Related papers: Sequential Nonparametric Regression
The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space.…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
For many machine learning problems, data is abundant and it may be prohibitive to make multiple passes through the full training set. In this context, we investigate strategies for dynamically increasing the effective sample size, when…
This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…
In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…
Theory and algorithms are developed for detecting changes in the distribution of statistically periodic random processes. The statistical periodicity is modeled using independent and periodically identically distributed processes, a new…
Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric…
We consider a semiparametric partly linear model identified by instrumental variables. We propose an estimation method that does not smooth on the instruments and we extend the Landweber-Fridman regularization scheme to the estimation of…
Increasing practical interest has been shown in regression problems where the errors, or disturbances, are centred in a way that reflects particular characteristics of the mechanism that generated the data. In economics this occurs in…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
To detect changes in the mean of a time series, one may use previsible detection procedures based on nonparametric kernel prediction smoothers which cover various classic detection statistics as special cases. Bandwidth selection,…
This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral…
We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on a finite time interval. Under suitable regularity…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…