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Average calibration of the uncertainties of machine learning regression tasks can be tested in two ways. One way is to estimate the calibration error (CE) as the difference between the mean absolute error (MSE) and the mean variance (MV) or mean squared uncertainty. The alternative is to compare the mean squared z-scores or scaled errors (ZMS) to 1. Both approaches might lead to different conclusion, as illustrated on an ensemble of datasets from the recent machine learning uncertainty quantification literature. It is shown here that the CE is very sensitive to the distribution of uncertainties, and notably to the presence of outlying uncertainties, and that it cannot be used reliably for calibration testing. By contrast, the ZMS statistic does not present this sensitivity issue and offers the most reliable approach in this context. Implications for the validation of conditional calibration are discussed.

Weak supervision searches have in principle the advantages of both being able to train on experimental data and being able to learn distinctive signal properties. However, the practical applicability of such searches is limited by the fact that successfully training a neural network via weak supervision can require a large amount of signal. In this work, we seek to create neural networks that can learn from less experimental signal by using transfer and meta-learning. The general idea is to first train a neural network on simulations, thereby learning concepts that can be reused or becoming a more efficient learner. The neural network would then be trained on experimental data and should require less signal because of its previous training. We find that transfer and meta-learning can substantially improve the performance of weak supervision searches.

Interactive segmentation, an integration of AI algorithms and human expertise, premises to improve the accuracy and efficiency of curating large-scale, detailed-annotated datasets in healthcare. Human experts revise the annotations predicted by AI, and in turn, AI improves its predictions by learning from these revised annotations. This interactive process continues to enhance the quality of annotations until no major revision is needed from experts. The key challenge is how to leverage AI predicted and expert revised annotations to iteratively improve the AI. Two problems arise: (1) The risk of catastrophic forgetting--the AI tends to forget the previously learned classes if it is only retrained using the expert revised classes. (2) Computational inefficiency when retraining the AI using both AI predicted and expert revised annotations; moreover, given the dominant AI predicted annotations in the dataset, the contribution of newly revised annotations--often account for a very small fraction--to the AI training remains marginal. This paper proposes Continual Tuning to address the problems from two perspectives: network design and data reuse. Firstly, we design a shared network for all classes followed by class-specific networks dedicated to individual classes. To mitigate forgetting, we freeze the shared network for previously learned classes and only update the class-specific network for revised classes. Secondly, we reuse a small fraction of data with previous annotations to avoid over-computing. The selection of such data relies on the importance estimate of each data. The importance score is computed by combining the uncertainty and consistency of AI predictions. Our experiments demonstrate that Continual Tuning achieves a speed 16x greater than repeatedly training AI from scratch without compromising the performance.

We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on Gaussian priors, leading to convenient conjugate formulae for posterior inference. We review recent results providing theoretical guarantees on the quality of the resulting posterior-based estimation and uncertainty quantification, and we discuss the application of the theory to the important classes of Gaussian series priors defined on the Dirichlet-Laplacian eigenbasis and Mat\'ern process priors. We provide an implementation of posterior inference for both classes of priors, and investigate its performance in a numerical simulation study.

We propose and analyse boundary-preserving schemes for the strong approximations of some scalar SDEs with non-globally Lipschitz drift and diffusion coefficients whose state-space is bounded. The schemes consists of a Lamperti transform followed by a Lie--Trotter splitting. We prove $L^{p}(\Omega)$-convergence of order $1$, for every $p \geq 1$, of the schemes and exploit the Lamperti transform to confine the numerical approximations to the state-space of the considered SDE. We provide numerical experiments that confirm the theoretical results and compare the proposed Lamperti-splitting schemes to other numerical schemes for SDEs.

Language models (LMs) may appear insensitive to word order changes in natural language understanding (NLU) tasks. In this paper, we propose that linguistic redundancy can explain this phenomenon, whereby word order and other linguistic cues such as case markers provide overlapping and thus redundant information. Our hypothesis is that models exhibit insensitivity to word order when the order provides redundant information, and the degree of insensitivity varies across tasks. We quantify how informative word order is using mutual information (MI) between unscrambled and scrambled sentences. Our results show the effect that the less informative word order is, the more consistent the model's predictions are between unscrambled and scrambled sentences. We also find that the effect varies across tasks: for some tasks, like SST-2, LMs' prediction is almost always consistent with the original one even if the Pointwise-MI (PMI) changes, while for others, like RTE, the consistency is near random when the PMI gets lower, i.e., word order is really important.

Modern instruction-tuned models have become highly capable in text generation tasks such as summarization, and are expected to be released at a steady pace. In practice one may now wish to choose confidently, but with minimal effort, the best performing summarization model when applied to a new domain or purpose. In this work, we empirically investigate the test sample size necessary to select a preferred model in the context of news summarization. Empirical results reveal that comparative evaluation converges quickly for both automatic and human evaluation, with clear preferences for a system emerging from under 100 examples. The human preference data allows us to quantify how well automatic scores can reproduce preference rankings across a variety of downstream summarization tasks. We find that, while automatic metrics are stable at smaller sample sizes, only some automatic metrics are able to moderately predict model win rates according to human preference.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the local geometry and update iteratively. Even though solving non-convex functions is NP-hard in the worst case, the optimization quality in practice is often not an issue -- optimizers are largely believed to find approximate global minima. Researchers hypothesize a unified explanation for this intriguing phenomenon: most of the local minima of the practically-used objectives are approximately global minima. We rigorously formalize it for concrete instances of machine learning problems.

Compared with cheap addition operation, multiplication operation is of much higher computation complexity. The widely-used convolutions in deep neural networks are exactly cross-correlation to measure the similarity between input feature and convolution filters, which involves massive multiplications between float values. In this paper, we present adder networks (AdderNets) to trade these massive multiplications in deep neural networks, especially convolutional neural networks (CNNs), for much cheaper additions to reduce computation costs. In AdderNets, we take the $\ell_1$-norm distance between filters and input feature as the output response. The influence of this new similarity measure on the optimization of neural network have been thoroughly analyzed. To achieve a better performance, we develop a special back-propagation approach for AdderNets by investigating the full-precision gradient. We then propose an adaptive learning rate strategy to enhance the training procedure of AdderNets according to the magnitude of each neuron's gradient. As a result, the proposed AdderNets can achieve 74.9% Top-1 accuracy 91.7% Top-5 accuracy using ResNet-50 on the ImageNet dataset without any multiplication in convolution layer.