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In this paper, we consider an experimental setting where units enter the experiment sequentially. Our goal is to form stopping rules which lead to estimators of treatment effects with a given precision. We propose a fixed-width confidence interval design (FWCID) where the experiment terminates once a pre-specified confidence interval width is achieved. We show that under this design, the difference-in-means estimator is a consistent estimator of the average treatment effect and standard confidence intervals have asymptotic guarantees of coverage and efficiency for several versions of the design. In addition, we propose a version of the design that we call fixed power design (FPD) where a given power is asymptotically guaranteed for a given treatment effect, without the need to specify the variances of the outcomes under treatment or control. In addition, this design also gives a consistent difference-in-means estimator with correct coverage of the corresponding standard confidence interval. We complement our theoretical findings with Monte Carlo simulations where we compare our proposed designs with standard designs in the sequential experiments literature, showing that our designs outperform these designs in several important aspects. We believe our results to be relevant for many experimental settings where units enter sequentially, such as in clinical trials, as well as in online A/B tests used by the tech and e-commerce industry.

First order shape optimization methods, in general, require a large number of iterations until they reach a locally optimal design. While higher order methods can significantly reduce the number of iterations, they exhibit only local convergence properties, necessitating a sufficiently close initial guess. In this work, we present an unregularized shape-Newton method and combine shape optimization with homotopy (or continuation) methods in order to allow for the use of higher order methods even if the initial design is far from a solution. The idea of homotopy methods is to continuously connect the problem of interest with a simpler problem and to follow the corresponding solution path by a predictor-corrector scheme. We use a shape-Newton method as a corrector and arbitrary order shape derivatives for the predictor. Moreover, we apply homotopy methods also to the case of multi-objective shape optimization to efficiently obtain well-distributed points on a Pareto front. Finally, our results are substantiated with a set of numerical experiments.

Design optimization problems, e.g., shape optimization, that involve deformable bodies in unilateral contact are challenging as they require robust contact solvers, complex optimization methods that are typically gradient-based, and sensitivity derivations. Notably, the problems are nonsmooth, adding significant difficulty to the optimization process. We study design optimization problems in frictionless unilateral contact subject to pressure constraints, using both gradient-based and gradient-free optimization methods, namely Bayesian optimization. The contact simulation problem is solved via the mortar contact and finite element methods. For the gradient-based method, we use the direct differentiation method to compute the sensitivities of the cost and constraint function with respect to the design variables. Then, we use Ipopt to solve the optimization problems. For the gradient-free approach, we use a constrained Bayesian optimization algorithm based on the standard Gaussian Process surrogate model. We present numerical examples that control the contact pressure, inspired by real-life engineering applications, to demonstrate the effectiveness, strengths and shortcomings of both methods. Our results suggest that both optimization methods perform reasonably well for these nonsmooth problems.

The evaluation of text-generative vision-language models is a challenging yet crucial endeavor. By addressing the limitations of existing Visual Question Answering (VQA) benchmarks and proposing innovative evaluation methodologies, our research seeks to advance our understanding of these models' capabilities. We propose a novel VQA benchmark based on well-known visual classification datasets which allows a granular evaluation of text-generative vision-language models and their comparison with discriminative vision-language models. To improve the assessment of coarse answers on fine-grained classification tasks, we suggest using the semantic hierarchy of the label space to ask automatically generated follow-up questions about the ground-truth category. Finally, we compare traditional NLP and LLM-based metrics for the problem of evaluating model predictions given ground-truth answers. We perform a human evaluation study upon which we base our decision on the final metric. We apply our benchmark to a suite of vision-language models and show a detailed comparison of their abilities on object, action, and attribute classification. Our contributions aim to lay the foundation for more precise and meaningful assessments, facilitating targeted progress in the exciting field of vision-language modeling.

When we think of model ensembling or ensemble modeling, there are many possibilities that come to mind in different disciplines. For example, one might think of a set of descriptions of a phenomenon in the world, perhaps a time series or a snapshot of multivariate space, and perhaps that set is comprised of data-independent descriptions, or perhaps it is quite intentionally fit *to* data, or even a suite of data sets with a common theme or intention. The very meaning of 'ensemble' - a collection together - conjures different ideas across and even within disciplines approaching phenomena. In this paper, we present a typology of the scope of these potential perspectives. It is not our goal to present a review of terms and concepts, nor is it to convince all disciplines to adopt a common suite of terms, which we view as futile. Rather, our goal is to disambiguate terms, concepts, and processes associated with 'ensembles' and 'ensembling' in order to facilitate communication, awareness, and possible adoption of tools across disciplines.

