We investigate the optimization dynamics of gradient descent in a non-convex and high-dimensional setting, with a focus on the phase retrieval problem as a case study for complex loss landscapes. We first study the high-dimensional limit where both the number $M$ and the dimension $N$ of the data are going to infinity at fixed signal-to-noise ratio $\alpha = M/N$. By analyzing how the local curvature changes during optimization, we uncover that for intermediate $\alpha$, the Hessian displays a downward direction pointing towards good minima in the first regime of the descent, before being trapped in bad minima at the end. Hence, the local landscape is benign and informative at first, before gradient descent brings the system into a uninformative maze. The transition between the two regimes is associated to a BBP-type threshold in the time-dependent Hessian. Through both theoretical analysis and numerical experiments, we show that in practical cases, i.e. for finite but even very large $N$, successful optimization via gradient descent in phase retrieval is achieved by falling towards the good minima before reaching the bad ones. This mechanism explains why successful recovery is obtained well before the algorithmic transition corresponding to the high-dimensional limit. Technically, this is associated to strong logarithmic corrections of the algorithmic transition at large $N$ with respect to the one expected in the $N\to\infty$ limit. Our analysis sheds light on such a new mechanism that facilitate gradient descent dynamics in finite large dimensions, also highlighting the importance of good initialization of spectral properties for optimization in complex high-dimensional landscapes.

Ensuring Conditional Independence (CI) constraints is pivotal for the development of fair and trustworthy machine learning models. In this paper, we introduce \sys, a framework that harnesses optimal transport theory for data repair under CI constraints. Optimal transport theory provides a rigorous framework for measuring the discrepancy between probability distributions, thereby ensuring control over data utility. We formulate the data repair problem concerning CIs as a Quadratically Constrained Linear Program (QCLP) and propose an alternating method for its solution. However, this approach faces scalability issues due to the computational cost associated with computing optimal transport distances, such as the Wasserstein distance. To overcome these scalability challenges, we reframe our problem as a regularized optimization problem, enabling us to develop an iterative algorithm inspired by Sinkhorn's matrix scaling algorithm, which efficiently addresses high-dimensional and large-scale data. Through extensive experiments, we demonstrate the efficacy and efficiency of our proposed methods, showcasing their practical utility in real-world data cleaning and preprocessing tasks. Furthermore, we provide comparisons with traditional approaches, highlighting the superiority of our techniques in terms of preserving data utility while ensuring adherence to the desired CI constraints.

Gradient-type distributed optimization methods have blossomed into one of the most important tools for solving a minimization learning task over a networked agent system. However, only one gradient update per iteration is difficult to achieve a substantive acceleration of convergence. In this paper, we propose an accelerated framework named as MUSIC allowing each agent to perform multiple local updates and a single combination in each iteration. More importantly, we equip inexact and exact distributed optimization methods into this framework, thereby developing two new algorithms that exhibit accelerated linear convergence and high communication efficiency. Our rigorous convergence analysis reveals the sources of steady-state errors arising from inexact policies and offers effective solutions. Numerical results based on synthetic and real datasets demonstrate both our theoretical motivations and analysis, as well as performance advantages.

The transportation sector remains a major contributor to greenhouse gas emissions. The understanding of energy-efficient driving behaviors and utilization of energy-efficient driving strategies are essential to reduce vehicles' fuel consumption. However, there is no comprehensive investigation into energy-efficient driving behaviors and strategies. Furthermore, many state-of-the-art AI models have been applied for the analysis of eco-friendly driving styles, but no overview is available. To fill the gap, this paper conducts a thorough literature review on ecological driving behaviors and styles and analyzes the driving factors influencing energy consumption and state-of-the-art methodologies. With a thorough scoping review process, the methodological and related data are compared. The results show that the factors that impact driving behaviors can be summarized into eleven features including speed, acceleration, deceleration, pedal, and so on. This paper finds that supervised/unsupervised learning algorithms and reinforcement learning frameworks have been popularly used to model the vehicle's energy consumption with multi-dimensional data. Furthermore, the literature shows that the driving data are collected from either simulators or real-world experiments, and the real-world data are mainly stored and transmitted by meters, controller area networks, onboard data services, smartphones, and additional sensors installed in the vehicle. Based on driving behavior factors, driver characteristics, and safety rules, this paper recommends nine energy-efficient driving styles including four guidelines for the drivers' selection and adjustment of the vehicle parameters, three recommendations for the energy-efficient driving styles in different driving scenarios, and two subjective suggestions for different types of drivers and employers.

Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by statistical sampling is challenging since it is typically not possible to create a large experimental design due to limitations in computing capacity. This paper presents a novel approach for the analytical estimation of fractional moments, directly from polynomial chaos expansions. Specifically, the first four statistical moments obtained from the deterministic PCE coefficients are used for an estimation of arbitrary fractional moments via H\"{o}lder's inequality. The proposed approach is utilized for an estimation of statistical moments and probability distributions in three numerical examples of increasing complexity. Obtained results show that the proposed approach achieves a superior performance in estimating the distribution of the response, in comparison to a standard Latin hypercube sampling in the presented examples.

