We study a multivariate version of trend filtering, called Kronecker trend filtering or KTF, for the case in which the design points form a lattice in $d$ dimensions. KTF is a natural extension of univariate trend filtering (Steidl et al., 2006; Kim et al., 2009; Tibshirani, 2014), and is defined by minimizing a penalized least squares problem whose penalty term sums the absolute (higher-order) differences of the parameter to be estimated along each of the coordinate directions. The corresponding penalty operator can be written in terms of Kronecker products of univariate trend filtering penalty operators, hence the name Kronecker trend filtering. Equivalently, one can view KTF in terms of an $\ell_1$-penalized basis regression problem where the basis functions are tensor products of falling factorial functions, a piecewise polynomial (discrete spline) basis that underlies univariate trend filtering. This paper is a unification and extension of the results in Sadhanala et al. (2016, 2017). We develop a complete set of theoretical results that describe the behavior of $k^{\mathrm{th}}$ order Kronecker trend filtering in $d$ dimensions, for every $k \geq 0$ and $d \geq 1$. This reveals a number of interesting phenomena, including the dominance of KTF over linear smoothers in estimating heterogeneously smooth functions, and a phase transition at $d=2(k+1)$, a boundary past which (on the high dimension-to-smoothness side) linear smoothers fail to be consistent entirely. We also leverage recent results on discrete splines from Tibshirani (2020), in particular, discrete spline interpolation results that enable us to extend the KTF estimate to any off-lattice location in constant-time (independent of the size of the lattice $n$).
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Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear inverse problems in noiseless settings, which significantly under-represents the complexity of real-world problems. In this work, we extend diffusion solvers to efficiently handle general noisy (non)linear inverse problems via approximation of the posterior sampling. Interestingly, the resulting posterior sampling scheme is a blended version of diffusion sampling with the manifold constrained gradient without a strict measurement consistency projection step, yielding a more desirable generative path in noisy settings compared to the previous studies. Our method demonstrates that diffusion models can incorporate various measurement noise statistics such as Gaussian and Poisson, and also efficiently handle noisy nonlinear inverse problems such as Fourier phase retrieval and non-uniform deblurring. Code available at //github.com/DPS2022/diffusion-posterior-sampling
Traceability, the ability to trace relevant software artifacts to support reasoning about the quality of the software and its development process, plays a crucial role in requirements and software engineering, particularly for safety-critical systems. In this chapter, we provide a comprehensive overview of the representative tasks in requirement traceability for which natural language processing (NLP) and related techniques have made considerable progress in the past decade. We first present the definition of traceability in the context of requirements and the overall engineering process, as well as other important concepts related to traceability tasks. Then, we discuss two tasks in detail, including trace link recovery and trace link maintenance. We also introduce two other related tasks concerning when trace links are used in practical contexts. For each task, we explain the characteristics of the task, how it can be approached through NLP techniques, and how to design and conduct the experiment to demonstrate the performance of the NLP techniques. We further discuss practical considerations on how to effectively apply NLP techniques and assess their effectiveness regarding the data set collection, the metrics selection, and the role of humans when evaluating the NLP approaches. Overall, this chapter prepares the readers with the fundamental knowledge of designing automated traceability solutions enabled by NLP in practice.
While advances continue to be made in model-based clustering, challenges persist in modeling various data types such as panel data. Multivariate panel data present difficulties for clustering algorithms due to the unique correlation structure, a consequence of taking observations on several subjects over multiple time points. Additionally, panel data are often plagued by missing data and dropouts, presenting issues for estimation algorithms. This research presents a family of hidden Markov models that compensate for the unique correlation structures that arise in panel data. A modified expectation-maximization algorithm capable of handling missing not at random data and dropout is presented and used to perform model estimation.
With the benefit of deep learning techniques, recent researches have made significant progress in image compression artifacts reduction. Despite their improved performances, prevailing methods only focus on learning a mapping from the compressed image to the original one but ignore the intrinsic attributes of the given compressed images, which greatly harms the performance of downstream parsing tasks. Different from these methods, we propose to decouple the intrinsic attributes into two complementary features for artifacts reduction,ie, the compression-insensitive features to regularize the high-level semantic representations during training and the compression-sensitive features to be aware of the compression degree. To achieve this, we first employ adversarial training to regularize the compressed and original encoded features for retaining high-level semantics, and we then develop the compression quality-aware feature encoder for compression-sensitive features. Based on these dual complementary features, we propose a Dual Awareness Guidance Network (DAGN) to utilize these awareness features as transformation guidance during the decoding phase. In our proposed DAGN, we develop a cross-feature fusion module to maintain the consistency of compression-insensitive features by fusing compression-insensitive features into the artifacts reduction baseline. Our method achieves an average 2.06 dB PSNR gains on BSD500, outperforming state-of-the-art methods, and only requires 29.7 ms to process one image on BSD500. Besides, the experimental results on LIVE1 and LIU4K also demonstrate the efficiency, effectiveness, and superiority of the proposed method in terms of quantitative metrics, visual quality, and downstream machine vision tasks.
