Performative prediction, as introduced by Perdomo et al., is a framework for studying social prediction in which the data distribution itself changes in response to the deployment of a model. Existing work in this field usually hinges on three assumptions that are easily violated in practice: that the performative risk is convex over the deployed model, that the mapping from the model to the data distribution is known to the model designer in advance, and the first-order information of the performative risk is available. In this paper, we initiate the study of performative prediction problems that do not require these assumptions. Specifically, we develop a reparameterization framework that reparametrizes the performative prediction objective as a function of the induced data distribution. We also develop a twolevel zeroth-order optimization procedure, where the first level performs iterative optimization on the distribution parameter space, and the second level learns the model that induced a particular target distribution parameter at each iteration. Under mild conditions, this reparameterization allows us to transform the non-convex objective into a convex one and achieve provable regret guarantees. In particular, we provide a regret bound that is sublinear in the total number of performative samples taken and is only polynomial in the dimension of the model parameter. On the application side, we believe our method is useful for large online recommendation systems like YouTube or TikTok, where the recommendation update frequency is high and might potentially reshape future preferences.

The core principle of Variational Inference (VI) is to convert the statistical inference problem of computing complex posterior probability densities into a tractable optimization problem. This property enables VI to be faster than several sampling-based techniques. However, the traditional VI algorithm is not scalable to large data sets and is unable to readily infer out-of-bounds data points without re-running the optimization process. Recent developments in the field, like stochastic-, black box-, and amortized-VI, have helped address these issues. Generative modeling tasks nowadays widely make use of amortized VI for its efficiency and scalability, as it utilizes a parameterized function to learn the approximate posterior density parameters. In this paper, we review the mathematical foundations of various VI techniques to form the basis for understanding amortized VI. Additionally, we provide an overview of the recent trends that address several issues of amortized VI, such as the amortization gap, generalization issues, inconsistent representation learning, and posterior collapse. Finally, we analyze alternate divergence measures that improve VI optimization.

This chapter presents a comparative study of the three portfolio optimization methods, MVP, HRP, and HERC, on the Indian stock market, particularly focusing on the stocks chosen from 15 sectors listed on the National Stock Exchange of India. The top stocks of each cluster are identified based on their free-float market capitalization from the report of the NSE published on July 1, 2022 (NSE Website). For each sector, three portfolios are designed on stock prices from July 1, 2019, to June 30, 2022, following three portfolio optimization approaches. The portfolios are tested over the period from July 1, 2022, to June 30, 2023. For the evaluation of the performances of the portfolios, three metrics are used. These three metrics are cumulative returns, annual volatilities, and Sharpe ratios. For each sector, the portfolios that yield the highest cumulative return, the lowest volatility, and the maximum Sharpe Ratio over the training and the test periods are identified.

Forecasting project expenses is a crucial step for businesses to avoid budget overruns and project failures. Traditionally, this has been done by financial analysts or data science techniques such as time-series analysis. However, these approaches can be uncertain and produce results that differ from the planned budget, especially at the start of a project with limited data points. This paper proposes a constrained non-negative matrix completion model that predicts expenses by learning the likelihood of the project correlating with certain expense patterns in the latent space. The model is constrained on three probability simplexes, two of which are on the factor matrices and the third on the missing entries. Additionally, the predicted expense values are guaranteed to meet the budget constraint without the need of post-processing. An inexact alternating optimization algorithm is developed to solve the associated optimization problem and is proven to converge to a stationary point. Results from two real datasets demonstrate the effectiveness of the proposed method in comparison to state-of-the-art algorithms.

In a previous work we introduced, in the context of gravitational wave science, an initial study on an automated domain-decomposition approach for reduced basis through hp-greedy refinement. The approach constructs local reduced bases of lower dimensionality than global ones, with the same or higher accuracy. These ``light'' local bases should imply both faster evaluations when predicting new waveforms and faster data analysis, in particular faster statistical inference (the forward and inverse problems, respectively). In this approach, however, we have previously found important dependence on several hyperparameters, which do not appear in global reduced basis. This naturally leads to the problem of hyperparameter optimization (HPO), which is the subject of this paper. We tackle the problem through a Bayesian optimization, and show its superiority when compared to grid or random searches. We find that for gravitational waves from the collision of two spinning but non-precessing black holes, for the same accuracy, local hp-greedy reduced bases with HPO have a lower dimensionality of up to $4 \times$ for the cases here studied, depending on the desired accuracy. This factor should directly translate in a parameter estimation speedup, for instance. Such acceleration might help in the near real-time requirements for electromagnetic counterparts of gravitational waves from compact binary coalescences. In addition, we find that the Bayesian approach used in this paper for HPO is two orders of magnitude faster than, for example, a grid search, with about a $100 \times$ acceleration. The code developed for this project is available as open source from public repositories.

The robotics community is increasingly interested in autonomous aerial transportation. Unmanned aerial vehicles with suspended payloads have advantages over other systems, including mechanical simplicity and agility, but pose great challenges in planning and control. To realize fully autonomous aerial transportation, this paper presents a systematic solution to address these difficulties. First, we present a real-time planning method that generates smooth trajectories considering the time-varying shape and non-linear dynamics of the system, ensuring whole-body safety and dynamic feasibility. Additionally, an adaptive NMPC with a hierarchical disturbance compensation strategy is designed to overcome unknown external perturbations and inaccurate model parameters. Extensive experiments show that our method is capable of generating high-quality trajectories online, even in highly constrained environments, and tracking aggressive flight trajectories accurately, even under significant uncertainty. We plan to release our code to benefit the community.

