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With infinitely many high-quality data points, infinite computational power, an infinitely large foundation model with a perfect training algorithm and guaranteed zero generalization error on the pretext task, can the model be used for…

Statisticians are largely focused on developing methods that perform well in a frequentist sense -- even the Bayesians. But the widely-publicized replication crisis suggests that these performance guarantees alone are not enough to instill…

Bayesian optimization (BO) is an effective approach to optimize expensive black-box functions, that seeks to trade-off between exploitation (selecting parameters where the maximum is likely) and exploration (selecting parameters where we…

The focal loss has demonstrated its effectiveness in many real-world applications such as object detection and image classification, but its theoretical understanding has been limited so far. In this paper, we first prove that the focal…

Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…

Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…

We generalize to non-flat geometries the formalism of Simon et al. (2005) to reconstruct the dark energy potential. This formalism makes use of quantities similar to the Horizon-flow parameters in inflation, can, in principle, be made…

The lack of evidence in favor of any new physics models means that the search for new physics beyond the Standard Model (BSM) is wide open, with no direction clearly more promising than any other. This marks a turn towards what can be…

Bayes factor, defined as the ratio of the marginal likelihood functions of two competing models, is the natural Bayesian procedure for model selection. Marginal likelihoods are usually computationally demanding and complex. This scenario is…

Feature engineering has become one of the most important steps to improve model prediction performance, and to produce quality datasets. However, this process requires non-trivial domain-knowledge which involves a time-consuming process.…

Multimodal foundation models offer promising advancements for enhancing driving perception systems, but their high computational and financial costs pose challenges. We develop a method that leverages foundation models to refine predictions…

Determining the best model or models for a particular data set, a process known as Bayesian model comparison, is a critical part of probabilistic inference. Typically, this process assumes a fixed model-space (that is, a fixed set of…

The conventional approach to Bayesian decision-theoretic experiment design involves searching over possible experiments to select a design that maximizes the expected value of a specified utility function. The expectation is over the joint…

We provide a brief overview of both Bayes and classical model selection. We argue tentatively that model selection has at least two major goals, that of finding the correct model or predicting well, and that in general both these goals may…

The inability of Moore's Law and other figure-of-merits (FOMs) to accurately explain the technology development of the semiconductor industry demands a holistic merit to guide the industry. Here we introduce a FOM termed CLEAR that…

Foundation models (FMs) are a popular topic of research in AI. Their ability to generalize to new tasks and datasets without retraining or needing an abundance of data makes them an appealing candidate for applications on specialist…

Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found…

Deep learning models often learn to make predictions that rely on sensitive social attributes like gender and race, which poses significant fairness risks, especially in societal applications, e.g., hiring, banking, and criminal justice.…

We constrain extensions to the $\Lambda$CDM model using measurements from the Dark Energy Survey's first three years of observations and external data. The DES data are the two-point correlation functions of weak gravitational lensing,…

Efficient exploration remains a challenging problem in reinforcement learning, especially for those tasks where rewards from environments are sparse. A commonly used approach for exploring such environments is to introduce some "intrinsic"…