Related papers: Canonical correlation regression with noisy data
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional…
Instrumental variables are a popular study design for the estimation of treatment effects in the presence of unobserved confounders. In the canonical instrumental variables design, the instrument is a binary variable. In many settings,…
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…
Recent developments in regularized Canonical Correlation Analysis (CCA) promise powerful methods for high-dimensional, multiview data analysis. However, justifying the structural assumptions behind many popular approaches remains a…
Sparse regression is frequently employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data that hampers both feature selection and estimation is the presence of strong correlations between…
This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…
The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal…
As with many other problems, real-world regression is plagued by the presence of noisy labels, an inevitable issue that demands our attention. Fortunately, much real-world data often exhibits an intrinsic property of continuously ordered…
Investigating the relationships between two sets of variables helps to understand their interactions and can be done with canonical correlation analysis (CCA). However, the correlation between the two sets can sometimes depend on a third…
Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…
We consider the problem of fitting a relationship (e.g. a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according…
A flow decomposition method based on canonical correlation analysis is proposed in this paper to optimally dissect complex flows into mutually orthogonal modes that are ranked by their cross-correlation with an observable. It is…
Scientific and business practices are increasingly resulting in large collections of randomized experiments. Analyzed together, these collections can tell us things that individual experiments in the collection cannot. We study how to learn…
Based on literature review about existing diffusion models and flow matching with a neural network to predict a predefined target from noisy data, a unified representation is first proposed for these models using two simple linear equations…
Second-order information -- such as curvature or data covariance -- is critical for optimisation, diagnostics, and robustness. However, in many modern settings, only the gradients are observable. We show that the gradients alone can reveal…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
The instrumental variable method consistently estimates the effect of a treatment when there is unmeasured confounding and a valid instrumental variable. A valid instrumental variable is a variable that is independent of unmeasured…
Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…
We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a post-selection inference approach to canonical correlation analysis. The challenge is to adjust for the selection…
Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in…