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We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity…
The deep-learning-based least squares method has shown successful results in solving high-dimensional non-linear partial differential equations (PDEs). However, this method usually converges slowly. To speed up the convergence of this…
This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: -We establish new minimax-rates for active learning under common…
We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and…
We consider the problem of learning a target function corresponding to a single hidden layer neural network, with a quadratic activation function after the first layer, and random weights. We consider the asymptotic limit where the input…
Active learning is an established technique to reduce the labeling cost to build high-quality machine learning models. A core component of active learning is the acquisition function that determines which data should be selected to…
Active learning is a machine learning paradigm that aims to improve the performance of a model by strategically selecting and querying unlabeled data. One effective selection strategy is to base it on the model's predictive uncertainty,…
We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting by combining marginal leverage score sampling with non-independent sampling strategies that promote spatial coverage. In particular, we…
Recently, deep learning-based algorithms are widely adopted due to the advantage of being able to establish anomaly detection models without or with minimal domain knowledge of the task. Instead, to train the artificial neural network more…
Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…
We focus on training machine learning regression models in scenarios where the availability of labeled training data is limited due to computational constraints or high labeling costs. Thus, selecting suitable training sets from unlabeled…
We propose an active-learning method for nonlinear minimax regression. Given a nonlinear function that can be arbitrarily evaluated over a compact set, we fit a surrogate model, such as a feedforward neural network, by minimizing the…
Active learning is typically used to label data, when the labeling process is expensive. Several active learning algorithms have been theoretically proved to perform better than their passive counterpart. However, these algorithms rely on…
Estimation of the density of regression errors is a fundamental issue in regression analysis and it is typically explored via a parametric approach. This article uses a nonparametric approach with the mean integrated squared error (MISE)…
Active learning can reduce the number of samples needed to perform a hypothesis test and to estimate the parameters of a model. In this paper, we revisit the work of Chernoff that described an asymptotically optimal algorithm for performing…
Adaptive bandwidth selection is a fundamental challenge in nonparametric regression. This paper introduces a new bandwidth selection procedure inspired by the optimality criteria for $\ell_0$-penalized regression. Although similar in spirit…
There is a large body of work on convergence rates either in passive or active learning. Here we first outline some of the main results that have been obtained, more specifically in a nonparametric setting under assumptions about the…
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of feedforward neural network. There are several interesting characteristics for the proposed estimator. First, the loss function is…
We propose a new active learning algorithm for parametric linear regression with random design. We provide finite sample convergence guarantees for general distributions in the misspecified model. This is the first active learner for this…