Compressed Sensing (CS) significantly speeds up Magnetic Resonance Image (MRI) processing and achieves accurate MRI reconstruction from under-sampled k-space data. According to the current research, there are still several problems with dynamic MRI k-space reconstruction based on CS. 1) There are differences between the Fourier domain and the Image domain, and the differences between MRI processing of different domains need to be considered. 2) As three-dimensional data, dynamic MRI has its spatial-temporal characteristics, which need to calculate the difference and consistency of surface textures while preserving structural integrity and uniqueness. 3) Dynamic MRI reconstruction is time-consuming and computationally resource-dependent. In this paper, we propose a novel robust low-rank dynamic MRI reconstruction optimization model via highly under-sampled and Discrete Fourier Transform (DFT) called the Robust Depth Linear Error Decomposition Model (RDLEDM). Our method mainly includes linear decomposition, double Total Variation (TV), and double Nuclear Norm (NN) regularizations. By adding linear image domain error analysis, the noise is reduced after under-sampled and DFT processing, and the anti-interference ability of the algorithm is enhanced. Double TV and NN regularizations can utilize both spatial-temporal characteristics and explore the complementary relationship between different dimensions in dynamic MRI sequences. In addition, Due to the non-smoothness and non-convexity of TV and NN terms, it is difficult to optimize the unified objective model. To address this issue, we utilize a fast algorithm by solving a primal-dual form of the original problem. Compared with five state-of-the-art methods, extensive experiments on dynamic MRI data demonstrate the superior performance of the proposed method in terms of both reconstruction accuracy and time complexity.

With the rapid advancement of artificial intelligence technology, the usage of machine learning models is gradually becoming part of our daily lives. High-quality models rely not only on efficient optimization algorithms but also on the training and learning processes built upon vast amounts of data and computational power. However, in practice, due to various challenges such as limited computational resources and data privacy concerns, users in need of models often cannot train machine learning models locally. This has led them to explore alternative approaches such as outsourced learning and federated learning. While these methods address the feasibility of model training effectively, they introduce concerns about the trustworthiness of the training process since computations are not performed locally. Similarly, there are trustworthiness issues associated with outsourced model inference. These two problems can be summarized as the trustworthiness problem of model computations: How can one verify that the results computed by other participants are derived according to the specified algorithm, model, and input data? To address this challenge, verifiable machine learning (VML) has emerged. This paper presents a comprehensive survey of zero-knowledge proof-based verifiable machine learning (ZKP-VML) technology. We first analyze the potential verifiability issues that may exist in different machine learning scenarios. Subsequently, we provide a formal definition of ZKP-VML. We then conduct a detailed analysis and classification of existing works based on their technical approaches. Finally, we discuss the key challenges and future directions in the field of ZKP-based VML.

First-order gradient descent has been the base of the most successful optimization algorithms ever implemented. On supervised learning problems with very high dimensionality, such as neural network optimization, it is almost always the algorithm of choice, mainly due to its memory and computational efficiency. However, it is a classical result in optimization that gradient descent converges to local minima on non-convex functions. Even more importantly, in certain high-dimensional cases, escaping the plateaus of large saddle points becomes intractable. On the other hand, black-box optimization methods are not sensitive to the local structure of a loss function's landscape but suffer the curse of dimensionality. Instead, memetic algorithms aim to combine the benefits of both. Inspired by this, we present Population Descent, a memetic algorithm focused on hyperparameter optimization. We show that an adaptive m-elitist selection approach combined with a normalized-fitness-based randomization scheme outperforms more complex state-of-the-art algorithms by up to 13% on common benchmark tasks.

Deep hashing has been intensively studied and successfully applied in large-scale image retrieval systems due to its efficiency and effectiveness. Recent studies have recognized that the existence of adversarial examples poses a security threat to deep hashing models, that is, adversarial vulnerability. Notably, it is challenging to efficiently distill reliable semantic representatives for deep hashing to guide adversarial learning, and thereby it hinders the enhancement of adversarial robustness of deep hashing-based retrieval models. Moreover, current researches on adversarial training for deep hashing are hard to be formalized into a unified minimax structure. In this paper, we explore Semantic-Aware Adversarial Training (SAAT) for improving the adversarial robustness of deep hashing models. Specifically, we conceive a discriminative mainstay features learning (DMFL) scheme to construct semantic representatives for guiding adversarial learning in deep hashing. Particularly, our DMFL with the strict theoretical guarantee is adaptively optimized in a discriminative learning manner, where both discriminative and semantic properties are jointly considered. Moreover, adversarial examples are fabricated by maximizing the Hamming distance between the hash codes of adversarial samples and mainstay features, the efficacy of which is validated in the adversarial attack trials. Further, we, for the first time, formulate the formalized adversarial training of deep hashing into a unified minimax optimization under the guidance of the generated mainstay codes. Extensive experiments on benchmark datasets show superb attack performance against the state-of-the-art algorithms, meanwhile, the proposed adversarial training can effectively eliminate adversarial perturbations for trustworthy deep hashing-based retrieval. Our code is available at https://github.com/xandery-geek/SAAT.