Information projections have found many important applications in probability theory, statistics, and related fields. In the field of hypothesis testing in particular, the reverse information projection (RIPr) has recently been shown to lead to so-called growth-rate optimal (GRO) e-statistics for testing simple alternatives against composite null hypotheses. However, the RIPr as well as the GRO criterion are only defined in cases where the infimum information divergence between the null and alternative is finite. Here, we show that under much weaker conditions there often still exists an element in the alternative that is `closest' to the null: the universal reverse information projection. The universal reverse information projection and its non-universal counterpart coincide whenever the KL is finite, and the strictness of this generalization will be shown by an example. Furthermore, the universal RIPr leads to optimal e-statistics in a sense that is a novel, but natural, extension of the GRO criterion. Finally, we discuss conditions under which the universal RIPr is a strict sub-probability distributions, and conditions under which an approximation of the universal RIPr leads to approximate e-statistics.
相關內容
Clans are representations of generalized algebraic theories that contain more information than the finite-limit categories associated to the l.f.p. categories of models via Gabriel-Ulmer duality. Refining Gabriel-Ulmer duality to account for this additional information, this article presents a duality theory between clans and l.f.p. categories equipped with a weak factorization system subject to axioms.
Formal methods were frequently shown to be effective and, perhaps because of that, practitioners are interested in using them more often. Still, these methods are far less applied than expected, particularly, in critical domains where they are strongly recommended and where they have the greatest potential. Our hypothesis is that formal methods still seem not to be applicable enough or ready for their intended use. In critical software engineering, what do we mean when we speak of a formal method? And what does it mean for such a method to be applicable both from a scientific and practical viewpoint? Based on what the literature tells about the first question, with this manifesto, we lay out a set of principles that when followed by a formal method give rise to its mature applicability in a given scope. Rather than exercising criticism of past developments, this manifesto strives to foster an increased use of formal methods to the maximum benefit.
We characterize absolutely continuous symmetric copulas with square integrable densities in this paper. This characterization is used to create new copula families, that are perturbations of the independence copula. The full study of mixing properties of Markov chains generated by these copula families is conducted. An extension that includes the Farlie-Gumbel-Morgenstern family of copulas is proposed. We propose some examples of copulas that generate non-mixing Markov chains, but whose convex combinations generate $\psi$-mixing Markov chains. Some general results on $\psi$-mixing are given. The Spearman's correlation $\rho_S$ and Kendall's $\tau$ are provided for the created copula families. Some general remarks are provided for $\rho_S$ and $\tau$. A central limit theorem is provided for parameter estimators in one example. A simulation study is conducted to support derived asymptotic distributions for some examples.
We present a method for learning multiple scene representations given a small labeled set, by exploiting the relationships between such representations in the form of a multi-task hypergraph. We also show how we can use the hypergraph to improve a powerful pretrained VisTransformer model without any additional labeled data. In our hypergraph, each node is an interpretation layer (e.g., depth or segmentation) of the scene. Within each hyperedge, one or several input nodes predict the layer at the output node. Thus, each node could be an input node in some hyperedges and an output node in others. In this way, multiple paths can reach the same node, to form ensembles from which we obtain robust pseudolabels, which allow self-supervised learning in the hypergraph. We test different ensemble models and different types of hyperedges and show superior performance to other multi-task graph models in the field. We also introduce Dronescapes, a large video dataset captured with UAVs in different complex real-world scenes, with multiple representations, suitable for multi-task learning.
Out-of-distribution detection is one of the most critical issue in the deployment of machine learning. The data analyst must assure that data in operation should be compliant with the training phase as well as understand if the environment has changed in a way that autonomous decisions would not be safe anymore. The method of the paper is based on eXplainable Artificial Intelligence (XAI); it takes into account different metrics to identify any resemblance between in-distribution and out of, as seen by the XAI model. The approach is non-parametric and distributional assumption free. The validation over complex scenarios (predictive maintenance, vehicle platooning, covert channels in cybersecurity) corroborates both precision in detection and evaluation of training-operation conditions proximity. Results are available via open source and open data at the following link: //github.com/giacomo97cnr/Rule-based-ODD.
