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 -generalized Bayesian, MDL, and empirical risk minimization estimators. …
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48 results for “witness condition”
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.
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.
We provide a new approach to training neural models to exhibit transparency in a well-defined, functional manner. Our approach naturally operates over structured data and tailors the predictor, functionally, towards a chosen family of (local) witnesses. The estimation problem is setup as a co-operative game between an …
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
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.
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.
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.
Proposes a new method to analyze the distributional effects of treatments.
problem Analyzing the full distributional impact of treatments beyond just the mean.
method Uses kernel conditional mean embeddings and U-statistic regression to investigate the CoDiTE.
result Demonstrates the effectiveness of the proposed method through experiments.
New proof shows equality in spacetime mass theorem.
problem Proving the equality case of spacetime positive mass theorem.
method Uses a new approach requiring only for near initial data sets.
result Initial data sets with null ADM energy-momentum must embed into Minkowski space.
One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been adjusted for. We introduce a novel approach for estimating causal effects that explo…
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.
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.
In this paper, we study the problem of structure learning for Bayesian networks in which nodes take discrete values. The problem is NP-hard in general but we show that under certain conditions we can recover the true structure of a Bayesian network with sufficient number of samples. We develop a mathematical model whic…
The paper formalizes robot environments using topological concepts.
problem Determining indistinguishable environments for robots.
method Formalizing robot systems as topological dynamical systems, using covering maps and bisimulation.
result Covering maps can witness indistinguishability of environments under general conditions.
In this paper we show that certain generalizations of the -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.
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…
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.
New bounds for non-convex estimators without Bernstein condition.
problem Sharp excess risk bounds for non-convex and improper estimators.
method Exponential-tail local Rademacher complexity risk bounds with offset condition.
result Sharp bounds for non-convex and improper estimators without Bernstein condition.
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.
We study the sample complexity of model-based reinforcement learning (henceforth RL) in general contextual decision processes that require strategic exploration to find a near-optimal policy. We design new algorithms for RL with a generic model class and analyze their statistical properties. Our algorithms have sample …
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 proposes methods to improve graph domain adaptation by decorrelating node features.
problem Challenges in transferring knowledge from one graph to another.
method Proposes decorrelating node features using GCN and graph transformer layers.
result Significant performance enhancements and clear visualizations of learned representations.
We present new, unified proofs for the cell-like, -, and -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…
The paper proposes a method to learn the structure of continuous-action games with non-parametric utilities using a limited number of samples.
problem Learning the exact structure of continuous-action games with non-parametric utility functions.
method An regularized method that encourages sparsity of the Fourier transform coefficients of the utility functions, accessed via a few Nash equilibria and their noisy utilities.
result The method recovers the exact structure of the utility functions and the game structure with provable theoretical guarantees.
We demonstrate that the primal-dual witness proof method may be used to establish variable selection consistency and -bounds for sparse regression problems, even when the loss function and/or regularizer are nonconvex. Using this method, we derive two theorems concerning support recovery and -…
Enhanced Momentum Transformer outperforms traditional trading strategies.
problem Improving trading performance in equities with evolving market conditions.
method Building a Momentum Transformer using an attention mechanism combined with LSTM, capturing long-term dependencies and transaction costs.
result Average returns of 4.14% and Sharpe ratio of 1.12, similar to original results but with higher volatility.
We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number theory on sets of integers with no three-term arithmetic progressions. We also carr…
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 -consistency and asymptotic normality for path-specific effect estimation.
The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimizat…
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.
In machine learning, we are given a dataset of the form , drawn as i.i.d. samples from an unknown probability distribution ; the marginal distribution for the 's being . We propose that rather than using a positive kernel such as the Gaussian for estimation of these…
Nuisance Function Tuning and Sample Splitting for Optimally Estimating a Doubly Robust Functionalmath.ST
Optimally estimates a functional using nuisance function tuning and sample splitting.
problem Estimating optimal rates for a doubly robust functional.
method Combines nuisance function tuning and sample splitting strategies.
result Shows optimal rates of convergence for various estimators.
Graph Cascades rewire graphs to improve structure-aware learning.
problem Improving graph neural networks and transformers for structure-aware learning.
method Graph Cascades uses contagion-based diffusion processes to construct an auxiliary graph with reinforced edges.
result Graph Cascades improves node-classification benchmarks across various graph types.
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 -jet-structures in homotopy type theory with one monadic modality. This yields a construction of this moduli stack for any -topos equipped with any stable factorization systems. In the intended applications of this theory, the factorization systems are …
Tabular Data Contrastive Learning via Class-Conditioned and Feature-Correlation Based Augmentationcs.LG
Improves tabular data augmentation for contrastive learning.
problem Ineffective augmentation techniques for tabular data.
method Class-conditioned and feature-correlation based augmentation.
result Consistently outperforms conventional corruption methods.
Given a closed simply connected manifold of dimension , we compare the ring of characteristic classes of smooth oriented bundles with fibre to the analogous ring resulting from replacing by the connected sum with an exotic sphere . We show that, after inverting the order of 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.
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.
Paper proposes MIM-DRCFR to learn disentangled factors for better treatment effect estimation.
problem Learning disentangled factors precisely for individual-level treatment effect estimation.
method Multi-task learning framework with MI minimization criteria.
result MIM-DRCFR outperforms state-of-the-art methods in treatment effect estimation.
It is feasible and practically-valuable to bridge the characteristics between graph neural networks (GNNs) and logical reasoning. Despite considerable efforts and successes witnessed to solve Boolean satisfiability (SAT), it remains a mystery of GNN-based solvers for more complex predicate logic formulae. In this work,…
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 at fourth roots of unity, or by considering the super Hopf algebra . In this paper, we show …