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Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Graphical models are widely used to model stochastic dependences among large collections of variables. We introduce a new method of estimating undirected conditional independence graphs based on the score matching loss, introduced by…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…
We propose a novel graphical model selection (GMS) scheme for high-dimensional stationary time series or discrete time process. The method is based on a natural generalization of the graphical LASSO (gLASSO), introduced originally for GMS…
While optimal input design for linear systems has been well-established, no systematic approach exists for nonlinear systems where robustness to extrapolation/interpolation errors is prioritized over minimizing estimated parameter variance.…
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models,…
In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were…
In this paper we present GeoThinneR, an R package for efficient and flexible spatial thinning of species occurrence data. Spatial thinning is a widely used preprocessing step in species distribution modeling (SDM) that can help reduce…
Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the Expectation…
Transfer learning for high-dimensional Gaussian graphical models (GGMs) is studied with the goal of estimating the target GGM by utilizing the data from similar and related auxiliary studies. The similarity between the target graph and each…
We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…
Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…
There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…
We introduce iterative tilting, a gradient-free method for fine-tuning diffusion models toward reward-tilted distributions. The method decomposes a large reward tilt $\exp(\lambda r)$ into $N$ sequential smaller tilts, each admitting a…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
Gaussian stochastic process emulation is a powerful tool for approximating computationally intensive computer models. However, estimation of parameters in the GaSP emulator is a challenging task. No closed-form estimator is available, and…
Implicit Neural Representations (INR) have been successfully employed for Arbitrary-scale Super-Resolution (ASR). However, INR-based models need to query the multi-layer perceptron module numerous times and render a pixel in each query,…