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We develop extreme data compression for use in Bayesian model comparison via the MOPED algorithm, as well as more general score compression. We find that Bayes factors from data compressed with the MOPED algorithm are identical to those…

There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…

A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of Subset Simulation for efficient rare-event simulation, first…

Bayesian optimization (BO) has been widely used in machine learning and simulation optimization. With the increase in computational resources and storage capacities in these fields, high-dimensional and large-scale problems are becoming…

Approximate Bayesian computation (ABC) methods can be used to sample from posterior distributions when the likelihood function is unavailable or intractable, as is often the case in biological systems. ABC methods suffer from inefficient…

Test-time adaptation (TTA) methods improve model performance under distribution shift but lack formal guarantees connecting shift magnitude to prediction reliability. We develop a PAC-Bayesian framework yielding generalization bounds…

The Naive-Bayes classifier is widely used due to its simplicity, speed and accuracy. However this approach fails when, for at least one attribute value in a test sample, there are no corresponding training samples with that attribute value.…

In mixture model-based clustering applications, it is common to fit several models from a family and report clustering results from only the `best' one. In such circumstances, selection of this best model is achieved using a model selection…

We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a…

Confidence calibration of classification models is a technique to estimate the true posterior probability of the predicted class, which is critical for ensuring reliable decision-making in practical applications. Existing confidence…

Most ML datasets today contain biases. When we train models on these datasets, they often not only learn these biases but can worsen them -- a phenomenon known as bias amplification. Several co-occurrence-based metrics have been proposed to…

Multimodal learning with variational autoencoders (VAEs) requires estimating joint distributions to evaluate the evidence lower bound (ELBO). Current methods, the product and mixture of experts, aggregate single-modality distributions…

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised…

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised…

Standard Bayesian inference is known to be sensitive to model misspecification, leading to unreliable uncertainty quantification and poor predictive performance. However, finding generally applicable and computationally feasible methods for…

Combination and aggregation techniques can significantly improve forecast accuracy. This also holds for probabilistic forecasting methods where predictive distributions are combined. There are several time-varying and adaptive weighting…

We establish concentration rates for estimation of treatment effects in experiments that incorporate prior sources of information -- such as past pilots, related studies, or expert assessments -- whose external validity is uncertain. Each…

Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about…

Projections of changes in extreme climate are sometimes predicted by using multi-model ensemble methods such as Bayesian model averaging (BMA) embedded with the generalized extreme value (GEV) distribution. BMA is a popular method for…

Uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. Although Bayesian Neural Networks (BNNs) allow for uncertainty in the predictions to be assessed,…