Related papers: Adaptive testing on a regression function at a poi…

We study classification problems using binary estimators where the decision boundary is described by horizon functions and where the data distribution satisfies a geometric margin condition. A key novelty of our work is the derivation of…

This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…

We study the error in approximating the minimum of a Brownian motion on the unit interval based on finitely many point evaluations. We construct an algorithm that adaptively chooses the points at which to evaluate the Brownian path. In…

Given an i.i.d. sample $\{(X_i,Y_i)\}_{i \in \{1 \ldots n\}}$ from the random design regression model $Y = f(X) + \epsilon$ with $(X,Y) \in [0,1] \times [-M,M]$, in this paper we consider the problem of testing the (simple) null hypothesis…

We present a new active learning algorithm based on nonparametric estimators of the regression function. Our investigation provides probabilistic bounds for the rates of convergence of the generalization error achievable by proposed method…

An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…

In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or…

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

In model checking for regressions, nonparametric estimation-based tests usually have tractable limiting null distributions and are sensitive to oscillating alternative models, but suffer from the curse of dimensionality. In contrast,…

The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…

We study one-way matching of a pair of datasets with low rank signals. Under a stylized model, we first derive information-theoretic limits of matching under a mismatch proportion loss. We then show that linear assignment with projected…

In this paper, we study the stochastic probing problem under a general monotone norm objective. Given a ground set $U = [n]$, each element $i \in U$ has an independent nonnegative random variable $X_i$ with known distribution. Probing an…

For positive integers $n, d$, consider the hypergrid $[n]^d$ with the coordinate-wise product partial ordering denoted by $\prec$. A function $f: [n]^d \mapsto \mathbb{N}$ is monotone if $\forall x \prec y$, $f(x) \leq f(y)$. A function $f$…

Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high dimensional linear regression with random design. We first establish the convergence rates of the minimax expected…

The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…

Most methods for decision-theoretic online learning are based on the Hedge algorithm, which takes a parameter called the learning rate. In most previous analyses the learning rate was carefully tuned to obtain optimal worst-case…

We consider here together the inference questions and the change-point problem in Poisson autoregressions (see Tj{\o}stheim, 2012). The conditional mean (or intensity) of the process is involved as a non-linear function of it past values…

We study the problem of estimating the number of defective items in adaptive Group testing by using a minimum number of queries. We improve the existing algorithm and prove a lower bound that show that, for constant estimation, the number…