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We propose an efficient algorithm for learning mappings between two metric spaces, $\X$ and $\Y$. Our procedure is strongly Bayes-consistent whenever $\X$ and $\Y$ are topologically separable and $\Y$ is "bounded in expectation" (our term;…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
Quantifying the influence of infinitesimal changes in training data on model performance is crucial for understanding and improving machine learning models. In this work, we reformulate this problem as a weighted empirical risk minimization…
Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature…
Accurately modeling local surface properties of objects is crucial to many robotic applications, from grasping to material recognition. Surface properties like friction are however difficult to estimate, as visual observation of the object…
The random-effects or normal-normal hierarchical model is commonly utilized in a wide range of meta-analysis applications. A Bayesian approach to inference is very attractive in this context, especially when a meta-analysis is based only on…
We introduce a new approach to prediction in graphical models with latent-shift adaptation, i.e., where source and target environments differ in the distribution of an unobserved confounding latent variable. Previous work has shown that as…
The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…
Random-effects models are central to meta-analysis, yet the between-study variance is often underestimated when the number of studies is small. In such settings, confidence intervals become unduly narrow and fail to attain the nominal…
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…
Linear Mixed Model (LMM) is a common statistical approach to model the relation between exposure and outcome while capturing individual variability through random effects. However, this model assumes the homogeneity of the error term's…
We study the problem of testing for the presence of random effects in mixed models with high-dimensional fixed effects. To this end, we propose a rank-based graph-theoretic approach to test whether a collection of random effects is zero.…
The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…
This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interactions between users in a social network. Our goal is to…
We develop a novel and general framework for reduced-bias $M$-estimation from asymptotically unbiased estimating functions. The framework relies on an empirical approximation of the bias by a function of derivatives of estimating function…
Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to…