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This work studies how the choice of the representation for parametric, spatially distributed inputs to elliptic partial differential equations (PDEs) affects the efficiency of a polynomial surrogate, based on Taylor expansion, for the parameter-to-solution map. In particular, we show potential advantages of representations using functions with localized supports. As model problem, we consider the steady-state diffusion equation, where the diffusion coefficient and right-hand side depend smoothly but potentially in a \textsl{highly nonlinear} way on a parameter $y\in [-1,1]^{\mathbb{N}}$. Following previous work for affine parameter dependence and for the lognormal case, we use pointwise instead of norm-wise bounds to prove $\ell^p$-summability of the Taylor coefficients of the solution. As application, we consider surrogates for solutions to elliptic PDEs on parametric domains. Using a mapping to a nominal configuration, this case fits in the general framework, and higher convergence rates can be attained when modeling the parametric boundary via spatially localized functions. The theoretical results are supported by numerical experiments for the parametric domain problem, illustrating the efficiency of the proposed approach and providing further insight on numerical aspects. Although the methods and ideas are carried out for the steady-state diffusion equation, they extend easily to other elliptic and parabolic PDEs.

While there is wide agreement that physical activity is an important component of a healthy lifestyle, it is unclear how many people adhere to public health recommendations on physical activity. The Physical Activity Guidelines (PAG), published by the CDC, provide guidelines to American adults, but it is difficult to assess compliance with these guidelines. The PAG further complicate adherence assessment by recommending activity to occur in at least 10 minute bouts. To better understand the measurement capabilities of various instruments to quantify activity, and to propose an approach to evaluate activity relative to the PAG, researchers at Iowa State University administered the Physical Activity Measurement Survey (PAMS) to over 1,000 participants in four different Iowa counties. In this paper, we develop a two-part Bayesian measurement error model and apply it to the PAMS data in order to assess compliance to the PAG in the Iowa adult population. The model accurately accounts for the 10 minute bout requirement put forth in the PAG. The measurement error model corrects biased estimates and accounts for day to day variation in activity. The model is also applied to the nationally representative National Health and Nutrition Examination Survey.

Robustness to adversarial attacks is typically evaluated with adversarial accuracy. While essential, this metric does not capture all aspects of robustness and in particular leaves out the question of how many perturbations can be found for each point. In this work, we introduce an alternative approach, adversarial sparsity, which quantifies how difficult it is to find a successful perturbation given both an input point and a constraint on the direction of the perturbation. We show that sparsity provides valuable insight into neural networks in multiple ways: for instance, it illustrates important differences between current state-of-the-art robust models them that accuracy analysis does not, and suggests approaches for improving their robustness. When applying broken defenses effective against weak attacks but not strong ones, sparsity can discriminate between the totally ineffective and the partially effective defenses. Finally, with sparsity we can measure increases in robustness that do not affect accuracy: we show for example that data augmentation can by itself increase adversarial robustness, without using adversarial training.

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for overdispersed count data, for example, and allows for categorical or grouped covariates as well as continuous covariates. A randomized group-regularized optimization problem is studied. The added randomization allows us to construct a post-selection likelihood which we show to be adequate for selective inference when conditioning on the event of the selection of the grouped covariates. This likelihood also provides a selective point estimator, accounting for the selection by the group lasso. Confidence regions for the regression parameters in the selected model take the form of Wald-type regions and are shown to have bounded volume. The selective inference method for grouped lasso is illustrated on data from the national health and nutrition examination survey while simulations showcase its behaviour and favorable comparison with other methods.

The purpose of the research is to determine if currently available self-supervised learning techniques can accomplish human level comprehension of visual images using the same degree and amount of sensory input that people acquire from. Initial research on this topic solely considered data volume scaling. Here, we scale both the volume of data and the quality of the image. This scaling experiment is a self-supervised learning method that may be done without any outside financing. We find that scaling up data volume and picture resolution at the same time enables human-level item detection performance at sub-human sizes.We run a scaling experiment with vision transformers trained on up to 200000 images up to 256 ppi.

A variant of the standard notion of branching bisimilarity for processes with discrete relative timing is proposed which is coarser than the standard notion. Using a version of ACP (Algebra of Communicating Processes) with abstraction for processes with discrete relative timing, it is shown that the proposed variant allows of both the functional correctness and the performance properties of the PAR (Positive Acknowledgement with Retransmission) protocol to be analyzed. In the version of ACP concerned, the difference between the standard notion of branching bisimilarity and its proposed variant is characterized by a single axiom schema.

This study focuses on comparing deep learning methods for the segmentation and quantification of uncertainty in prostate segmentation from MRI images. The aim is to improve the workflow of prostate cancer detection and diagnosis. Seven different U-Net-based architectures, augmented with Monte-Carlo dropout, are evaluated for automatic segmentation of the central zone, peripheral zone, transition zone, and tumor, with uncertainty estimation. The top-performing model in this study is the Attention R2U-Net, achieving a mean Intersection over Union (IoU) of 76.3% and Dice Similarity Coefficient (DSC) of 85% for segmenting all zones. Additionally, Attention R2U-Net exhibits the lowest uncertainty values, particularly in the boundaries of the transition zone and tumor, when compared to the other models.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.