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Found 30 papers, 1 papers with code
The Sample Complexity of Simple Binary Hypothesis Testing
In this paper, we derive a formula that characterizes the sample complexity (up to multiplicative constants that are independent of $p$, $q$, and all error parameters) for: (i) all $0 \le \alpha, \beta \le 1/8$ in the prior-free setting; and (ii) all $\delta \le \alpha/4$ in the Bayesian setting.
Robust empirical risk minimization via Newton's method
A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing literature on robust mean estimation for multivariate data.
Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraints
For the sample complexity of simple hypothesis testing under pure LDP constraints, we establish instance-optimal bounds for distributions with binary support; minimax-optimal bounds for general distributions; and (approximately) instance-optimal, computationally efficient algorithms for general distributions.
Communication-constrained hypothesis testing: Optimality, robustness, and reverse data processing inequalities
We show that the sample complexity of simple binary hypothesis testing under communication constraints is at most a logarithmic factor larger than in the unconstrained setting and this bound is tight.
On the identifiability of mixtures of ranking models
Mixtures of ranking models are standard tools for ranking problems.
Differentially private inference via noisy optimization
We propose a general optimization-based framework for computing differentially private M-estimators and a new method for constructing differentially private confidence regions.
Robust W-GAN-Based Estimation Under Wasserstein Contamination
Robust estimation is an important problem in statistics which aims at providing a reasonable estimator when the data-generating distribution lies within an appropriately defined ball around an uncontaminated distribution.
Robust regression with covariate filtering: Heavy tails and adversarial contamination
We study the problem of linear regression where both covariates and responses are potentially (i) heavy-tailed and (ii) adversarially contaminated.
Provable Training Set Debugging for Linear Regression
We first formulate a general statistical algorithm for identifying buggy points and provide rigorous theoretical guarantees under the assumption that the data follow a linear model.
Boosting Algorithms for Estimating Optimal Individualized Treatment Rules
We present nonparametric algorithms for estimating optimal individualized treatment rules.
Extracting robust and accurate features via a robust information bottleneck
We propose a novel strategy for extracting features in supervised learning that can be used to construct a classifier which is more robust to small perturbations in the input space.
Robustifying deep networks for image segmentation
Materials and Methods: In this retrospective study, the accuracy of brain tumor segmentation was studied in subjects with low- and high-grade gliomas.
Estimating location parameters in entangled single-sample distributions
In the multivariate setting, we generalize our theory to mean estimation for mixtures of radially symmetric distributions, and derive minimax lower bounds on the expected error of any estimator that is agnostic to the scales of individual data points.
Does Data Augmentation Lead to Positive Margin?
Data augmentation (DA) is commonly used during model training, as it significantly improves test error and model robustness.
Scale calibration for high-dimensional robust regression
However, the variance of the error term in the linear model is intricately connected to the optimal parameter used to define the shape of the Huber loss.
Adversarial Risk Bounds via Function Transformation
We derive bounds for a notion of adversarial risk, designed to characterize the robustness of linear and neural network classifiers to adversarial perturbations.
Online learning with graph-structured feedback against adaptive adversaries
When the adversary is allowed a bounded memory of size 1, we show that a matching lower bound of $\widetilde\Omega(T^{2/3})$ is achieved in the case of full-information feedback.
Graph-Based Ascent Algorithms for Function Maximization
We also provide simulations showing the relative convergence rates of our algorithms in comparison to an unbiased random walk, as a function of the smoothness of the graph function.
Generalization Error Bounds for Noisy, Iterative Algorithms
In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data.
Computing and maximizing influence in linear threshold and triggering models
We quantify the gap between our upper and lower bounds in the case of the linear threshold model and illustrate the gains of our upper bounds for independent cascade models in relation to existing results.
Adversarial Influence Maximization
We consider the problem of influence maximization in fixed networks for contagion models in an adversarial setting.
Confidence Sets for the Source of a Diffusion in Regular Trees
At the core of our proofs is a probabilistic analysis of P\'{o}lya urns corresponding to the number of uninfected neighbors in specific subtrees of the infection tree.
On model misspecification and KL separation for Gaussian graphical models
We establish bounds on the KL divergence between two multivariate Gaussian distributions in terms of the Hamming distance between the edge sets of the corresponding graphical models.
Statistical consistency and asymptotic normality for high-dimensional robust M-estimators
We first establish a form of local statistical consistency for the penalized regression estimators under fairly mild conditions on the error distribution: When the derivative of the loss function is bounded and satisfies a local restricted curvature condition, all stationary points within a constant radius of the true regression vector converge at the minimax rate enjoyed by the Lasso with sub-Gaussian errors.
Support recovery without incoherence: A case for nonconvex regularization
We demonstrate that the primal-dual witness proof method may be used to establish variable selection consistency and $\ell_\infty$-bounds for sparse regression problems, even when the loss function and/or regularizer are nonconvex.
Concavity of reweighted Kikuchi approximation
We establish sufficient conditions for the concavity of our reweighted objective function in terms of weight assignments in the Kikuchi expansion, and show that a reweighted version of the sum product algorithm applied to the Kikuchi region graph will produce global optima of the Kikuchi approximation whenever the algorithm converges.
High-dimensional learning of linear causal networks via inverse covariance estimation
We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model.
Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima
We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions.
Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses
We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph.
High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity
On the statistical side, we provide non-asymptotic bounds that hold with high probability for the cases of noisy, missing, and/or dependent data.
