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Retrieval-augmented language models (LMs) use non-parametric memory to substantially outperform their non-retrieval counterparts on perplexity-based evaluations, but it is an open question whether they achieve similar gains in few- and…
In this paper we study continuous time adaptive extremum localization of an arbitrary quadratic function $F(\cdot)$ based on Hessian estimation, using measured the signal intensity by a sensory agent. The function $F(\cdot)$ represents a…
We introduce a novel \textit{k}-nearest neighbor (\textit{k}-NN) regression method for joint estimation of the conditional mean and variance. The proposed algorithm preserves the computational efficiency and manifold-learning capabilities…
While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an…
We want to recover the regression function in the single-index model. Using an aggregation algorithm with local polynomial estimators, we answer in particular to the second part of Question~2 from Stone (1982) on the optimal convergence…
In this study, we develop an asymptotic theory of nonparametric regression for a locally stationary functional time series. First, we introduce the notion of a locally stationary functional time series (LSFTS) that takes values in a…
Building on the successes of local kernel methods for approximating the solutions to partial differential equations (PDE) and the evaluation of definite integrals (quadrature/cubature), a local estimate of the error in such approximations…
We propose to approximate the conditional expectation of a spatial random variable given its nearest-neighbour observations by an additive function. The setting is meaningful in practice and requires no unilateral ordering. It is capable of…
Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general,…
In this paper, we develop a multi-step estimation procedure to simultaneously estimate the varying-coefficient functions using a local-linear generalized method of moments (GMM) based on continuous moment conditions. To incorporate spatial…
Suppose that $n$ statistical units are observed, each following the model $Y(x_j)=m(x_j)+ \epsilon(x_j),\, j=1,...,N,$ where $m$ is a regression function, $0 \leq x_1 <...<x_N \leq 1$ are observation times spaced according to a sampling…
Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…
This study introduces a novel spatial autoregressive model in which the dependent variable is a function that may exhibit functional autocorrelation with the outcome functions of nearby units. This model can be characterized as a…
This paper presents a new methodology, called AFSSEN, to simultaneously select significant predictors and produce smooth estimates in a high-dimensional function-on-scalar linear model with a sub-Gaussian errors. Outcomes are assumed to lie…
The local regularity of functional time series is studied under $L^p-m-$appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity…
In this paper, we propose a new regularization technique called "functional SCAD". We then combine this technique with the smoothing spline method to develop a smooth and locally sparse (i.e., zero on some sub-regions) estimator for the…
K-nearest neighbors (KNN) is one of the earliest and most established algorithms in machine learning. For regression tasks, KNN averages the targets within a neighborhood which poses a number of challenges: the neighborhood definition is…
In this paper, we propose a new test for the detection of a change in a non-linear (auto-)regressive time series as well as a corresponding estimator for the unknown time point of the change. To this end, we consider an at-most-one-change…
We enlarge the number of available functional depths by introducing the kernelized functional spatial depth (KFSD). KFSD is a local-oriented and kernel-based version of the recently proposed functional spatial depth (FSD) that may be useful…
Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging…