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Isotonic regression in general dimensions
We study the least squares regression function estimator over the class of real-valued functions on $[0,1]^d$ that are increasing in each coordinate. For uniformly bounded signals and with a fixed,Expand
Convergence rates of least squares regression estimators with heavy-tailed errors
We study the performance of the Least Squares Estimator (LSE) in a general nonparametric regression model, when the errors are independent of the covariates but may only have a $p$-th moment ($p\geqExpand
In this paper, we study the approximation and estimation of s-concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s-concave density existsExpand
Multivariate convex regression: global risk bounds and adaptation
We study the problem of estimating a multivariate convex function defined on a convex body in a regression setting with random design. We are interested in optimal rates of convergence under aExpand
Exploiting Tradeoffs for Exact Recovery in Heterogeneous Stochastic Block Models
We exploit the tradeoffs among the various parameters of heterogenous SBM and provide recovery guarantees for many new interesting SBM configurations that are efficiently recoverable via semidefinite programs. Expand
Relative Density and Exact Recovery in Heterogeneous Stochastic Block Models
The Stochastic Block Model (SBM) is a widely used random graph model for networks with communities. Despite the recent burst of interest in recovering communities in the SBM from statistical andExpand
A sharp multiplier inequality with applications to heavy-tailed regression problems
∥ F is determined jointly by the growth rate of the corresponding empirical process, and the size of the maxima of the multipliers. The new inequality sheds light on the long-standing open questionExpand
Global empirical risk minimizers with "shape constraints" are rate optimal in general dimensions
Entropy integrals are widely used as a powerful tool to obtain upper bounds for the rates of convergence of global empirical risk minimizers (ERMs), in standard settings such as density estimationExpand
Robustness of shape-restricted regression estimators: an envelope perspective
Classical least squares estimators are well-known to be robust with respect to moment assumptions concerning the error distribution in a wide variety of finite-dimensional statistical problems;Expand
On a phase transition in general order spline regression
In the Gaussian sequence model $Y= \theta_0 + \varepsilon$ in $\mathbb{R}^n$, we study the fundamental limit of approximating the signal $\theta_0$ by a class $\Theta(d,d_0,k)$ of (generalized)Expand