In this paper, we introduce a novel approach to improve the diversity of Top-N recommendations while maintaining recommendation performance. Our approach employs a user-centric pre-processing strategy aimed at exposing users to a wide array of content categories and topics. We personalize this strategy by selectively adding and removing a percentage of interactions from user profiles. This personalization ensures we remain closely aligned with user preferences while gradually introducing distribution shifts. Our pre-processing technique offers flexibility and can seamlessly integrate into any recommender architecture. To evaluate our approach, we run extensive experiments on two publicly available data sets for news and book recommendations. We test various standard and neural network-based recommender system algorithms. Our results show that our approach generates diverse recommendations, ensuring users are exposed to a wider range of items. Furthermore, leveraging pre-processed data for training leads to recommender systems achieving performance levels comparable to, and in some cases, better than those trained on original, unmodified data. Additionally, our approach promotes provider fairness by facilitating exposure to minority or niche categories.

Recently, there has been a significant focus on exploring the theoretical aspects of deep learning, especially regarding its performance in classification tasks. Bayesian deep learning has emerged as a unified probabilistic framework, seeking to integrate deep learning with Bayesian methodologies seamlessly. However, there exists a gap in the theoretical understanding of Bayesian approaches in deep learning for classification. This study presents an attempt to bridge that gap. By leveraging PAC-Bayes bounds techniques, we present theoretical results on the prediction or misclassification error of a probabilistic approach utilizing Spike-and-Slab priors for sparse deep learning in classification. We establish non-asymptotic results for the prediction error. Additionally, we demonstrate that, by considering different architectures, our results can achieve minimax optimal rates in both low and high-dimensional settings, up to a logarithmic factor. Moreover, our additional logarithmic term yields slight improvements over previous works. Additionally, we propose and analyze an automated model selection approach aimed at optimally choosing a network architecture with guaranteed optimality.

Most of the existing diffusion models use Gaussian noise for training and sampling across all time steps, which may not optimally account for the frequency contents reconstructed by the denoising network. Despite the diverse applications of correlated noise in computer graphics, its potential for improving the training process has been underexplored. In this paper, we introduce a novel and general class of diffusion models taking correlated noise within and across images into account. More specifically, we propose a time-varying noise model to incorporate correlated noise into the training process, as well as a method for fast generation of correlated noise mask. Our model is built upon deterministic diffusion models and utilizes blue noise to help improve the generation quality compared to using Gaussian white (random) noise only. Further, our framework allows introducing correlation across images within a single mini-batch to improve gradient flow. We perform both qualitative and quantitative evaluations on a variety of datasets using our method, achieving improvements on different tasks over existing deterministic diffusion models in terms of FID metric.

We introduce the Birkhoff completion as the smallest distributive lattice in which a given finite lattice can be embedded as semi-lattice. We discuss its relationship to implicational theories, in particular to R. Wille's simply-implicational theories. By an example, we show how the Birkhoff completion can be used as a tool for ordinal data science.

In this study, we introduce Generative Manufacturing Systems (GMS) as a novel approach to effectively manage and coordinate autonomous manufacturing assets, thereby enhancing their responsiveness and flexibility to address a wide array of production objectives and human preferences. Deviating from traditional explicit modeling, GMS employs generative AI, including diffusion models and ChatGPT, for implicit learning from envisioned futures, marking a shift from a model-optimum to a training-sampling decision-making. Through the integration of generative AI, GMS enables complex decision-making through interactive dialogue with humans, allowing manufacturing assets to generate multiple high-quality global decisions that can be iteratively refined based on human feedback. Empirical findings showcase GMS's substantial improvement in system resilience and responsiveness to uncertainties, with decision times reduced from seconds to milliseconds. The study underscores the inherent creativity and diversity in the generated solutions, facilitating human-centric decision-making through seamless and continuous human-machine interactions.