Related papers: Nonlinear Regression without i.i.d. Assumption
Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…
This article considers nonparametric regression models with multivariate covariates and with responses missing at random. We estimate the regression function with a local polynomial smoother. The residual-based empirical distribution…
In randomized controlled trials without interference, regression adjustment is widely used to enhance the efficiency of treatment effect estimation. This paper extends this efficiency principle to settings with network interference, where a…
Nonparametric and machine learning methods are flexible methods for obtaining accurate predictions. Nowadays, data sets with a large number of predictors and complex structures are fairly common. In the presence of item nonresponse,…
We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We assume that objects are endowed with intrinsic qualities and that the probability with which an object…
We study a class of statistical inverse problems with non-linear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the non-linearity.…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs…
Isotonic distributional regression (IDR) is a powerful nonparametric technique for the estimation of conditional distributions under order restrictions. In a nutshell, IDR learns conditional distributions that are calibrated, and…
Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas,…
We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…
We revisit a classical assumption for analyzing stochastic gradient algorithms where the squared norm of the stochastic subgradient (or the variance for smooth problems) is allowed to grow as fast as the squared norm of the optimization…
Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications.…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
Many machine learning techniques rely on minimizing the covariance between output feature dimensions to extract minimally redundant representations from data. However, these methods do not eliminate all dependencies/redundancies, as…
Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax…
We provide algorithms for regression with adversarial responses under large classes of non-i.i.d. instance sequences, on general separable metric spaces, with provably minimal assumptions. We also give characterizations of learnability in…
This paper studies the problem of nonparametric estimation of a smooth function with data distributed across multiple machines. We assume an independent sample from a white noise model is collected at each machine, and an estimator of the…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…