Related papers: On the Post Selection Inference constant under Res…

Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…

In this paper, we estimate the high dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator (SCIO) estimator \cite{liu2015fast} and derive its…

In this paper, we address the question of information preservation in ill-posed, non-linear inverse problems, assuming that the measured data is close to a low-dimensional model set. We provide necessary and sufficient conditions for the…

As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm…

For propensity score analysis and sparse estimation, we develop an information criterion for determining the regularization parameters needed in variable selection. First, for Gaussian distribution-based causal inference models, we extend…

Partially observable Markov decision processes (POMDPs) are a general framework for sequential decision-making under latent state uncertainty, yet learning in POMDPs is intractable in the worst case. Motivated by sensing and probing…

The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression…

We present simple low-level conditions for identification in regression discontinuity designs using a potential outcome framework for the manipulation of the running variable. Using this framework, we replace the existing identification…

It is in general challenging to provide confidence intervals for individual variables in high-dimensional regression without making strict or unverifiable assumptions on the design matrix. We show here that a "group-bound" confidence…

We present a new method for post-selection inference for L1 (lasso)-penalized likelihood models, including generalized regression models. Our approach generalizes the post-selection framework presented in Lee et al (2014). The method…

Inequalities may appear in many models. They can be as simple as assuming a parameter is nonnegative, possibly a regression coefficient or a treatment effect. This paper focuses on the case that there is only one inequality and proposes a…

Investigators often use the data to generate interesting hypotheses and then perform inference for the generated hypotheses. P-values and confidence intervals must account for this explorative data analysis. A fruitful method for doing so…

Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…

We present a framework for the theoretical analysis of ensembles of low-complexity empirical risk minimisers trained on independent random compressions of high-dimensional data. First we introduce a general distribution-dependent…

Some consequences of the Restricted Isometry Property (RIP) of matrices have been applied to develop a greedy algorithm called "ROMP" (Regularized Orthogonal Matching Pursuit) to recover sparse signals and to approximate non-sparse ones.…

The performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space is analyzed. Support recovery is formulated as a multiple-hypothesis testing problem. Both upper and lower…

We consider statistical inference for impulse responses in sparse, structural high-dimensional vector autoregressive (SVAR) systems. We introduce consistent estimators of impulse responses in the high-dimensional setting and suggest valid…

Conformal inference is a popular tool for constructing prediction intervals (PI). We consider here the scenario of post-selection/selective conformal inference, that is PIs are reported only for individuals selected from an unlabeled test…

This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…

Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…