Since the advent of Deepfakes in digital media, the development of robust and reliable detection mechanism is urgently called for. In this study, we explore a novel approach to Deepfake detection by utilizing electroencephalography (EEG) measured from the neural processing of a human participant who viewed and categorized Deepfake stimuli from the FaceForensics++ datset. These measurements serve as input features to a binary support vector classifier, trained to discriminate between real and manipulated facial images. We examine whether EEG data can inform Deepfake detection and also if it can provide a generalized representation capable of identifying Deepfakes beyond the training domain. Our preliminary results indicate that human neural processing signals can be successfully integrated into Deepfake detection frameworks and hint at the potential for a generalized neural representation of artifacts in computer generated faces. Moreover, our study provides next steps towards the understanding of how digital realism is embedded in the human cognitive system, possibly enabling the development of more realistic digital avatars in the future.
We model a Markov decision process, parametrized by an unknown parameter, and study the asymptotic behavior of a sampling-based algorithm, called Thompson sampling. The standard definition of regret is not always suitable to evaluate a policy, especially when the underlying chain structure is general. We show that the standard (expected) regret can grow (super-)linearly and fails to capture the notion of learning in realistic settings with non-trivial state evolution. By decomposing the standard (expected) regret, we develop a new metric, called the expected residual regret, which forgets the immutable consequences of past actions. Instead, it measures regret against the optimal reward moving forward from the current period. We show that the expected residual regret of the Thompson sampling algorithm is upper bounded by a term which converges exponentially fast to 0. We present conditions under which the posterior sampling error of Thompson sampling converges to 0 almost surely. We then introduce the probabilistic version of the expected residual regret and present conditions under which it converges to 0 almost surely. Thus, we provide a viable concept of learning for sampling algorithms which will serve useful in broader settings than had been considered previously.
We propose the characteristic generator, a novel one-step generative model that combines the efficiency of sampling in Generative Adversarial Networks (GANs) with the stable performance of flow-based models. Our model is driven by characteristics, along which the probability density transport can be described by ordinary differential equations (ODEs). Specifically, We estimate the velocity field through nonparametric regression and utilize Euler method to solve the probability flow ODE, generating a series of discrete approximations to the characteristics. We then use a deep neural network to fit these characteristics, ensuring a one-step mapping that effectively pushes the prior distribution towards the target distribution. In the theoretical aspect, we analyze the errors in velocity matching, Euler discretization, and characteristic fitting to establish a non-asymptotic convergence rate for the characteristic generator in 2-Wasserstein distance. To the best of our knowledge, this is the first thorough analysis for simulation-free one step generative models. Additionally, our analysis refines the error analysis of flow-based generative models in prior works. We apply our method on both synthetic and real datasets, and the results demonstrate that the characteristic generator achieves high generation quality with just a single evaluation of neural network.
We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and high-dimensional nature of random variables, a byproduct of the adaptive mechanisms inherent in sequential decision processes. Our work features a novel construction of a stopped process, facilitating the analysis of a sequence of concentration events that are interconnected in a sequential manner. By employing the method of mixtures within a self-normalized process, derived from the stopped process, we achieve a desired non-asymptotic probability bound. This bound represents a non-trivial martingale extension of the Johnson-Lindenstrauss (JL) lemma, marking a pioneering contribution to the literature on random projection and sequential analysis.
Generative AI models are often used to perform mimicry attacks, where a pretrained model is fine-tuned on a small sample of images to learn to mimic a specific artist of interest. While researchers have introduced multiple anti-mimicry protection tools (Mist, Glaze, Anti-Dreambooth), recent evidence points to a growing trend of mimicry models using videos as sources of training data. This paper presents our experiences exploring techniques to disrupt style mimicry on video imagery. We first validate that mimicry attacks can succeed by training on individual frames extracted from videos. We show that while anti-mimicry tools can offer protection when applied to individual frames, this approach is vulnerable to an adaptive countermeasure that removes protection by exploiting randomness in optimization results of consecutive (nearly-identical) frames. We develop a new, tool-agnostic framework that segments videos into short scenes based on frame-level similarity, and use a per-scene optimization baseline to remove inter-frame randomization while reducing computational cost. We show via both image level metrics and an end-to-end user study that the resulting protection restores protection against mimicry (including the countermeasure). Finally, we develop another adaptive countermeasure and find that it falls short against our framework.
Benefit from the quick development of deep learning techniques, salient object detection has achieved remarkable progresses recently. However, there still exists following two major challenges that hinder its application in embedded devices, low resolution output and heavy model weight. To this end, this paper presents an accurate yet compact deep network for efficient salient object detection. More specifically, given a coarse saliency prediction in the deepest layer, we first employ residual learning to learn side-output residual features for saliency refinement, which can be achieved with very limited convolutional parameters while keep accuracy. Secondly, we further propose reverse attention to guide such side-output residual learning in a top-down manner. By erasing the current predicted salient regions from side-output features, the network can eventually explore the missing object parts and details which results in high resolution and accuracy. Experiments on six benchmark datasets demonstrate that the proposed approach compares favorably against state-of-the-art methods, and with advantages in terms of simplicity, efficiency (45 FPS) and model size (81 MB).
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