Generative models trained with Differential Privacy (DP) are becoming increasingly prominent in the creation of synthetic data for downstream applications. Existing literature, however, primarily focuses on basic benchmarking datasets and tends to report promising results only for elementary metrics and relatively simple data distributions. In this paper, we initiate a systematic analysis of how DP generative models perform in their natural application scenarios, specifically focusing on real-world gene expression data. We conduct a comprehensive analysis of five representative DP generation methods, examining them from various angles, such as downstream utility, statistical properties, and biological plausibility. Our extensive evaluation illuminates the unique characteristics of each DP generation method, offering critical insights into the strengths and weaknesses of each approach, and uncovering intriguing possibilities for future developments. Perhaps surprisingly, our analysis reveals that most methods are capable of achieving seemingly reasonable downstream utility, according to the standard evaluation metrics considered in existing literature. Nevertheless, we find that none of the DP methods are able to accurately capture the biological characteristics of the real dataset. This observation suggests a potential over-optimistic assessment of current methodologies in this field and underscores a pressing need for future enhancements in model design.

The Simplified General Perturbations 4 (SGP4) orbital propagation method is widely used for predicting the positions and velocities of Earth-orbiting objects rapidly and reliably. Despite continuous refinement, SGP models still lack the precision of numerical propagators, which offer significantly smaller errors. This study presents dSGP4, a novel differentiable version of SGP4 implemented using PyTorch. By making SGP4 differentiable, dSGP4 facilitates various space-related applications, including spacecraft orbit determination, state conversion, covariance transformation, state transition matrix computation, and covariance propagation. Additionally, dSGP4's PyTorch implementation allows for embarrassingly parallel orbital propagation across batches of Two-Line Element Sets (TLEs), leveraging the computational power of CPUs, GPUs, and advanced hardware for distributed prediction of satellite positions at future times. Furthermore, dSGP4's differentiability enables integration with modern machine learning techniques. Thus, we propose a novel orbital propagation paradigm, ML-dSGP4, where neural networks are integrated into the orbital propagator. Through stochastic gradient descent, this combined model's inputs, outputs, and parameters can be iteratively refined, surpassing SGP4's precision. Neural networks act as identity operators by default, adhering to SGP4's behavior. However, dSGP4's differentiability allows fine-tuning with ephemeris data, enhancing precision while maintaining computational speed. This empowers satellite operators and researchers to train the model using specific ephemeris or high-precision numerical propagation data, significantly advancing orbital prediction capabilities.

Understanding preferences, opinions, and sentiment of the workforce is paramount for effective employee lifecycle management. Open-ended survey responses serve as a valuable source of information. This paper proposes a machine learning approach for aspect-based sentiment analysis (ABSA) of Dutch open-ended responses in employee satisfaction surveys. Our approach aims to overcome the inherent noise and variability in these responses, enabling a comprehensive analysis of sentiments that can support employee lifecycle management. Through response clustering we identify six key aspects (salary, schedule, contact, communication, personal attention, agreements), which we validate by domain experts. We compile a dataset of 1,458 Dutch survey responses, revealing label imbalance in aspects and sentiments. We propose few-shot approaches for ABSA based on Dutch BERT models, and compare them against bag-of-words and zero-shot baselines. Our work significantly contributes to the field of ABSA by demonstrating the first successful application of Dutch pre-trained language models to aspect-based sentiment analysis in the domain of human resources (HR).

A growing awareness of multi-view learning as an important component in data science and machine learning is a consequence of the increasing prevalence of multiple views in real-world applications, especially in the context of networks. In this paper we introduce a new scalability framework for multi-view subspace clustering. An efficient optimization strategy is proposed, leveraging kernel feature maps to reduce the computational burden while maintaining good clustering performance. The scalability of the algorithm means that it can be applied to large-scale datasets, including those with millions of data points, using a standard machine, in a few minutes. We conduct extensive experiments on real-world benchmark networks of various sizes in order to evaluate the performance of our algorithm against state-of-the-art multi-view subspace clustering methods and attributed-network multi-view approaches.

