Related papers: Fr\'echet Sufficient Dimension Reduction for Rando…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…
Inverse medium scattering problems arise in many applications, but in practice, the measurement data are often restricted to a limited aperture by physical or experimental constraints. Classical sampling methods, such as MUSIC and the…
Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss…
While there exists a well-developed asymptotic theory of Fr\'echet means of random variables taking values in a general "finite-dimensional" metric space, there are only a few known results in which the random variables can take values in…
Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…
Individualized treatment regimes (ITRs) aim to improve clinical outcomes by assigning treatment based on patient-specific characteristics. However, existing methods often struggle with high-dimensional covariates, limiting accuracy,…
We propose a new method for dimension reduction in regression using the first two inverse moments. We develop corresponding weighted chi-squared tests for the dimension of the regression. The proposed method considers linear combinations of…
A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…
This paper explores the field of semi-supervised Fr\'echet regression, driven by the significant costs associated with obtaining non-Euclidean labels. Methodologically, we propose two novel methods: semi-supervised NW Fr\'echet regression…
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,…
Many machine learning tasks that involve predicting an output response can be solved by training a weighted regression model. Unfortunately, the predictive power of this type of models may severely deteriorate under low sample sizes or…
This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…
In this paper we introduce a general theory for nonlinear sufficient dimension reduction, and explore its ramifications and scope. This theory subsumes recent work employing reproducing kernel Hilbert spaces, and reveals many parallels…
Distribution-as-response regression problems are gaining wider attention, especially within biomedical settings where observation-rich patient specific data sets are available, such as feature densities in CT scans (Petersen et al., 2021)…
Suppose that $Y$ is a scalar and $X$ is a second-order stochastic process, where $Y$ and $X$ are conditionally independent given the random variables $\xi_1,...,\xi_p$ which belong to the closed span $L_X^2$ of $X$. This paper investigates…
Modern time series analysis requires the ability to handle datasets that are inherently high-dimensional; examples include applications in climatology, where measurements from numerous sensors must be taken into account, or inventory…
In this paper, we consider nonparametric estimation over general Dirichlet metric measure spaces. Unlike the more commonly studied reproducing kernel Hilbert space, whose elements may be defined pointwise, a Dirichlet space typically only…