Related papers: True and Pseudo-True Parameters

Large-scale optimization problems are ubiquitous in the physical sciences; yet, high-fidelity models can often be complex and computationally prohibitive for optimization. A practical alternative is to use a low-fidelity model to facilitate…

Possible parameter values in a random sampling model are shown by definition to have uniform base-rate prior probabilities. This allows a frequentist posterior probability distribution to be calculated for such possible parameter values…

When using incorrect or inaccurate signal models to perform parameter estimation on a gravitational wave signal, biased parameter estimates will in general be obtained. For a single event this bias may be consistent with the posterior, but…

While data are the primary fuel for machine learning models, they often suffer from missing values, especially when collected in real-world scenarios. However, many off-the-shelf machine learning models, including artificial neural network…

Results on two different settings of asymptotic behavior of approximation characteristics of individual functions are presented. First, we discuss the following classical question for sparse approximation. Is it true that for any individual…

Clinical researchers often select among and evaluate risk prediction models using standard machine learning metrics based on confusion matrices. However, if these models are used to allocate interventions to patients, standard metrics…

Simulation-based Bayesian inference (SBI) methods are widely used for parameter estimation in complex models where evaluating the likelihood is challenging but generating simulations is relatively straightforward. However, these methods…

Mathematical models are routinely applied to interpret biological data, with common goals that include both prediction and parameter estimation. A challenge in mathematical biology, in particular, is that models are often complex and…

Misclassification of binary responses, if ignored, may severely bias the maximum likelihood estimators (MLE) of regression parameters. For such data, a binary regression model incorporating misclassification probabilities is extensively…

Variable selection for a multiple regression model (Noisy Linear Perceptron) is studied with a mean field approximation. In our Bayesian framework, variable selection is formulated as estimation of discrete parameters that indicate a subset…

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…

\noindent Hyper-parameter selection is a central practical problem in modern machine learning, governing regularization strength, model capacity, and robustness choices. Cross-validation is often computationally prohibitive at scale, while…

Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…

In Bayesian hypothesis testing and model selection, prior distributions must be chosen carefully. For example, setting arbitrarily large prior scales for location parameters, which is common practice in estimation problems, can lead to…

A surprising phenomenon in modern machine learning is the ability of a highly overparameterized model to generalize well (small error on the test data) even when it is trained to memorize the training data (zero error on the training data).…

The empirical Bayes estimators in mixed models are useful for small area estimation in the sense of increasing precision of prediction for small area means, and one wants to know the prediction errors of the empirical Bayes estimators based…

An overarching goal in machine learning is to build a generalizable model with few samples. To this end, overparameterization has been the subject of immense interest to explain the generalization ability of deep nets even when the size of…

The Bayesian approach provides powerful methods for variable selection. The ability to incorporate sparsity through prior beliefs and account for parameter uncertainty allows Bayesian variable selection to consistently identify which of the…

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in…

Bounded confidence opinion dynamics model the propagation of information in social networks. However in the existing literature, opinions are only viewed as abstract quantities without semantics rather than as part of a decision-making…