We consider nonconvex stochastic optimization problems in the asynchronous centralized distributed setup where the communication times from workers to a server can not be ignored, and the computation and communication times are potentially different for all workers. Using an unbiassed compression technique, we develop a new method-Shadowheart SGD-that provably improves the time complexities of all previous centralized methods. Moreover, we show that the time complexity of Shadowheart SGD is optimal in the family of centralized methods with compressed communication. We also consider the bidirectional setup, where broadcasting from the server to the workers is non-negligible, and develop a corresponding method.

An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive literature has been dedicated to the non-parametric estimation of both the linear and non-linear Hawkes process, there remains a significant gap in the literature regarding the marked Hawkes process. In response to this, we propose a methodology for estimating the conditional intensity of the marked Hawkes process. We introduce two distinct models: \textit{Shallow Neural Hawkes with marks}- for Hawkes processes with excitatory kernels and \textit{Neural Network for Non-Linear Hawkes with Marks}- for non-linear Hawkes processes. Both these approaches take the past arrival times and their corresponding marks as the input to obtain the arrival intensity. This approach is entirely non-parametric, preserving the interpretability associated with the marked Hawkes process. To validate the efficacy of our method, we subject the method to synthetic datasets with known ground truth. Additionally, we apply our method to model cryptocurrency order book data, demonstrating its applicability to real-world scenarios.

A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more success. However, we believe that with these variants, the balance constraints can be too restrictive for some applications like for clustering of imbalanced datasets, while not being restrictive enough for when searching for perfectly balanced partitions. Here, we propose a new graph cut algorithm for partitioning graphs under arbitrary size constraints. We formulate the graph cut problem as a regularized Gromov-Wasserstein problem. We then propose to solve it using accelerated proximal GD algorithm which has global convergence guarantees, results in sparse solutions and only incurs an additional ratio of $\mathcal{O}(\log(n))$ compared to the classical spectral clustering algorithm but was seen to be more efficient.

We present a theoretical and empirical analysis of the adaptive entry point selection for graph-based approximate nearest neighbor search (ANNS). We introduce novel concepts: $b\textit{-monotonic path}$ and $B\textit{-MSNET}$, which better capture an actual graph in practical algorithms than existing concepts like MSNET. We prove that adaptive entry point selection offers better performance upper bound than the fixed central entry point under more general conditions than previous work. Empirically, we validate the method's effectiveness in accuracy, speed, and memory usage across various datasets, especially in challenging scenarios with out-of-distribution data and hard instances. Our comprehensive study provides deeper insights into optimizing entry points for graph-based ANNS for real-world high-dimensional data applications.

Block Principal Component Analysis (Block PCA) of a data matrix A, where loadings Z are determined by maximization of AZ 2 over unit norm orthogonal loadings, is difficult to use for the design of sparse PCA by 1 regularization, due to the difficulty of taking care of both the orthogonality constraint on loadings and the non differentiable 1 penalty. Our objective in this paper is to relax the orthogonality constraint on loadings by introducing new objective functions expvar(Y) which measure the part of the variance of the data matrix A explained by correlated components Y = AZ. So we propose first a comprehensive study of mathematical and numerical properties of expvar(Y) for two existing definitions Zou et al. [2006], Shen and Huang [2008] and four new definitions. Then we show that only two of these explained variance are fit to use as objective function in block PCA formulations for A rid of orthogonality constraints.

This study investigates leveraging stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We propose weak and strong regularity conditions for the target operator to depict its intrinsic structure and complexity. Under these conditions, we establish upper bounds for convergence rates of the SGD algorithm and conduct a minimax lower bound analysis, further illustrating that our convergence analysis and regularity conditions quantitatively characterize the tractability of solving operator learning problems using the SGD algorithm. It is crucial to highlight that our convergence analysis is still valid for nonlinear operator learning. We show that the SGD estimator will converge to the best linear approximation of the nonlinear target operator. Moreover, applying our analysis to operator learning problems based on vector-valued and real-valued reproducing kernel Hilbert spaces yields new convergence results, thereby refining the conclusions of existing literature.