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Found 30 papers, 2 papers with code
Blessings and Curses of Covariate Shifts: Adversarial Learning Dynamics, Directional Convergence, and Equilibria
In particular, we establish two directional convergence results that exhibit distinctive phenomena: (1) a blessing in regression, the adversarial covariate shifts in an exponential rate to an optimal experimental design for rapid subsequent learning, (2) a curse in classification, the adversarial covariate shifts in a subquadratic rate fast to the hardest experimental design trapping subsequent learning.
High-dimensional Asymptotics of Langevin Dynamics in Spiked Matrix Models
We provide a "path-wise" characterization of the overlap between the output of the Langevin algorithm and the planted signal.
Online Learning to Transport via the Minimal Selection Principle
Motivated by robust dynamic resource allocation in operations research, we study the \textit{Online Learning to Transport} (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object.
Reversible Gromov-Monge Sampler for Simulation-Based Inference
Motivated by the seminal work on distance and isomorphism between metric measure spaces, we propose a new notion called the Reversible Gromov-Monge (RGM) distance and study how RGM can be used to design new transform samplers to perform simulation-based inference.
Universal Prediction Band via Semi-Definite Programming
We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model.
Interpolating Classifiers Make Few Mistakes
Under the assumption that the data is independently and identically distributed, the mistake bound implies that MNIC generalizes at a rate proportional to the norm of the interpolating solution and inversely proportional to the number of data points.
Deep Learning for Individual Heterogeneity: An Automatic Inference Framework
These functions are the key inputs into the finite-dimensional parameter of inferential interest.
Mehler's Formula, Branching Process, and Compositional Kernels of Deep Neural Networks
We utilize a connection between compositional kernels and branching processes via Mehler's formula to study deep neural networks.
A Precise High-Dimensional Asymptotic Theory for Boosting and Minimum-$\ell_1$-Norm Interpolated Classifiers
This paper establishes a precise high-dimensional asymptotic theory for boosting on separable data, taking statistical and computational perspectives.
Estimating Certain Integral Probability Metric (IPM) is as Hard as Estimating under the IPM
Curiously, we show that estimating the IPM itself between probability measures, is not significantly easier than estimating the probability measures under the IPM.
On the Multiple Descent of Minimum-Norm Interpolants and Restricted Lower Isometry of Kernels
We study the risk of minimum-norm interpolants of data in Reproducing Kernel Hilbert Spaces.
On the Minimax Optimality of Estimating the Wasserstein Metric
We study the minimax optimal rate for estimating the Wasserstein-$1$ metric between two unknown probability measures based on $n$ i. i. d.
Training Neural Networks as Learning Data-adaptive Kernels: Provable Representation and Approximation Benefits
The result formalizes the representation and approximation benefits of neural networks.
How Well Generative Adversarial Networks Learn Distributions
On the nonparametric end, we derive the optimal minimax rates for distribution estimation under the adversarial framework.
Deep Neural Networks for Estimation and Inference
We establish novel rates of convergence for deep feedforward neural nets.
Just Interpolate: Kernel "Ridgeless" Regression Can Generalize
In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly.
Local Optimality and Generalization Guarantees for the Langevin Algorithm via Empirical Metastability
For a particular local optimum of the empirical risk, with an arbitrary initialization, we show that, with high probability, at least one of the following two events will occur: (1) the Langevin trajectory ends up somewhere outside the $\varepsilon$-neighborhood of this particular optimum within a short recurrence time; (2) it enters this $\varepsilon$-neighborhood by the recurrence time and stays there until a potentially exponentially long escape time.
Interaction Matters: A Note on Non-asymptotic Local Convergence of Generative Adversarial Networks
Motivated by the pursuit of a systematic computational and algorithmic understanding of Generative Adversarial Networks (GANs), we present a simple yet unified non-asymptotic local convergence theory for smooth two-player games, which subsumes several discrete-time gradient-based saddle point dynamics.
How Well Can Generative Adversarial Networks Learn Densities: A Nonparametric View
We study in this paper the rate of convergence for learning densities under the Generative Adversarial Networks (GAN) framework, borrowing insights from nonparametric statistics.
Statistical Inference for the Population Landscape via Moment Adjusted Stochastic Gradients
Modern statistical inference tasks often require iterative optimization methods to compute the solution.
Fisher-Rao Metric, Geometry, and Complexity of Neural Networks
We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint.
Weighted Message Passing and Minimum Energy Flow for Heterogeneous Stochastic Block Models with Side Information
We develop an optimally weighted message passing algorithm to reconstruct labels for SBM based on the minimum energy flow and the eigenvectors of a certain Markov transition matrix.
Adaptive Feature Selection: Computationally Efficient Online Sparse Linear Regression under RIP
Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the squared loss.
On Detection and Structural Reconstruction of Small-World Random Networks
In this paper, we study detection and fast reconstruction of the celebrated Watts-Strogatz (WS) small-world random graph model \citep{watts1998collective} which aims to describe real-world complex networks that exhibit both high clustering and short average length properties.
Inference via Message Passing on Partially Labeled Stochastic Block Models
We study the community detection and recovery problem in partially-labeled stochastic block models (SBM).
Learning with Square Loss: Localization through Offset Rademacher Complexity
We consider regression with square loss and general classes of functions without the boundedness assumption.
Computational and Statistical Boundaries for Submatrix Localization in a Large Noisy Matrix
The second threshold, $\sf SNR_s$, captures the statistical boundary, below which no method can succeed with probability going to one in the minimax sense.
Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions
We consider the problem of optimizing an approximately convex function over a bounded convex set in $\mathbb{R}^n$ using only function evaluations.
Geometric Inference for General High-Dimensional Linear Inverse Problems
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion.
On Zeroth-Order Stochastic Convex Optimization via Random Walks
The method is based on a random walk (the \emph{Ball Walk}) on the epigraph of the function.
