We consider the best arm identification problem, where the goal is to identify the arm with the highest mean reward from a set of $K$ arms under a limited sampling budget. This problem models many practical scenarios such as A/B testing. We consider a class of algorithms for this problem, which is provably minimax optimal up to a constant factor. This idea is a generalization of existing works in fixed-budget best arm identification, which are limited to a particular choice of risk measures. Based on the framework, we propose Almost Tracking, a closed-form algorithm that has a provable guarantee on the popular risk measure $H_1$. Unlike existing algorithms, Almost Tracking does not require the total budget in advance nor does it need to discard a significant part of samples, which gives a practical advantage. Through experiments on synthetic and real-world datasets, we show that our algorithm outperforms existing anytime algorithms as well as fixed-budget algorithms.

We introduce a highly expressive yet distinctly tractable family for black-box variational inference (BBVI). Each member of this family is a weighted product of experts (PoE), and each weighted expert in the product is proportional to a multivariate $t$-distribution. These products of experts can model distributions with skew, heavy tails, and multiple modes, but to use them for BBVI, we must be able to sample from their densities. We show how to do this by reformulating these products of experts as latent variable models with auxiliary Dirichlet random variables. These Dirichlet variables emerge from a Feynman identity, originally developed for loop integrals in quantum field theory, that expresses the product of multiple fractions (or in our case, $t$-distributions) as an integral over the simplex. We leverage this simplicial latent space to draw weighted samples from these products of experts -- samples which BBVI then uses to find the PoE that best approximates a target density. Given a collection of experts, we derive an iterative procedure to optimize the exponents that determine their geometric weighting in the PoE. At each iteration, this procedure minimizes a regularized Fisher divergence to match the scores of the variational and target densities at a batch of samples drawn from the current approximation. This minimization reduces to a convex quadratic program, and we prove under general conditions that these updates converge exponentially fast to a near-optimal weighting of experts. We conclude by evaluating this approach on a variety of synthetic and real-world target distributions.

In response to the efficiency problem, recent studies show that dense PLMs can be replaced with sparse subnetworks without hurting the performance. Such subnetworks can be found in three scenarios: 1) the fine-tuned PLMs, 2) the raw PLMs and then fine-tuned in isolation, and even inside 3) PLMs without any parameter fine-tuning. However, these results are only obtained in the in-distribution (ID) setting.

We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent variable model, which we refer to as a Gaussian latent machine. This leads to a general sampling approach that unifies and generalizes many existing sampling algorithms in the literature. Most notably, it yields a highly efficient and effective two-block Gibbs sampling approach in the general case, while also specializing to direct sampling algorithms in particular cases. Finally, we present detailed numerical experiments that demonstrate the efficiency and effectiveness of our proposed sampling approach across a wide range of prior and posterior sampling problems from Bayesian imaging.

Purpose: We present a virtual model to optimize point of entry (POE) in lung biopsy planning systems. Our model allows to compute the quality of a biopsy sample taken from potential POE, taking into account the margin of error that arises from discrepancies between the orientation in the planning simulation and the actual orientation during the operation. Additionally, the study examines the impact of the characteristics of the lesion. Methods: The quality of the biopsy is given by a heatmap projected onto the skeleton of a patient-specific model of airways. The skeleton provides a 3D representation of airways structure, while the heatmap intensity represents the potential amount of tissue that it could be extracted from each POE. This amount of tissue is determined by the intersection of the lesion with a cone that represents the uncertainty area in the introduction of biopsy instruments. The cone, lesion, and skeleton are modelled as graphical objects that define a 3D scene of the intervention. Results: We have simulated different settings of the intervention scene from a single anatomy extracted from a CT scan and two lesions with regular and irregular shapes. The different scenarios are simulated by systematic rotation of each lesion placed at different distances from airways. Analysis of the heatmaps for the different settings show a strong impact of lesion orientation for irregular shape and the distance for both shapes. Conclusion: The proposed heatmaps help to visually assess the optimal POE and identify whether multiple optimal POEs exist in different zones of the bronchi. They also allow us to model the maximum allowable error in navigation systems and study which variables have the greatest influence on the success of the operation. Additionally, they help determine at what point this influence could potentially jeopardize the operation.