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We propose a closed-form spectral framework for relative log-density estimation in linearly parameterized probabilistic models, including unnormalized and conditional models. This is achieved by representing the Kullback-Leibler (KL)…

We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…

This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a…

In system identification, estimating parameters of a model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model…

Kernel logistic regression (KLR) is a powerful classification method widely applied across diverse domains. In many real-world scenarios, indefinite kernels capture more domain-specific structural information than positive definite kernels.…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

Lipschitz Bound Estimation is an effective method of regularizing deep neural networks to make them robust against adversarial attacks. This is useful in a variety of applications ranging from reinforcement learning to autonomous systems.…

One of the most popular methodologies for estimating the average treatment effect at the threshold in a regression discontinuity design is local linear regression (LLR), which places larger weight on units closer to the threshold. We…

We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…

Simple regression methods provide robust, near-optimal solutions for optimal switching problems, including high-dimensional ones (up to 50). While the theory requires solving intractable PDE systems, the Longstaff-Schwartz algorithm with…

Suppose an $n \times d$ design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number $k \ll n$ of the responses, and then produce a…

Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…

We report measurements of the critical exponents of the classical three-dimensional Heisenberg model on simple cubic lattices of size $L^3$ with $L$ = 12, 16, 20, 24, 32, 40, and 48. The data was obtained from a few long single-cluster…

Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it…

We consider an on-line least squares regression problem with optimal solution $\theta^*$ and Hessian matrix H, and study a time-average stochastic gradient descent estimator of $\theta^*$. For $k\ge2$, we provide an unbiased estimator of…

We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator.…

We introduce a new type of test for complete spatial randomness that applies to mapped point patterns in a rectangle or a cube of any dimension. This is the first test of its kind to be based on characteristic functions and utilizes a…

We investigate the application of randomized quasi-Monte Carlo (RQMC) methods in random feature approximations for kernel-based learning. Compared to the classical Monte Carlo (MC) approach \citep{rahimi2007random}, RQMC improves the…

The regression function is one of the key objects of binary classification, since it not only determines a Bayes optimal classifier, hence, defines an optimal decision boundary, but also encodes the conditional distribution of the output…

Although kernel methods are widely used in many learning problems, they have poor scalability to large datasets. To address this problem, sketching and stochastic gradient methods are the most commonly used techniques to derive efficient…