Autoencoders have been extensively used in the development of recent anomaly detection techniques. The premise of their application is based on the notion that after training the autoencoder on normal training data, anomalous inputs will exhibit a significant reconstruction error. Consequently, this enables a clear differentiation between normal and anomalous samples. In practice, however, it is observed that autoencoders can generalize beyond the normal class and achieve a small reconstruction error on some of the anomalous samples. To improve the performance, various techniques propose additional components and more sophisticated training procedures. In this work, we propose a remarkably straightforward alternative: instead of adding neural network components, involved computations, and cumbersome training, we complement the reconstruction loss with a computationally light term that regulates the norm of representations in the latent space. The simplicity of our approach minimizes the requirement for hyperparameter tuning and customization for new applications which, paired with its permissive data modality constraint, enhances the potential for successful adoption across a broad range of applications. We test the method on various visual and tabular benchmarks and demonstrate that the technique matches and frequently outperforms alternatives. We also provide a theoretical analysis and numerical simulations that help demonstrate the underlying process that unfolds during training and how it can help with anomaly detection. This mitigates the black-box nature of autoencoder-based anomaly detection algorithms and offers an avenue for further investigation of advantages, fail cases, and potential new directions.
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Diffusion probabilistic models (DPMs) are a powerful class of generative models known for their ability to generate high-fidelity image samples. A major challenge in the implementation of DPMs is the slow sampling process. In this work, we bring a high-efficiency sampler for DPMs. Specifically, we propose a score-based exact solution paradigm for the diffusion ODEs corresponding to the sampling process of DPMs, which introduces a new perspective on developing numerical algorithms for solving diffusion ODEs. To achieve an efficient sampler, we propose a recursive derivative estimation (RDE) method to reduce the estimation error. With our proposed solution paradigm and RDE method, we propose the score-integrand solver with the convergence order guarantee as efficient solver (SciRE-Solver) for solving diffusion ODEs. The SciRE-Solver attains state-of-the-art (SOTA) sampling performance with a limited number of score function evaluations (NFE) on both discrete-time and continuous-time DPMs in comparison to existing training-free sampling algorithms. Such as, we achieve $3.48$ FID with $12$ NFE and $2.42$ FID with $20$ NFE for continuous-time DPMs on CIFAR10, respectively. Different from other samplers, SciRE-Solver has the promising potential to surpass the FIDs achieved in the original papers of some pre-trained models with just fewer NFEs. For example, we reach SOTA value of $2.40$ FID with $100$ NFE for continuous-time DPM and of $3.15$ FID with $84$ NFE for discrete-time DPM on CIFAR-10, as well as of $2.17$ ($2.02$) FID with $18$ ($50$) NFE for discrete-time DPM on CelebA 64$\times$64.
Making inference with spatial extremal dependence models can be computationally burdensome since they involve intractable and/or censored likelihoods. Building on recent advances in likelihood-free inference with neural Bayes estimators, that is, neural networks that approximate Bayes estimators, we develop highly efficient estimators for censored peaks-over-threshold models that encode censoring information in the neural network architecture. Our new method provides a paradigm shift that challenges traditional censored likelihood-based inference methods for spatial extremal dependence models. Our simulation studies highlight significant gains in both computational and statistical efficiency, relative to competing likelihood-based approaches, when applying our novel estimators to make inference with popular extremal dependence models, such as max-stable, $r$-Pareto, and random scale mixture process models. We also illustrate that it is possible to train a single neural Bayes estimator for a general censoring level, precluding the need to retrain the network when the censoring level is changed. We illustrate the efficacy of our estimators by making fast inference on hundreds-of-thousands of high-dimensional spatial extremal dependence models to assess extreme particulate matter 2.5 microns or less in diameter (PM2.5) concentration over the whole of Saudi Arabia.
