distributions without flow.
method Zero-flow discrepancy (ZFD) and zero-flow two-sample test (ZF2ST).
result ZF2ST can detect strong differences in structured distributions.
This note shows how to transform high-probability to in-expectation guarantees in machine learning.
problem The challenge of constructing reliable machine learning models due to sampling randomness.
method Transforming high-probability to in-expectation guarantees using a witness condition for unbounded loss functions.
result A technical transformation method for generalization guarantees in machine learning.
Unified approach for multicalibration in weakly supervised learning.
problem Existing multicalibration methods require clean input-label pairs, which are unavailable in weakly supervised learning.
method Developed estimators and post-hoc correction methods for multicalibration under weak supervision.
result Unified framework for estimating and correcting multicalibration under weak supervision with finite-sample guarantees.
Paper develops efficient algorithms for zero-sum Markov games with general function classes.
problem Challenging settings in zero-sum Markov games with parameterized value functions or models.
method Developed new model-free and model-based algorithms for decoupled and coordinated settings.
result Improved sample complexity and regret bounds for various settings.
We present new, unified proofs for the cell-like, Z / p \mathbb{Z}/p Z / p -, and Q \mathbb{Q} Q -resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems involving cohomology groups by converting them into problems about homology groups…
Study shows how online personalization can lead to unfair models due to biased user responses.
problem Fairness issues in online personalization systems due to biased user responses.
method Formulated a regularization-based approach to mitigate biases in machine learning models.
result Demonstrated that online personalization can cause models to learn unfair behavior from biased user responses.
We present new excess risk bounds for general unbounded loss functions including log loss and squared loss, where the distribution of the losses may be heavy-tailed. The bounds hold for general estimators, but they are optimized when applied to η η η -generalized Bayesian, MDL, and empirical risk minimization estimators. …
New methods estimate causal effects through mediators, handling confounding without strict assumptions.
problem Estimating causal effects through mediators while accounting for unmeasured confounding.
method Developed four nonparametric identification strategies using proximal confounding bridge functions, efficient influence function, and quadruply robust estimator. Proposed proximal debiased machine learning approach for high-dimensional nuisance parameters.
result Achieved n \sqrt{n} n -consistency and asymptotic normality for path-specific effect estimation. Proposes DR-ME test for interpretable distributional treatment effects.
problem Detects invisible differences in treatment effects on distributional outcomes.
method Semiparametrically efficient finite-location test using kernel witnesses and orthogonal features.
result DR-ME reveals causal-discrepancy coordinates and has noncentral chi-square local power.
We study a continuous-time version of the intermediation model of Grossman and Miller (1988). To wit, we solve for the competitive equilibrium prices at which liquidity takers' demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an exogenous open market …
This article constructs the moduli stack of torsionfree G G G -jet-structures in homotopy type theory with one monadic modality. This yields a construction of this moduli stack for any ∞ \infty ∞ -topos equipped with any stable factorization systems. In the intended applications of this theory, the factorization systems are …
Foundation for learning in changing conditions.
problem Learning under varying conditions and states.
method Admissible transport, protected-core preservation, and evaluator-aware learning evolution.
result Established first theorem-supporting layer for regime-varying learning.
Given a closed simply connected manifold M M M of dimension 2 n ≥ 6 2n\ge6 2 n ≥ 6 , we compare the ring of characteristic classes of smooth oriented bundles with fibre M M M to the analogous ring resulting from replacing M M M by the connected sum M ♯ Σ M\sharpΣ M ♯Σ with an exotic sphere Σ Σ Σ . We show that, after inverting the order of Σ Σ Σ in the …
Proposes GFMMD for comparing signals on graphs.
problem Computing distances between distributions on graphs.
method Graph Fourier MMD (GFMMD) using optimal witness functions.
result Analytical solution and embedding of distributions.
A new method uses Hermite polynomials to improve machine learning models.
problem Improving the accuracy of machine learning models using non-positive kernels.
method Using multi-variate Hermite polynomials and a permutation test to approximate measures and classify data.
result The witness function method can reliably identify in-class vs out-of-class regions.
Sharp comparison for sub-Gaussian random variables in convex order.
problem Comparing sub-Gaussian random variables in convex order.
method Proving dominance using moment generating functions and convex functions.
result Sharp comparison established between specific sub-Gaussian random variables.
Optimal bounds proven for ordinal embedding convergence rate.
problem Optimal bounds for ordinal embedding convergence rate in 1D.
method Utilized results from additive number theory and conducted computational experiments.
result Proved optimal bounds for convergence rate in 1D.
Survey of DRO, a robust optimization framework.
problem Risk-aversion and chance-constrained optimization challenges.
method Distributionally robust optimization (DRO) framework.
result DRO's growing importance in operations research and statistics.
Oleg Viro studied in arXiv:math/0204290 two interpretations of the (multivariable) Alexander polynomial as a quantum link invariant: either by considering the quasi triangular Hopf algebra associated to U q s l ( 2 ) U_q sl(2) U q s l ( 2 ) at fourth roots of unity, or by considering the super Hopf algebra U q g l ( 1 ∣ 1 ) U_q gl(1|1) U q g l ( 1∣1 ) . In this paper, we show …
Survey on AI math foundations, focusing on neural networks.
problem Lack of rigorous mathematical foundation for AI.
method Survey and discussion of theoretical directions in AI.
result Discussion of open problems in AI math.
We propose a new NFT price index to track the digital art market.
problem Lack of a comprehensive NFT price index.
method Developed a new methodology to create a NFT Price Index.
result Demonstrated the dynamics and performances of NFT markets.
The study shows that several properties are not profinite invariants.
problem Determining which properties are profinite invariants.
method Combining Rips constructions and iterated group-theoretic Dehn filling on hyperbolic virtually special groups.
result Several properties (stable commutator length, quasimorphisms, property NL, property FW ∞ _\infty ∞ , property FA, and non-abelian free subgroups) are not profinite invariants. Transformer models improve query-document retrieval efficiency and accuracy.
problem Efficiently retrieve relevant documents from large corpora for query matching.
method Designed paragraph-level pre-training tasks to optimize embedding-based Transformer models.
result Transformer models significantly outperform BM-25 and non-Transformer embedding models.
A framework for analyzing financial systems under scenario constraints.
problem Quantifying worst-case and best-case performance in financial systems.
method Quantitative automata-based framework integrating event history automata and weighted finance finite automata.
result Exact calculation of upper and lower payoff bounds with interpretable witness event histories.