Link prediction typically studies the probability of future interconnection among nodes with the observation in a single social network. More often than not, real scenario is presented as a multiplex network with common (anchor) users active in multiple social networks. In the literature, most existing works study either the intra-link prediction in a single network or inter-link prediction among networks (a.k.a. network alignment), and consider two learning tasks are independent from each other, which is still away from the fact. On the representation space, the vast majority of existing methods are built upon the traditional Euclidean space, unaware of the inherent geometry of social networks. The third issue is on the scarce anchor users. Annotating anchor users is laborious and expensive, and thus it is impractical to work with quantities of anchor users. Herein, in light of the issues above, we propose to study a challenging yet practical problem of Geometry-aware Collective Link Prediction across Multiplex Network. To address this problem, we present a novel contrastive model, RCoCo, which collaborates intra- and inter-network behaviors in Riemannian spaces. In RCoCo, we design a curvature-aware graph attention network ($\kappa-$GAT), conducting attention mechanism in Riemannian manifold whose curvature is estimated by the Ricci curvatures over the network. Thereafter, we formulate intra- and inter-contrastive loss in the manifolds, in which we augment graphs by exploring the high-order structure of community and information transfer on anchor users. Finally, we conduct extensive experiments with 14 strong baselines on 8 real-world datasets, and show the effectiveness of RCoCo.

Differentially private (DP) machine learning is considered the gold-standard solution for training a model from sensitive data while still preserving privacy. However, a major barrier to achieving this ideal is its sub-optimal privacy-accuracy trade-off, which is particularly visible in DP representation learning. Specifically, it has been shown that under modest privacy budgets, most models learn representations that are not significantly better than hand-crafted features. In this work, we show that effective DP representation learning can be done via image captioning and scaling up to internet-scale multimodal datasets. Through a series of engineering tricks, we successfully train a DP image captioner (DP-Cap) on a 233M subset of LAION-2B from scratch using a reasonable amount of computation, and obtaining unprecedented high-quality image features that can be used in a variety of downstream vision and vision-language tasks. For example, under a privacy budget of $\varepsilon=8$, a linear classifier trained on top of learned DP-Cap features attains 65.8% accuracy on ImageNet-1K, considerably improving the previous SOTA of 56.5%. Our work challenges the prevailing sentiment that high-utility DP representation learning cannot be achieved by training from scratch.

The task of stock earnings forecasting has received considerable attention due to the demand investors in real-world scenarios. However, compared with financial institutions, it is not easy for ordinary investors to mine factors and analyze news. On the other hand, although large language models in the financial field can serve users in the form of dialogue robots, it still requires users to have financial knowledge to ask reasonable questions. To serve the user experience, we aim to build an automatic system, FinReport, for ordinary investors to collect information, analyze it, and generate reports after summarizing. Specifically, our FinReport is based on financial news announcements and a multi-factor model to ensure the professionalism of the report. The FinReport consists of three modules: news factorization module, return forecasting module, risk assessment module. The news factorization module involves understanding news information and combining it with stock factors, the return forecasting module aim to analysis the impact of news on market sentiment, and the risk assessment module is adopted to control investment risk. Extensive experiments on real-world datasets have well verified the effectiveness and explainability of our proposed FinReport. Our codes and datasets are available at https://github.com/frinkleko/FinReport.

Machine learning models, while progressively advanced, rely heavily on the IID assumption, which is often unfulfilled in practice due to inevitable distribution shifts. This renders them susceptible and untrustworthy for deployment in risk-sensitive applications. Such a significant problem has consequently spawned various branches of works dedicated to developing algorithms capable of Out-of-Distribution (OOD) generalization. Despite these efforts, much less attention has been paid to the evaluation of OOD generalization, which is also a complex and fundamental problem. Its goal is not only to assess whether a model's OOD generalization capability is strong or not, but also to evaluate where a model generalizes well or poorly. This entails characterizing the types of distribution shifts that a model can effectively address, and identifying the safe and risky input regions given a model. This paper serves as the first effort to conduct a comprehensive review of OOD evaluation. We categorize existing research into three paradigms: OOD performance testing, OOD performance prediction, and OOD intrinsic property characterization, according to the availability of test data. Additionally, we briefly discuss OOD evaluation in the context of pretrained models. In closing, we propose several promising directions for future research in OOD evaluation.

Over the broad landscape of experimental design, regression has been a powerful tool to accurately predict the outcome metrics of a system or model given a set of parameters, but has been traditionally restricted to methods which are only applicable to a specific task. In this paper, we propose OmniPred, a framework for training language models as universal end-to-end regressors over $(x,y)$ evaluation data from diverse real world experiments. Using data sourced from Google Vizier, one of the largest blackbox optimization databases in the world, our extensive experiments demonstrate that through only textual representations of mathematical parameters and values, language models are capable of very precise numerical regression, and if given the opportunity to train over multiple tasks, can significantly outperform traditional regression models.