相关论文: Parameter Adjustment in Bayes Networks. The genera…

This is a writeup, with some elaboration, of the talks by the two authors (a physicist and a statistician) at the first PHYSTAT Informal review on January 24, 2024. We discuss Bayesian and frequentist approaches to dealing with nuisance…

Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…

Peer grading systems aggregate noisy reports from multiple students to approximate a true grade as closely as possible. Most current systems either take the mean or median of reported grades; others aim to estimate students' grading…

We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…

PAC-Bayesian is an analysis framework where the training error can be expressed as the weighted average of the hypotheses in the posterior distribution whilst incorporating the prior knowledge. In addition to being a pure generalization…

The human brain copes with sensory uncertainty in accordance with Bayes' rule. However, it is unknown how the brain makes predictions in the presence of parameter uncertainty. Here, we tested whether and how humans take parameter…

This report works out the details of a closed-form, fully Bayesian, multiclass, openset, generative pattern classifier using multivariate Gaussian likelihoods, with conjugate priors. The generative model has a common within-class…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…

The number of probability distributions required to populate a conditional probability table (CPT) in a Bayesian network, grows exponentially with the number of parent-nodes associated with that table. If the table is to be populated…

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…

A Bayesian Belief Network (BN) is a model of a joint distribution over a setof n variables, with a DAG structure to represent the immediate dependenciesbetween the variables, and a set of parameters (aka CPTables) to represent thelocal…

Bayesian Neural Networks (BNNs) offer probability distributions for model parameters, enabling uncertainty quantification in predictions. However, they often underperform compared to deterministic neural networks. Utilizing mutual learning…

We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…

The new field of adaptive data analysis seeks to provide algorithms and provable guarantees for models of machine learning that allow researchers to reuse their data, which normally falls outside of the usual statistical paradigm of static…

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…

We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow…

This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…