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We consider the parameter estimation problem in the deviated Gaussian mixture of experts in which the data are generated from $(1 - \lambda^{\ast}) g_0(Y| X)+ \lambda^{\ast} \sum_{i = 1}^{k_{\ast}} p_{i}^{\ast} f(Y|(a_{i}^{\ast})^{\top}X+b_i^{\ast},\sigma_{i}^{\ast})$, where $X, Y$ are respectively a covariate vector and a response variable, $g_{0}(Y|X)$ is a known function, $\lambda^{\ast} \in [0, 1]$ is true but unknown mixing proportion, and $(p_{i}^{\ast}, a_{i}^{\ast}, b_{i}^{\ast}, \sigma_{i}^{\ast})$ for $1 \leq i \leq k^{\ast}$ are unknown parameters of the Gaussian mixture of experts. This problem arises from the goodness-of-fit test when we would like to test whether the data are generated from $g_{0}(Y|X)$ (null hypothesis) or they are generated from the whole mixture (alternative hypothesis). Based on the algebraic structure of the expert functions and the distinguishability between $g_0$ and the mixture part, we construct novel Voronoi-based loss functions to capture the convergence rates of maximum likelihood estimation (MLE) for our models. We further demonstrate that our proposed loss functions characterize the local convergence rates of parameter estimation more accurately than the generalized Wasserstein, a loss function being commonly used for estimating parameters in the Gaussian mixture of experts.

Diffusion models (DMs) have gained attention in Missing Data Imputation (MDI), but there remain two long-neglected issues to be addressed: (1). Inaccurate Imputation, which arises from inherently sample-diversification-pursuing generative process of DMs. (2). Difficult Training, which stems from intricate design required for the mask matrix in model training stage. To address these concerns within the realm of numerical tabular datasets, we introduce a novel principled approach termed Kernelized Negative Entropy-regularized Wasserstein gradient flow Imputation (KnewImp). Specifically, based on Wasserstein gradient flow (WGF) framework, we first prove that issue (1) stems from the cost functionals implicitly maximized in DM-based MDI are equivalent to the MDI's objective plus diversification-promoting non-negative terms. Based on this, we then design a novel cost functional with diversification-discouraging negative entropy and derive our KnewImp approach within WGF framework and reproducing kernel Hilbert space. After that, we prove that the imputation procedure of KnewImp can be derived from another cost functional related to the joint distribution, eliminating the need for the mask matrix and hence naturally addressing issue (2). Extensive experiments demonstrate that our proposed KnewImp approach significantly outperforms existing state-of-the-art methods.

Sentiment Analysis (SA) is a crucial aspect of Natural Language Processing (NLP), addressing subjective assessments in textual content. Syntactic parsing is useful in SA because explicit syntactic information can improve accuracy while providing explainability, but it tends to be a computational bottleneck in practice due to the slowness of parsing algorithms. This paper addresses said bottleneck by using a SEquence Labeling Syntactic Parser (SELSP) to inject syntax into SA. By treating dependency parsing as a sequence labeling problem, we greatly enhance the speed of syntax-based SA. SELSP is trained and evaluated on a ternary polarity classification task, demonstrating its faster performance and better accuracy in polarity prediction tasks compared to conventional parsers like Stanza and to heuristic approaches that use shallow syntactic rules for SA like VADER. This increased speed and improved accuracy make SELSP particularly appealing to SA practitioners in both research and industry. In addition, we test several sentiment dictionaries on our SELSP to see which one improves the performance in polarity prediction tasks. Moreover, we compare the SELSP with Transformer-based models trained on a 5-label classification task. The results show that dictionaries that capture polarity judgment variation provide better results than dictionaries that ignore polarity judgment variation. Moreover, we show that SELSP is considerably faster than Transformer-based models in polarity prediction tasks.

In the Levenshtein's sequence reconstruction problem a codeword is transmitted through $N$ channels and in each channel a set of errors is introduced to the transmitted word. In previous works, the restriction that each channel provides a unique output word has been essential. In this work, we assume only that each channel introduces a unique set of errors to the transmitted word and hence some output words can also be identical. As we will discuss, this interpretation is both natural and useful for deletion and insertion errors. We give properties, techniques and (optimal) results for this situation. Quaternary alphabets are relevant due to applications related to DNA-memories. Hence, we introduce an efficient Las Vegas style decoding algorithm for simultaneous insertion, deletion and substitution errors in $q$-ary Hamming spaces for $q \geq 4$.

