Related papers: Targeting functional parameters with semiparametri…
In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in…
Let $X_1,\ldots,X_n$ be a random sample from an unknown probability distribution $P$ on the sample space ${\cal X}$, and let $\theta=\theta(P)$ be a parameter of interest. The present paper proposes a nonparametric `Bayesian bootstrap'…
We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
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…
It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a…
We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…
Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
Penalized B-splines are routinely used in additive models to describe smooth changes in a response with quantitative covariates. It is typically done through the conditional mean in the exponential family using generalized additive models…
Bayesian inference is a powerful tool for combining information in complex settings, a task of increasing importance in modern applications. However, Bayesian inference with a flawed model can produce unreliable conclusions. This review…
We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an a~priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
Neural networks are powerful function approximators with tremendous potential in learning complex distributions. However, they are prone to overfitting on spurious patterns. Bayesian inference provides a principled way to regularize neural…
The conventional approach to Bayesian decision-theoretic experiment design involves searching over possible experiments to select a design that maximizes the expected value of a specified utility function. The expectation is over the joint…
Two of the principle tasks of causal inference are to define and estimate the effect of a treatment on an outcome of interest. Formally, such treatment effects are defined as a possibly functional summary of the data generating…
Instrumental variable methods are widely used for inferring the causal effect in the presence of unmeasured confounders. Existing instrumental variable methods for nonlinear outcome models require stringent identifiability conditions. This…
We develop a model-free theory of general types of parametric regression for iid observations. The theory replaces the parameters of parametric models with statistical functionals, to be called "regression functionals'', defined on large…
Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and…