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Semi-definite programs represent a frontier of efficient computation. While there has been much progress on semi-definite optimization, with moderate-sized instances currently solvable in practice by the interior-point method, the basic problem of sampling semi-definite solutions remains a formidable challenge. The direct application of known polynomial-time algorithms for sampling general convex bodies to semi-definite sampling leads to a prohibitively high running time. In addition, known general methods require an expensive rounding phase as pre-processing. Here we analyze the Dikin walk, by first adapting it to general metrics, then devising suitable metrics for the PSD cone with affine constraints. The resulting mixing time and per-step complexity are considerably smaller, and by an appropriate choice of the metric, the dependence on the number of constraints can be made polylogarithmic. We introduce a refined notion of self-concordant matrix functions and give rules for combining different metrics. Along the way, we further develop the theory of interior-point methods for sampling.

Online Food Recommendation Service (OFRS) has remarkable spatiotemporal characteristics and the advantage of being able to conveniently satisfy users' needs in a timely manner. There have been a variety of studies that have begun to explore its spatiotemporal properties, but a comprehensive and in-depth analysis of the OFRS spatiotemporal features is yet to be conducted. Therefore, this paper studies the OFRS based on three questions: how spatiotemporal features play a role; why self-attention cannot be used to model the spatiotemporal sequences of OFRS; and how to combine spatiotemporal features to improve the efficiency of OFRS. Firstly, through experimental analysis, we systemically extracted the spatiotemporal features of OFRS, identified the most valuable features and designed an effective combination method. Secondly, we conducted a detailed analysis of the spatiotemporal sequences, which revealed the shortcomings of self-attention in OFRS, and proposed a more optimized spatiotemporal sequence method for replacing self-attention. In addition, we also designed a Dynamic Context Adaptation Model to further improve the efficiency and performance of OFRS. Through the offline experiments on two large datasets and online experiments for a week, the feasibility and superiority of our model were proven.

Before and after study frameworks are widely adopted to evaluate the effectiveness of transportation policies and emerging technologies. However, many factors such as seasonal factors, holidays, and lane closure might interfere with the evaluation process by inducing variation in traffic volume during the before and after periods. In practice, limited effort has been made to eliminate the effects of these factors. In this study, an extreme gradient boosting (XGBoost)-based propensity score matching method is proposed to reduce the biases caused by traffic volume variation during the before and after periods. In order to evaluate the effectiveness of the proposed method, a corridor in the City of Chandler, Arizona where an advanced traffic signal control system has been recently implemented was selected. The results indicated that the proposed method is able to effectively eliminate the variation in traffic volume caused by the COVID-19 global Pandemic during the evaluation process. In addition, the results of the t-test and Kolmogorov-Smirnov (KS) test demonstrated that the proposed method outperforms other conventional propensity score matching methods. The application of the proposed method is also transferrable to other before and after evaluation studies and can significantly assist the transportation engineers to eliminate the impacts of traffic volume variation on the evaluation process.

The concept of the federated Cloud-Edge-IoT continuum promises to alleviate many woes of current systems, improving resource use, energy efficiency, quality of service, and more. However, this continuum is still far from being realized in practice, with no comprehensive solutions for developing, deploying, and managing continuum-native applications. Breakthrough innovations and novel system architectures are needed to cope with the ever-increasing heterogeneity and the multi-stakeholder nature of computing resources. This work proposes a novel architecture for choreographing workloads in the continuum, attempting to address these challenges. The architecture that tackles this issue comprehensively, spanning from the workloads themselves, through networking and data exchange, up to the orchestration and choreography mechanisms. The concept emphasizes the use of varied AI techniques, enabling autonomous and intelligent management of resources and workloads. Open standards are also a key part of the proposition, making it possible to fully engage third parties in multi-stakeholder scenarios. Although the presented architecture is promising, much work is required to realize it in practice. To this end, the key directions for future research are outlined.

