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While scale-invariant modeling has substantially boosted the performance of visual recognition tasks, it remains largely under-explored in deep networks based image restoration. Naively applying those scale-invariant techniques (e.g.…
This paper studies estimation in functional linear quantile regression in which the dependent variable is scalar while the covariate is a function, and the conditional quantile for each fixed quantile index is modeled as a linear functional…
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…
Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…
We propose a spatial autoregressive model for a multivariate response variable and functional covariates. The approach is based on the notion of signature, which represents a function as an infinite series of its iterated integrals and…
Image-to-image regression is an important learning task, used frequently in biological imaging. Current algorithms, however, do not generally offer statistical guarantees that protect against a model's mistakes and hallucinations. To…
We describe a diffeomorphic registration algorithm that allows groups of images to be accurately aligned to a common space, which we intend to incorporate into the SPM software. The idea is to perform inference in a probabilistic graphical…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
We propose a regression model for count data when the classical generalized linear model approach is too rigid due to a high outcome of zero counts and a nonlinear influence of continuous covariates. Zero-Inflation is applied to take into…
Recent technological developments have enabled us to collect complex and high-dimensional data in many scientific fields, such as population health, meteorology, econometrics, geology, and psychology. It is common to encounter such datasets…
Disaggregation regression has become an important tool in spatial disease mapping for making fine-scale predictions of disease risk from aggregated response data. By including high resolution covariate information and modelling the data…
We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing ad hoc approach, such as the last value carried forward, is biased. We propose a…
In various applications with large spatial regions, the relationship between the response variable and the covariates is expected to exhibit complex spatial patterns. We propose a spatially clustered varying coefficient model, where the…
The multi-index model is a simple yet powerful high-dimensional regression model which circumvents the curse of dimensionality assuming $ \mathbb{E} [ Y | X ] = g(A^\top X) $ for some unknown index space $A$ and link function $g$. In this…
In this paper, we develop a novel spatial variable selection method for scalar on vector-valued image regression in a multi-group setting. Here, 'vector-valued image' refers to the imaging datasets that contain vector-valued information at…
We propose a class of robust estimates for multivariate linear models. Based on the approach of MM estimation (Yohai 1987), we estimate the regression coefficients and the covariance matrix of the errors simultaneously. These estimates have…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling…