Related papers: Consistent Estimation of Pricing Kernels from Nois…

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…

Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…

We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…

We introduce several new estimation methods that leverage shape constraints in auction models to estimate various objects of interest, including the distribution of a bidder's valuations, the bidder's ex ante expected surplus, and the…

The log-likelihood of a generative model often involves both positive and negative terms. For a temporal multivariate point process, the negative term sums over all the possible event types at each time and also integrates over all the…

Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…

We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…

The rank minimization problem is to find the lowest-rank matrix in a given set. Nuclear norm minimization has been proposed as an convex relaxation of rank minimization. Recht, Fazel, and Parrilo have shown that nuclear norm minimization…

Kernels are key in machine learning for modeling interactions. Unfortunately, brute-force computation of the related kernel sums scales quadratically with the number of samples. Recent Fourier-slicing methods lead to an improved linear…

Short-term patterns in financial time series form the cornerstone of many algorithmic trading strategies, yet extracting these patterns reliably from noisy market data remains a formidable challenge. In this paper, we propose an…

Models that learn spurious correlations from training data often fail when deployed in new environments. While many methods aim to learn invariant representations to address this, they often underperform standard empirical risk minimization…

Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in…

We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence…

In this paper, we deal with nonparametric regression for circular data, meaning that observations are represented by points lying on the unit circle. We propose a kernel estimation procedure with data-driven selection of the bandwidth…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…

We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM…

Machine learning in asset pricing typically predicts expected returns as point estimates, ignoring uncertainty. We develop new methods to construct forecast confidence intervals for expected returns obtained from neural networks. We show…