This paper introduces a "proof of concept" for a new approach to assistive robotics, integrating edge computing with Natural Language Processing (NLP) and computer vision to enhance the interaction between humans and robotic systems. Our "proof of concept" demonstrates the feasibility of using large language models (LLMs) and vision systems in tandem for interpreting and executing complex commands conveyed through natural language. This integration aims to improve the intuitiveness and accessibility of assistive robotic systems, making them more adaptable to the nuanced needs of users with disabilities. By leveraging the capabilities of edge computing, our system has the potential to minimize latency and support offline capability, enhancing the autonomy and responsiveness of assistive robots. Experimental results from our implementation on a robotic arm show promising outcomes in terms of accurate intent interpretation and object manipulation based on verbal commands. This research lays the groundwork for future developments in assistive robotics, focusing on creating highly responsive, user-centric systems that can significantly improve the quality of life for individuals with disabilities.

This paper introduces a novel formulation of the clustering problem, namely the Minimum Sum-of-Squares Clustering of Infinitely Tall Data (MSSC-ITD), and presents HPClust, an innovative set of hybrid parallel approaches for its effective solution. By utilizing modern high-performance computing techniques, HPClust enhances key clustering metrics: effectiveness, computational efficiency, and scalability. In contrast to vanilla data parallelism, which only accelerates processing time through the MapReduce framework, our approach unlocks superior performance by leveraging the multi-strategy competitive-cooperative parallelism and intricate properties of the objective function landscape. Unlike other available algorithms that struggle to scale, our algorithm is inherently parallel in nature, improving solution quality through increased scalability and parallelism, and outperforming even advanced algorithms designed for small and medium-sized datasets. Our evaluation of HPClust, featuring four parallel strategies, demonstrates its superiority over traditional and cutting-edge methods by offering better performance in the key metrics. These results also show that parallel processing not only enhances the clustering efficiency, but the accuracy as well. Additionally, we explore the balance between computational efficiency and clustering quality, providing insights into optimal parallel strategies based on dataset specifics and resource availability. This research advances our understanding of parallelism in clustering algorithms, demonstrating that a judicious hybridization of advanced parallel approaches yields optimal results for MSSC-ITD. Experiments on synthetic data further confirm HPClust's exceptional scalability and robustness to noise.

This paper presents a set-partitioning formulation and a novel decomposition heuristic (D-H) solution algorithm to solve large-scale instances of the urban crowdsourced shared-trip delivery (CSD) problem. The CSD problem involves dedicated vehicles (DVs) and shared personal vehicles (SPVs) fulfilling delivery orders, wherein the SPVs have their own trip origins and destinations. The D-H begins by assigning as many package delivery orders (PDOs) to SPVs as possible, where the D-H enumerates the set of routes each SPV can feasibly traverse and then solves a PDO-SPV-route assignment problem. For PDO-DV assignment and DV routing, the D-H solves a multi-vehicle routing problem with time-window, tour duration, and capacity constraints using an insertion heuristic. Finally, the D-H seeks potential solution improvements by switching PDOs between SPV and DV routes through a simulated annealing (SA)-inspired procedure. The D-H outperforms a commercial solver in terms of computational efficiency while obtaining near-optimal solutions for small problem instances. The SA-inspired switching procedure outperforms a large neighborhood search algorithm regarding run time, and the two are comparable regarding solution quality. Finally, the paper uses the D-H to analyze the impact of several relevant factors on city-scale CSD system performance, namely the number of participating SPVs and the maximum willingness to detour of SPVs. Consistent with the existing literature, we find that CSD can substantially reduce delivery costs. However, we find that CSD can increase vehicle miles traveled. Our findings provide meaningful insights for logistics practitioners, while the algorithms illustrate promise for large real-world systems.

This paper introduces AnyTrans, an all-encompassing framework for the task-Translate AnyText in the Image (TATI), which includes multilingual text translation and text fusion within images. Our framework leverages the strengths of large-scale models, such as Large Language Models (LLMs) and text-guided diffusion models, to incorporate contextual cues from both textual and visual elements during translation. The few-shot learning capability of LLMs allows for the translation of fragmented texts by considering the overall context. Meanwhile, the advanced inpainting and editing abilities of diffusion models make it possible to fuse translated text seamlessly into the original image while preserving its style and realism. Additionally, our framework can be constructed entirely using open-source models and requires no training, making it highly accessible and easily expandable. To encourage advancement in the TATI task, we have meticulously compiled a test dataset called MTIT6, which consists of multilingual text image translation data from six language pairs.

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.