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Found 14 papers, 2 papers with code
Semi-Supervised U-statistics
Semi-supervised datasets are ubiquitous across diverse domains where obtaining fully labeled data is costly or time-consuming.
Revisiting Le Cam's Equation: Exact Minimax Rates over Convex Density Classes
We study the classical problem of deriving minimax rates for density estimation over convex density classes.
Adversarial Sign-Corrupted Isotonic Regression
We develop \texttt{ASCIFIT}, a three-step estimation procedure under the \texttt{ASCI} setting.
Non-Sparse PCA in High Dimensions via Cone Projected Power Iteration
Our numerical experiments on simulated and real data, show that our method achieves shorter run time and smaller error in comparison to the ordinary power iteration and some sparse principal component analysis algorithms if the principal eigenvector is in a convex cone.
High-Temperature Structure Detection in Ferromagnets
The goal is to distinguish whether the underlying graph is empty, i. e., the model consists of independent Rademacher variables, versus the alternative that the underlying graph contains a subgraph of a certain structure.
Misspecified Nonconvex Statistical Optimization for Phase Retrieval
Existing nonconvex statistical optimization theory and methods crucially rely on the correct specification of the underlying "true" statistical models.
Property Testing in High Dimensional Ising models
In terms of methodological development, we propose two types of correlation based tests: computationally efficient screening for ferromagnets, and score type tests for general models, including a fast cycle presence test.
Adaptive Inferential Method for Monotone Graph Invariants
In this paper, we propose a new inferential framework for testing nested multiple hypotheses and constructing confidence intervals of the unknown graph invariants under undirected graphical models.
Surrogate Aided Unsupervised Recovery of Sparse Signals in Single Index Models for Binary Outcomes
We consider the recovery of regression coefficients, denoted by $\boldsymbol{\beta}_0$, for a single index model (SIM) relating a binary outcome $Y$ to a set of possibly high dimensional covariates $\boldsymbol{X}$, based on a large but 'unlabeled' dataset $\mathcal{U}$, with $Y$ never observed.
Agnostic Estimation for Misspecified Phase Retrieval Models
The goal of noisy high-dimensional phase retrieval is to estimate an $s$-sparse parameter $\boldsymbol{\beta}^*\in \mathbb{R}^d$ from $n$ realizations of the model $Y = (\boldsymbol{X}^{\top} \boldsymbol{\beta}^*)^2 + \varepsilon$.
Combinatorial Inference for Graphical Models
We propose a new family of combinatorial inference problems for graphical models.
L1-Regularized Least Squares for Support Recovery of High Dimensional Single Index Models with Gaussian Designs
In the present paper we analyze algorithms based on covariance screening and least squares with $L_1$ penalization (i. e. LASSO) and demonstrate that they can also enjoy optimal (up to a scalar) rescaled sample size in terms of support recovery, albeit under slightly different assumptions on $f$ and $\varepsilon$ compared to the SIR based algorithms.
Signed Support Recovery for Single Index Models in High-Dimensions
When $s=O(p^{1-\delta})$ for some $\delta>0$, we demonstrate that both procedures can succeed in recovering the support of $\boldsymbol{\beta}$ as long as the rescaled sample size $\kappa=\frac{n}{s\log(p-s)}$ is larger than a certain critical threshold.
A Unified Theory of Confidence Regions and Testing for High Dimensional Estimating Equations
Our main theoretical contribution is to establish a unified Z-estimation theory of confidence regions for high dimensional problems.
