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Profile likelihoods are rarely used in geostatistical models due to the computational burden imposed by repeated decompositions of large variance matrices. Accounting for uncertainty in covariance parameters can be highly consequential in…

Spatial generalized linear mixed models (SGLMMs) are popular for analyzing non-Gaussian spatial data. These models assume a prescribed link function that relates the underlying spatial field with the mean response. There are circumstances,…

Deep-learning has proved in recent years to be a powerful tool for image analysis and is now widely used to segment both 2D and 3D medical images. Deep-learning segmentation frameworks rely not only on the choice of network architecture but…

Handling missing values at test time is challenging for machine learning models, especially when aiming for both high accuracy and interpretability. Established approaches often add bias through imputation or excessive model complexity via…

The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…

We introduce the loss kernel, an interpretability method for measuring similarity between data points according to a trained neural network. The kernel is the covariance matrix of per-sample losses computed under a distribution of…

In this paper we model the loss function of high-dimensional optimization problems by a Gaussian random field, or equivalently a Gaussian process. Our aim is to study gradient descent in such loss functions or energy landscapes and compare…

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Many problems in statistics and machine learning can be formulated as model selection problems, where the goal is to choose an optimal parsimonious model among a set of candidate models. It is typical to conduct model selection by…

We study statistical problems, such as planted clique, its variants, and sparse principal component analysis in the context of average-case communication complexity. Our motivation is to understand the statistical-computational trade-offs…

The standard regression tree method applied to observations within clusters poses both methodological and implementation challenges. Effectively leveraging these data requires methods that account for both individual-level and sample-level…

In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness.…

We study the dynamics of the generalized Lotka-Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us…

The generalized Ridge penalty is a powerful tool for dealing with overfitting and for high-dimensional regressions. The generalized Ridge regression can be derived as the mean of a posterior distribution with a Normal prior and a given…

Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing…

We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on…