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Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…
A novel approach of accurately reconstructing storage ring's linear optics from turn-by-turn (TbT) data containing measurement error is introduced. This approach adopts a Bayesian inference based on the Markov Chain Monte-Carlo (MCMC)…
Reward models are central to aligning language models with human preferences via reinforcement learning (RL). As RL is increasingly applied to settings such as verifiable rewards and multi-objective alignment, RMs are expected to encode…
Bayesian inference is used to estimate continuous parameter values given measured data in many fields of science. The method relies on conditional probability densities to describe information about both data and parameters, yet the notion…
Randomized experiments have long been the gold standard for scientists seeking to learn about cause and effect. When randomized experiments are infeasible, scientists often resort to observational studies, which are widely available and…
Matching is a widely used causal inference design that aims to approximate a randomized experiment using observational data by forming matched sets of treated and control units based on similarities in their covariates. Ideally, treated…
Inverse reinforcement learning (IRL) is the problem of inferring a reward function from expert behavior. There are several approaches to IRL, but most are designed to learn a Markovian reward. However, a reward function might be…
Empirical Bayes estimators are based on minimizing the average risk with the hyper-parameters in the weighting function being estimated from observed data. The performance of an empirical Bayes estimator is typically evaluated by its mean…
We consider observations $(X,y)$ from single index models with unknown link function, Gaussian covariates and a regularized M-estimator $\hat\beta$ constructed from convex loss function and regularizer. In the regime where sample size $n$…
For civil structures, structural damage due to severe loading events such as earthquakes, or due to long-term environmental degradation, usually occurs in localized areas of a structure. A new sparse Bayesian probabilistic framework for…
The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical…
We study a nonparametric approach to Bayesian computation via feature means, where the expectation of prior features is updated to yield expected kernel posterior features, based on regression from learned neural net or kernel features of…
Estimating individual level treatment effects (ITE) from observational data is a challenging and important area in causal machine learning and is commonly considered in diverse mission-critical applications. In this paper, we propose an…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
The location-scale model is usually present in physics and chemistry in connection to the Birge ratio method for the adjustment of fundamental physical constants such as the Planck constant or the Newtonian constant of gravitation, while…
When model uncertainty is handled by Bayesian model averaging (BMA) or Bayesian model selection (BMS), the posterior distribution possesses a desirable "oracle property" for parametric inference, if for large enough data it is nearly as…
Regression is a fundamental tool in scientific research. Ordinary least squares (OLS), one of the most widely used regression methods, enjoys several desirable properties, including the best linear unbiased estimator (BLUE) property. It is…
Machine learning models traditionally assume that training and test data are independently and identically distributed. However, in real-world applications, the test distribution often differs from training. This problem, known as…
Restricted Boltzmann machine (RBM) provide a general framework for modeling physical systems, but their behavior is dependent on hyperparameters such as the learning rate, the number of hidden nodes and the form of the threshold function.…
We consider a sparse linear regression model, when the number of available predictors, $p$, is much larger than the sample size, $n$, and the number of non-zero coefficients, $p_0$, is small. To choose the regression model in this…