Numerical methods for Inverse Kinematics (IK) employ iterative, linear approximations of the IK until the end-effector is brought from its initial pose to the desired final pose. These methods require the computation of the Jacobian of the Forward Kinematics (FK) and its inverse in the linear approximation of the IK. Despite all the successful implementations reported in the literature, Jacobian-based IK methods can still fail to preserve certain useful properties if an improper matrix inverse, e.g. Moore-Penrose (MP), is employed for incommensurate robotic systems. In this paper, we propose a systematic, robust and accurate numerical solution for the IK problem using the Mixed (MX) Generalized Inverse (GI) applied to any type of Jacobians (e.g., analytical, numerical or geometric) derived for any commensurate and incommensurate robot. This approach is robust to whether the system is under-determined (less than 6 DoF) or over-determined (more than 6 DoF). We investigate six robotics manipulators with various Degrees of Freedom (DoF) to demonstrate that commonly used GI's fail to guarantee the same system behaviors when the units are varied for incommensurate robotics manipulators. In addition, we evaluate the proposed methodology as a global IK solver and compare against well-known IK methods for redundant manipulators. Based on the experimental results, we conclude that the right choice of GI is crucial in preserving certain properties of the system (i.e. unit-consistency).

Spectral methods have myriad applications in high-dimensional statistics and data science, and while previous works have primarily focused on $\ell_2$ or $\ell_{2,\infty}$ eigenvector and singular vector perturbation theory, in many settings these analyses fall short of providing the fine-grained guarantees required for various inferential tasks. In this paper we study statistical inference for linear functions of eigenvectors and principal components with a particular emphasis on the setting where gaps between eigenvalues may be extremely small relative to the corresponding spiked eigenvalue, a regime which has been oft-neglected in the literature. It has been previously established that linear functions of eigenvectors and principal components incur a non-negligible bias, so in this work we provide Berry-Esseen bounds for empirical linear forms and their debiased counterparts respectively in the matrix denoising model and the spiked principal component analysis model, both under Gaussian noise. Next, we propose data-driven estimators for the appropriate bias and variance quantities resulting in approximately valid confidence intervals, and we demonstrate our theoretical results through numerical simulations. We further apply our results to obtain distributional theory and confidence intervals for eigenvector entries, for which debiasing is not necessary. Crucially, our proposed confidence intervals and bias-correction procedures can all be computed directly from data without sample-splitting and are asymptotically valid under minimal assumptions on the eigengap and signal strength. Furthermore, our Berry-Esseen bounds clearly reflect the effects of both signal strength and eigenvalue closeness on the estimation and inference tasks.

Bridging the huge disparity between neural and symbolic representation can potentially enable the incorporation of symbolic thinking into neural networks from essence. Motivated by how human gradually builds complex symbolic representation from the prototype symbols that are learned through perception and environmental interactions. We propose a Neural-Symbolic Transitional Dictionary Learning (TDL) framework that employs an EM algorithm to learn a transitional representation of data that compresses high-dimension information of visual parts of an input into a set of tensors as neural variables and discover the implicit predicate structure in a self-supervised way. We implement the framework with a diffusion model by regarding the decomposition of input as a cooperative game, then learn predicates by prototype clustering. We additionally use RL enabled by the Markovian of diffusion models to further tune the learned prototypes by incorporating subjective factors. Extensive experiments on 3 abstract compositional visual objects datasets that require the model to segment parts without any visual features like texture, color, or shadows apart from shape and 3 neural/symbolic downstream tasks demonstrate the learned representation enables interpretable decomposition of visual input and smooth adaption to downstream tasks which are not available by existing methods.

The goal of our research was to investigate the effects of collaboration between academia and industry on Natural Language Processing (NLP). To do this, we created a pipeline to extract affiliations and citations from NLP papers and divided them into three categories: academia, industry, and hybrid (collaborations between academia and industry). Our empirical analysis found that there is a trend towards an increase in industry and academia-industry collaboration publications and that these types of publications tend to have a higher impact compared to those produced solely within academia.

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.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.