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We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. This is used to show that experimental designs that are optimal under an assumption of independent, homoscedastic responses can be minimax robust, in broad classes of alternate covariance structures. In particular it can justify the common practice of disregarding possible dependence, or heteroscedasticity, at the design stage of an experiment.

In plug-and-play (PnP) regularization, the proximal operator in algorithms such as ISTA and ADMM is replaced by a powerful denoiser. This formal substitution works surprisingly well in practice. In fact, PnP has been shown to give state-of-the-art results for various imaging applications. The empirical success of PnP has motivated researchers to understand its theoretical underpinnings and, in particular, its convergence. It was shown in prior work that for kernel denoisers such as the nonlocal means, PnP-ISTA provably converges under some strong assumptions on the forward model. The present work is motivated by the following questions: Can we relax the assumptions on the forward model? Can the convergence analysis be extended to PnP-ADMM? Can we estimate the convergence rate? In this letter, we resolve these questions using the contraction mapping theorem: (i) for symmetric denoisers, we show that (under mild conditions) PnP-ISTA and PnP-ADMM exhibit linear convergence; and (ii) for kernel denoisers, we show that PnP-ISTA and PnP-ADMM converge linearly for image inpainting. We validate our theoretical findings using reconstruction experiments.

With the rapid progress in virtual reality (VR) technology, the scope of VR applications has greatly expanded across various domains. However, the superiority of VR training over traditional methods and its impact on learning efficacy are still uncertain. To investigate whether VR training is more effective than traditional methods, we designed virtual training systems for mechanical assembly on both VR and desktop platforms, subsequently conducting pre-test and post-test experiments. A cohort of 53 students, all enrolled in engineering drawing course without prior knowledge distinctions, was randomly divided into three groups: physical training, desktop virtual training, and immersive VR training. Our investigation utilized analysis of covariance (ANCOVA) to examine the differences in post-test scores among the three groups while controlling for pre-test scores. The group that received VR training showed the highest scores on the post-test. Another facet of our study delved into the presence of the virtual system. We developed a specialized scale to assess this aspect for our research objectives. Our findings indicate that VR training can enhance the sense of presence, particularly in terms of sensory factors and realism factors. Moreover, correlation analysis uncovers connections between the various dimensions of presence. This study confirms that using VR training can improve learning efficacy and the presence in the context of mechanical assembly, surpassing traditional training methods. Furthermore, it provides empirical evidence supporting the integration of VR technology in higher education and engineering training. This serves as a reference for the practical application of VR technology in different fields.

Atomic congestion games are a classic topic in network design, routing, and algorithmic game theory, and are capable of modeling congestion and flow optimization tasks in various application areas. While both the price of anarchy for such games as well as the computational complexity of computing their Nash equilibria are by now well-understood, the computational complexity of computing a system-optimal set of strategies -- that is, a centrally planned routing that minimizes the average cost of agents -- is severely understudied in the literature. We close this gap by identifying the exact boundaries of tractability for the problem through the lens of the parameterized complexity paradigm. After showing that the problem remains highly intractable even on extremely simple networks, we obtain a set of results which demonstrate that the structural parameters which control the computational (in)tractability of the problem are not vertex-separator based in nature (such as, e.g., treewidth), but rather based on edge separators. We conclude by extending our analysis towards the (even more challenging) min-max variant of the problem.

Current quantum computers can only solve optimization problems of a very limited size. For larger problems, decomposition methods are required in which the original problem is broken down into several smaller sub-problems. These are then solved on the quantum computer and their solutions are merged into a final solution for the original problem. Often, these decomposition methods do not take the specific problem structure into account. In this paper, we present a tailored method using a divide-and-conquer strategy to solve the number partitioning problem (NPP) with a large number of variables. The idea is to perform a specialized decomposition into smaller NPPs, which can be solved on a quantum computer, and then recombine the results into another small auxiliary NPP. Solving this auxiliary problem yields an approximate solution of the original larger problem. We experimentally verify that our method allows to solve NPPs with over a thousand variables using a D-Wave quantum annealer.

Financial sentiment analysis plays a crucial role in uncovering latent patterns and detecting emerging trends, enabling individuals to make well-informed decisions that may yield substantial advantages within the constantly changing realm of finance. Recently, Large Language Models (LLMs) have demonstrated their effectiveness in diverse domains, showcasing remarkable capabilities even in zero-shot and few-shot in-context learning for various Natural Language Processing (NLP) tasks. Nevertheless, their potential and applicability in the context of financial sentiment analysis have not been thoroughly explored yet. To bridge this gap, we employ two approaches: in-context learning (with a focus on gpt-3.5-turbo model) and fine-tuning LLMs on a finance-domain dataset. Given the computational costs associated with fine-tuning LLMs with large parameter sizes, our focus lies on smaller LLMs, spanning from 250M to 3B parameters for fine-tuning. We then compare the performances with state-of-the-art results to evaluate their effectiveness in the finance-domain. Our results demonstrate that fine-tuned smaller LLMs can achieve comparable performance to state-of-the-art fine-tuned LLMs, even with models having fewer parameters and a smaller training dataset. Additionally, the zero-shot and one-shot performance of LLMs produces comparable results with fine-tuned smaller LLMs and state-of-the-art outcomes. Furthermore, our analysis demonstrates that there is no observed enhancement in performance for finance-domain sentiment analysis when the number of shots for in-context learning is increased.

The concept of causality plays an important role in human cognition . In the past few decades, causal inference has been well developed in many fields, such as computer science, medicine, economics, and education. With the advancement of deep learning techniques, it has been increasingly used in causal inference against counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective optimization functions to estimate counterfactual data unbiasedly based on the different optimization methods. This paper focuses on the survey of the deep causal models, and its core contributions are as follows: 1) we provide relevant metrics under multiple treatments and continuous-dose treatment; 2) we incorporate a comprehensive overview of deep causal models from both temporal development and method classification perspectives; 3) we assist a detailed and comprehensive classification and analysis of relevant datasets and source code.

The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized models. Overparameterized models are excessively complex with respect to the size of the training dataset, which results in them perfectly fitting (i.e., interpolating) the training data, which is usually noisy. Such interpolation of noisy data is traditionally associated with detrimental overfitting, and yet a wide range of interpolating models -- from simple linear models to deep neural networks -- have recently been observed to generalize extremely well on fresh test data. Indeed, the recently discovered double descent phenomenon has revealed that highly overparameterized models often improve over the best underparameterized model in test performance. Understanding learning in this overparameterized regime requires new theory and foundational empirical studies, even for the simplest case of the linear model. The underpinnings of this understanding have been laid in very recent analyses of overparameterized linear regression and related statistical learning tasks, which resulted in precise analytic characterizations of double descent. This paper provides a succinct overview of this emerging theory of overparameterized ML (henceforth abbreviated as TOPML) that explains these recent findings through a statistical signal processing perspective. We emphasize the unique aspects that define the TOPML research area as a subfield of modern ML theory and outline interesting open questions that remain.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.