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An adaptive method for parabolic partial differential equations that combines sparse wavelet expansions in time with adaptive low-rank approximations in the spatial variables is constructed and analyzed. The method is shown to converge and…
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…
This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least…
Nanomechanical resonant sensors that are based on detecting and tracking the resonance frequency deviations due to events of interest are being advocated for a variety of applications. All sensor schemes currently in use are subject to a…
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index…
Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…
Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…
In this paper, we introduce the first principled adaptive-sampling procedure for learning a convex function in the $L_\infty$ norm, a problem that arises often in the behavioral and social sciences. We present a function-specific measure of…
When training automated systems, it has been shown to be beneficial to adapt the representation of data by learning a problem-specific metric. This metric is global. We extend this idea and, for the widely used family of k nearest neighbors…
We constuct a sequential adaptive procedure for estimating the autoregressive function at a given point in nonparametric autoregression models with Gaussian noise. We make use of the sequential kernel estimators. The optimal adaptive…
Wireless sensor networks (WSNs) have attracted considerable attention in recent years and motivate a host of new challenges for distributed signal processing. The problem of distributed or decentralized estimation has often been considered…
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating a unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk, i.e.…
Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in…
In this paper, a practical estimation method for a regression model is proposed using semiparametric efficient score functions applicable to data with various shapes of errors. First, I derive semiparametric efficient score vectors for a…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…
In oversampled adaptive sensing (OAS), noisy measurements are collected in multiple subframes. The sensing basis in each subframe is adapted according to some posterior information exploited from previous measurements. The framework is…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…