Counterfactual explanations are an emerging tool to enhance interpretability of deep learning models. Given a sample, these methods seek to find and display to the user similar samples across the decision boundary. In this paper, we propose a generative adversarial counterfactual approach for satellite image time series in a multi-class setting for the land cover classification task. One of the distinctive features of the proposed approach is the lack of prior assumption on the targeted class for a given counterfactual explanation. This inherent flexibility allows for the discovery of interesting information on the relationship between land cover classes. The other feature consists of encouraging the counterfactual to differ from the original sample only in a small and compact temporal segment. These time-contiguous perturbations allow for a much sparser and, thus, interpretable solution. Furthermore, plausibility/realism of the generated counterfactual explanations is enforced via the proposed adversarial learning strategy.
Text-to-image person re-identification (TIReID) is a compelling topic in the cross-modal community, which aims to retrieve the target person based on a textual query. Although numerous TIReID methods have been proposed and achieved promising performance, they implicitly assume the training image-text pairs are correctly aligned, which is not always the case in real-world scenarios. In practice, the image-text pairs inevitably exist under-correlated or even false-correlated, a.k.a noisy correspondence (NC), due to the low quality of the images and annotation errors. To address this problem, we propose a novel Robust Dual Embedding method (RDE) that can learn robust visual-semantic associations even with NC. Specifically, RDE consists of two main components: 1) A Confident Consensus Division (CCD) module that leverages the dual-grained decisions of dual embedding modules to obtain a consensus set of clean training data, which enables the model to learn correct and reliable visual-semantic associations. 2) A Triplet-Alignment Loss (TAL) relaxes the conventional triplet-ranking loss with hardest negatives, which tends to rapidly overfit NC, to a log-exponential upper bound over all negatives, thus preventing the model from overemphasizing false image-text pairs. We conduct extensive experiments on three public benchmarks, namely CUHK-PEDES, ICFG-PEDES, and RSTPReID, to evaluate the performance and robustness of our RDE. Our method achieves state-of-the-art results both with and without synthetic noisy correspondences on all three datasets.
Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical simulators are required to train a model to accurately predict the complex physical behaviors associated with this process. In practice, the available training data are always limited in large-scale 3D problems due to the high computational cost. Therefore, we propose to use a multi-fidelity Fourier Neural Operator to solve large-scale GCS problems with more affordable multi-fidelity training datasets. The Fourier Neural Operator has a desirable grid-invariant property, which simplifies the transfer learning procedure between datasets with different discretization. We first test the model efficacy on a GCS reservoir model being discretized into 110k grid cells. The multi-fidelity model can predict with accuracy comparable to a high-fidelity model trained with the same amount of high-fidelity data with 81% less data generation costs. We further test the generalizability of the multi-fidelity model on a same reservoir model with a finer discretization of 1 million grid cells. This case was made more challenging by employing high-fidelity and low-fidelity datasets generated by different geostatistical models and reservoir simulators. We observe that the multi-fidelity FNO model can predict pressure fields with reasonable accuracy even when the high-fidelity data are extremely limited.
Contrastive loss has been increasingly used in learning representations from multiple modalities. In the limit, the nature of the contrastive loss encourages modalities to exactly match each other in the latent space. Yet it remains an open question how the modality alignment affects the downstream task performance. In this paper, based on an information-theoretic argument, we first prove that exact modality alignment is sub-optimal in general for downstream prediction tasks. Hence we advocate that the key of better performance lies in meaningful latent modality structures instead of perfect modality alignment. To this end, we propose three general approaches to construct latent modality structures. Specifically, we design 1) a deep feature separation loss for intra-modality regularization; 2) a Brownian-bridge loss for inter-modality regularization; and 3) a geometric consistency loss for both intra- and inter-modality regularization. Extensive experiments are conducted on two popular multi-modal representation learning frameworks: the CLIP-based two-tower model and the ALBEF-based fusion model. We test our model on a variety of tasks including zero/few-shot image classification, image-text retrieval, visual question answering, visual reasoning, and visual entailment. Our method achieves consistent improvements over existing methods, demonstrating the effectiveness and generalizability of our proposed approach on latent modality structure regularization.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191