25th Annual Conference on Learning Theory Reconstruction from Anisotropic Random Measurements

Citations in the corpus

Breaking the curse of dimensionality in regression (2017, unknown): “By Theorem 6 in Rudelson and Zhou (2013) and the rate condition regarding s∗,γ and s∗,θ, there exists a constant κ > 0, such that P(Dn(s∗,θ, κ)) → 1 under Condition 1(i) and P(Dn(s∗,γ , κ))→ 1 under Condition 1(ii), where for s ≥ 1, Dn(s, κ) = { min J0⊆{1,··· ,p},|J0|≤s min δ 6=0,‖δJc0‖1≤‖δJ0‖1…”
Linear and conic programming estimators in high dimensional errors‐in‐variables models (2014, methodology): “An extension of the MU selector to generalized linear models is discussed in Sørensen et al. (2014). In Rosenbaum and Tsybakov (2013), a modification of the MU selector was suggested.”
Debiasing the lasso: Optimal sample size for Gaussian designs (2015, methodology): “L) f2Rp: 9S[p];jSj= s 0;k Sck 1 Lk Sk 1g: (15) 8 In high-dimension, the empirical covariance is singular. However, we can ask for non-singularityb of for vectors inb C(s 0;L). Rudelson and Zhou [RZ13] prove a reduction principle that bounds the restricted eigenvalues of the empirical covariance in t”
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, background): “See, for example, Rudelson and Zhou (2013) for details.”
Post-Selection Inference for Generalized Linear Models With Many Controls (2013, methodology): “Since the weights wi’s in the resulting weighted Lasso problem are estimated, with estimation errors depending upon the response variable di , estimation of the optimal instru- ment creates interesting technical challenges in the analysis of Lasso or Post-Lasso that are dealt with in the online Appe”
Statistical inference for model parameters in stochastic gradient descent (2016, unknown): “By [31], 1 nD ⊤ ·,−jD·,−j satisfies the Upper-RE condition in [20, Equation 2.”
Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, background): “1 = min RE(¯c) √ s kδ 2,N kδT k1 (3.2) Assumption 3.7 (RE(¯c)). For a given ¯c > 1, Restricted Eigenvalue is bounded from zero: κ(Q,T,˜ ¯c) > 0 Assumption 3.7 has been proven for i.i.d. case by Rudelson and Zhou (2013). We assume that it holds under plausible weak dependence conditions. Deﬁnit”
High-dimensional simultaneous inference with the bootstrap (2016, methodology): “Alternatively, by Maurey’s empirical method (Rudelson and Zhou 2013), (B3) and (A5) directly imply the compatibility condition for deterministic design.”
Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems (2013, background): “2 in [25] (see also [33] and [1]) for i.”
Orthogonal Machine Learning for Demand Estimation: High Dimensional Causal Inference in Dynamic Panels (2017, background): “1 = min RE(¯c) √ s kδ 2,N kδT k1 (3.2) Assumption 3.7 (RE(¯c)). For a given ¯c > 1, Restricted Eigenvalue is bounded from zero: κ(Q,T,˜ ¯c) > 0 Assumption 3.7 has been proven for i.i.d. case by Rudelson and Zhou (2013). We assume that it holds under plausible weak dependence conditions. Deﬁnit”
Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression (2018, methodology): “It is worth mentioning that the assumption of Rudelson and Zhou (2013) is that of jointly sub-Gaussian random vectors.”
Efficient Inference of Average Treatment Effects in High Dimensions via Approximate Residual Balancing (2016, methodology): “ et al., 2009;Hastie et al.,2015) that require X c to satisfy a form of the restricted eigenvalue condition. Below, we make a restricted eigenvalue assumption on 1=2 c ; then, we will use results fromRudelson and Zhou (2013) to verify that this also implies a restricted eigenvalue condition on X c. ”
Hypothesis Testing in High-Dimensional Regression Under the Gaussian Random Design Model: Asymptotic Theory (2013, background): “(Indeed Theorem 6 of [58] ensures that this holds with probability at least 1 − e− (n(p)), and hence almost surely for all p large enough by Borel-Cantelli lemma.”