Statistical models are at the heart of any empirical study for hypothesis testing. We present a new cross-platform Python-based package which employs different likelihood prescriptions through a plug-in system. This framework empowers users to propose, examine, and publish new likelihood prescriptions without developing software infrastructure, ultimately unifying and generalising different ways of constructing likelihoods and employing them for hypothesis testing, all in one place. Within this package, we propose a new simplified likelihood prescription that surpasses its predecessors' approximation accuracy by incorporating asymmetric uncertainties. Furthermore, our package facilitates the inclusion of various likelihood combination routines, thereby broadening the scope of independent studies through a meta-analysis. By remaining agnostic to the source of the likelihood prescription and the signal hypothesis generator, our platform allows for the seamless implementation of packages with different likelihood prescriptions, fostering compatibility and interoperability.
The approach to analysing compositional data has been dominated by the use of logratio transformations, to ensure exact subcompositional coherence and, in some situations, exact isometry as well. A problem with this approach is that data zeros, found in most applications, have to be replaced to allow the logarithmic transformation. An alternative new approach, called the `chiPower' transformation, which allows data zeros, is to combine the standardization inherent in the chi-square distance in correspondence analysis, with the essential elements of the Box-Cox power transformation. The chiPower transformation is justified because it} defines between-sample distances that tend to logratio distances for strictly positive data as the power parameter tends to zero, and are then equivalent to transforming to logratios. For data with zeros, a value of the power can be identified that brings the chiPower transformation as close as possible to a logratio transformation, without having to substitute the zeros. Especially in the area of high-dimensional data, this alternative approach can present such a high level of coherence and isometry as to be a valid approach to the analysis of compositional data. Furthermore, in a supervised learning context, if the compositional variables serve as predictors of a response in a modelling framework, for example generalized linear models, then the power can be used as a tuning parameter in optimizing the accuracy of prediction through cross-validation. The chiPower-transformed variables have a straightforward interpretation, since they are each identified with single compositional parts, not ratios.
Solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional approximations in polynomials are computed as in stochastic Galerkin and stochastic collocations methods. This work investigates a residual based adaptive algorithm used to approximate the solution of the stationary diffusion equation with lognormal coefficients. It is known that the refinement procedure is reliable, but the theoretical convergence of the scheme for this class of unbounded coefficients remains a challenging open question. This paper advances the theoretical results by providing a quasi-error reduction results for the adaptive solution of the lognormal stationary diffusion problem. A computational example supports the theoretical statement.
Characterizing shapes of high-dimensional objects via Ricci curvatures plays a critical role in many research areas in mathematics and physics. However, even though several discretizations of Ricci curvatures for discrete combinatorial objects such as networks have been proposed and studied by mathematicians, the computational complexity aspects of these discretizations have escaped the attention of theoretical computer scientists to a large extent. In this paper, we study one such discretization, namely the Ollivier-Ricci curvature, from the perspective of efficient computation by fine-grained reductions and local query-based algorithms. Our main contributions are the following. (a) We relate our curvature computation problem to minimum weight perfect matching problem on complete bipartite graphs via fine-grained reduction. (b) We formalize the computational aspects of the curvature computation problems in suitable frameworks so that they can be studied by researchers in local algorithms. (c) We provide the first known lower and upper bounds on queries for query-based algorithms for the curvature computation problems in our local algorithms framework. En route, we also illustrate a localized version of our fine-grained reduction. We believe that our results bring forth an intriguing set of research questions, motivated both in theory and practice, regarding designing efficient algorithms for curvatures of objects.
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.
Defensive deception is a promising approach for cyberdefense. Although defensive deception is increasingly popular in the research community, there has not been a systematic investigation of its key components, the underlying principles, and its tradeoffs in various problem settings. This survey paper focuses on defensive deception research centered on game theory and machine learning, since these are prominent families of artificial intelligence approaches that are widely employed in defensive deception. This paper brings forth insights, lessons, and limitations from prior work. It closes with an outline of some research directions to tackle major gaps in current defensive deception research.
Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.
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