Related papers: On identification in ill-posed linear regression

In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…

Identifiability is a desirable property of a statistical model: it implies that the true model parameters may be estimated to any desired precision, given sufficient computational resources and data. We study identifiability in the context…

Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…

This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…

Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural…

We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a…

Inverse optimization seeks to recover unknown objective parameters from observed decisions, yet fundamental questions about when recovery is possible have received limited formal treatment. This paper develops a comprehensive theoretical…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…

This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…

Balancing the model complexity and the representation capability towards the process to be captured remains one of the main challenges in nonlinear system identification. One possibility to reduce model complexity is to impose structure on…

Machine learning (ML) and deep learning models are extensively used for parameter optimization and regression problems. However, not all inverse problems in ML are ``identifiable,'' indicating that model parameters may not be uniquely…

The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…

We study identifiability of the parameters in autoregressions defined on a network. Most identification conditions that are available for these models either rely on the network being observed repeatedly, are only sufficient, or require…

We introduce a new framework for characterizing identified sets of structural and counterfactual parameters in econometric models. By reformulating the identification problem as a set membership question, we leverage the separating…

While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of…

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 parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case,…

This paper proposes a recursive interval-valued estimation framework for identifying the parameters of linearly parameterized systems which may be slowly time-varying. It is assumed that the model error (which may consist in measurement…

An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…