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Found 33 papers, 5 papers with code
Bayesian Analysis for Over-parameterized Linear Model without Sparsity
In high-dimensional Bayesian statistics, several methods have been developed, including many prior distributions that lead to the sparsity of estimated parameters.
Asymptotically Minimax Optimal Fixed-Budget Best Arm Identification for Expected Simple Regret Minimization
This result contrasts with the results of Bubeck et al. (2011), which shows that drawing each treatment arm with an equal ratio is minimax optimal in a bounded outcome setting.
Adversarially Slicing Generative Networks: Discriminator Slices Feature for One-Dimensional Optimal Transport
Generative adversarial networks (GANs) learn a target probability distribution by optimizing a generator and a discriminator with minimax objectives.
Best Arm Identification with Contextual Information under a Small Gap
We then develop the ``Random Sampling (RS)-Augmented Inverse Probability weighting (AIPW) strategy,'' which is asymptotically optimal in the sense that the probability of misidentification under the strategy matches the lower bound when the budget goes to infinity in the small-gap regime.
Benign Overfitting in Time Series Linear Model with Over-Parameterization
Then, we derive bounds of risks by the estimator for the cases where the temporal correlation of each coordinate of dependent data is homogeneous and heterogeneous, respectively.
Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regression
We study the benign overfitting theory in the prediction of the conditional average treatment effect (CATE), with linear regression models.
Unified Perspective on Probability Divergence via Maximum Likelihood Density Ratio Estimation: Bridging KL-Divergence and Integral Probability Metrics
This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE).
Optimal Best Arm Identification in Two-Armed Bandits with a Fixed Budget under a Small Gap
We show that a strategy following the Neyman allocation rule (Neyman, 1934) is asymptotically optimal when the gap between the expected rewards is small.
On generalization bounds for deep networks based on loss surface implicit regularization
We argue that under reasonable assumptions, the local geometry forces SGD to stay close to a low dimensional subspace and that this induces another form of implicit regularization and results in tighter bounds on the generalization error for deep neural networks.
Minimax Analysis for Inverse Risk in Nonparametric Planer Invertible Regression
The derived minimax rate corresponds to that of the non-invertible bi-Lipschitz function, which rejects the expectation of whether invertibility improves the minimax rate, similar to other shape constraints.
Exponential escape efficiency of SGD from sharp minima in non-stationary regime
An "escape efficiency" has been an attractive notion to tackle this question, which measures how SGD efficiently escapes from sharp minima with potentially low generalization performance.
Learning Causal Relationships from Conditional Moment Restrictions by Importance Weighting
We consider learning causal relationships under conditional moment restrictions.
Learning Causal Models from Conditional Moment Restrictions by Importance Weighting
To address this issue, we propose a method that transforms conditional moment restrictions to unconditional moment restrictions through importance weighting, using a conditional density ratio estimator.
Minimum sharpness: Scale-invariant parameter-robustness of neural networks
Toward achieving robust and defensive neural networks, the robustness against the weight parameters perturbations, i. e., sharpness, attracts attention in recent years (Sun et al., 2020).
Instrument Space Selection for Kernel Maximum Moment Restriction
Kernel maximum moment restriction (KMMR) recently emerges as a popular framework for instrumental variable (IV) based conditional moment restriction (CMR) models with important applications in conditional moment (CM) testing and parameter estimation for IV regression and proximal causal learning.
Asymptotic Risk of Overparameterized Likelihood Models: Double Descent Theory for Deep Neural Networks
We investigate the asymptotic risk of a general class of overparameterized likelihood models, including deep models.
Understanding Higher-order Structures in Evolving Graphs: A Simplicial Complex based Kernel Estimation Approach
In this paper, we overcome these obstacles by capturing higher-order interactions succinctly as \textit{simplices}, model their neighborhood by face-vectors, and develop a nonparametric kernel estimator for simplices that views the evolving graph from the perspective of a time process (i. e., a sequence of graph snapshots).
Finite Sample Analysis of Minimax Offline Reinforcement Learning: Completeness, Fast Rates and First-Order Efficiency
We offer a theoretical characterization of off-policy evaluation (OPE) in reinforcement learning using function approximation for marginal importance weights and $q$-functions when these are estimated using recent minimax methods.
Higher-order Structure Prediction in Evolving Graph Simplicial Complexes
In this paper, we overcome these obstacles by capturing higher-order interactions succinctly as simplices, model their neighborhood by face-vectors, and develop a nonparametric kernel estimator for simplices that views the evolving graph from the perspective of a time process (i. e., a sequence of graph snapshots).
On Gaussian Approximation for M-Estimator
This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions.
Statistics Theory Statistics Theory
Advantage of Deep Neural Networks for Estimating Functions with Singularity on Hypersurfaces
We develop a minimax rate analysis to describe the reason that deep neural networks (DNNs) perform better than other standard methods.
Instrumental Variable Regression via Kernel Maximum Moment Loss
We investigate a simple objective for nonlinear instrumental variable (IV) regression based on a kernelized conditional moment restriction (CMR) known as a maximum moment restriction (MMR).
Improved Generalization Bounds of Group Invariant / Equivariant Deep Networks via Quotient Feature Spaces
To describe the effect of invariance and equivariance on generalization, we develop a notion of a \textit{quotient feature space}, which measures the effect of group actions for the properties.
Improved Generalization Bound of Permutation Invariant Deep Neural Networks
Learning problems with data that are invariant to permutations are frequently observed in various applications, for example, point cloud data and graph neural networks.
Adaptive Approximation and Generalization of Deep Neural Network with Intrinsic Dimensionality
In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that determines the performance of deep neural networks (DNNs).
On Random Subsampling of Gaussian Process Regression: A Graphon-Based Analysis
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective.
Understanding GANs via Generalization Analysis for Disconnected Support
This paper focuses the situation where the target probability measure satisfies the disconnected support property, which means a separate support of a probability, and relates it with the advantage of GANs.
Deep Neural Networks Learn Non-Smooth Functions Effectively
We theoretically discuss why deep neural networks (DNNs) performs better than other models in some cases by investigating statistical properties of DNNs for non-smooth functions.
On Tensor Train Rank Minimization : Statistical Efficiency and Scalable Algorithm
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors.
Tensor Decomposition with Smoothness
Real data tensors are usually high dimensional but their intrinsic information is preserved in low-dimensional space, which motivates to use tensor decompositions such as Tucker decomposition.
On Tensor Train Rank Minimization: Statistical Efficiency and Scalable Algorithm
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors.
Consistent Nonparametric Different-Feature Selection via the Sparsest $k$-Subgraph Problem
We show that the proposed method is computationally efficient and does not require any extra computation for model selection.
Doubly Decomposing Nonparametric Tensor Regression
Nonparametric extension of tensor regression is proposed.
