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 …
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48 results for “Witness Function”
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
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.
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.
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.
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.
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.
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.
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. …
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.
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.
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.
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…
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…
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 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.
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.
Computing Nash equilibrium (NE) of multi-player games has witnessed renewed interest due to recent advances in generative adversarial networks. However, computing equilibrium efficiently is challenging. To this end, we introduce the Gradient-based Nikaido-Isoda (GNI) function which serves: (i) as a merit function, vani…
The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-base…
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.
Gaussian processes (GPs) have been proven to be powerful tools in various areas of machine learning. However, there are very few applications of GPs in the scenario of multi-view learning. In this paper, we present a new GP model for multi-view learning. Unlike existing methods, it combines multiple views by regularizi…
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.
Machine learning has witnessed tremendous success in solving tasks depending on a single hyperparameter. When considering simultaneously a finite number of tasks, multi-task learning enables one to account for the similarities of the tasks via appropriate regularizers. A step further consists of learning a continuum of…
NVGD uses neural networks to infer distributions without kernel choices.
problem Challenges in choosing kernel functions for SVGD.
method NVGD parameterizes the witness function of the Stein discrepancy with a neural network.
result NVGD achieves good performance on various inference problems.
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 …
MM for Penalized Estimationstat.CO
Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The majorization-minimization (MM) algorithm is a computational scheme for stability and simplicity, and …
Survey on quantum computing and neural networks.
problem Understanding and comparing quantum computing and neural networks.
method Introduction to quantum computing concepts, explanation of quantum computing paradigms, and analysis of quantum neural networks.
result Current state-of-the-art in quantum neural networks.
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.
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…
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 -…
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…
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.
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.
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…
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.
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.
Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce the R package BDgraph which performs Bayesian structure learning for general undirected graphical models (decomposable and non-decom…
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.
This paper extends geometric study of neural networks to non-differentiable layers and random walks.
problem Understanding the geometric properties of neural networks, especially those with non-differentiable activation functions.
method Singular Riemannian geometry approach to convolutional, residual, and recursive neural networks.
result Illustrated geometric findings with numerical experiments on image classification and thermodynamic problems.
AdaDetectGPT improves text authorship detection with statistical guarantees.
problem Determining if text is authored by a human or an LLM.
method Adaptive learning of a witness function from training data to enhance logits-based detectors.
result AdaDetectGPT nearly uniformly improves text authorship detection, with up to 37% improvement.
Face recall is a basic human cognitive process performed routinely, e.g., when meeting someone and determining if we have met that person before. Assisting a subject during face recall by suggesting candidate faces can be challenging. One of the reasons is that the search space - the face space - is quite large and lac…
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 …
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.
Study compares adaptive vs fixed query learning methods.
problem Comparing adaptive and fixed query learning methods for task approximation.
method Examined in-context and agentic learning in two settings: unrestricted and realizable.
result Adaptivity does not hinder performance in unrestricted setting but can in realizable setting.