Related papers: The Ridge Path Estimator for Linear Instrumental V…
A basis expansion with regularization methods is much appealing to the flexible or robust nonlinear regression models for data with complex structures. When the underlying function has inhomogeneous smoothness, it is well known that…
We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…
The performance of penalized likelihood approaches depends profoundly on the selection of the tuning parameter; however, there is no commonly agreed-upon criterion for choosing the tuning parameter. Moreover, penalized likelihood estimation…
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…
In sparse linear regression, the SLOPE estimator generalizes LASSO by penalizing different coordinates of the estimate according to their magnitudes. In this paper, we present a precise performance characterization of SLOPE in the…
Modern computational models in supervised machine learning are often highly parameterized universal approximators. As such, the value of the parameters is unimportant, and only the out of sample performance is considered. On the other hand…
Many statistical problems can be reduced to a linear inverse problem in which only a noisy version of the operator is available. Particular examples include random design regression, deconvolution problem, instrumental variable regression,…
Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF…
Existing online continuous-time parameter estimation laws provide exact (asymptotic/exponential or finite/fixed time) identification of dynamical linear/nonlinear systems parameters only if the external perturbations are equaled to zero or…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
The endogeneity issue is fundamentally important as many empirical applications may suffer from the omission of explanatory variables, measurement error, or simultaneous causality. Recently, \cite{hllt17} propose a "Deep Instrumental…
We propose a quantum algorithm based on ridge regression model, which get the optimal fitting parameters w and a regularization hyperparameter {\alpha} by analysing the training dataset. The algorithm consists of two subalgorithms. One is…
Instrumental variable (IV) regression is a standard strategy for learning causal relationships between confounded treatment and outcome variables from observational data by utilizing an instrumental variable, which affects the outcome only…
Understanding when and why interpolating methods generalize well has recently been a topic of interest in statistical learning theory. However, systematically connecting interpolating methods to achievable notions of optimality has only…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…
Recent developments in linear system identification have proposed the use of non-parameteric methods, relying on regularization strategies, to handle the so-called bias/variance trade-off. This paper introduces an impulse response estimator…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
The use of random sampling in decision-making and control has become popular with the ease of access to graphic processing units that can generate and calculate multiple random trajectories for real-time robotic applications. In contrast to…
Regression models usually tend to recover a noisy signal in the form of a combination of regressors, also called features in machine learning, themselves being the result of a learning process.The alignment of the prior covariance feature…
For finite samples with binary outcomes penalized logistic regression such as ridge logistic regression (RR) has the potential of achieving smaller mean squared errors (MSE) of coefficients and predictions than maximum likelihood…