Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems. In this work, we propose kernel-based methods for identifying and forecasting Hamiltonian systems directly from data. We present two approaches: a two-step method that reconstructs trajectories before learning the Hamiltonian, and a one-step method that jointly infers both. Across several benchmark systems, including mass-spring dynamics, a nonlinear pendulum, and the Henon-Heiles system, we demonstrate that our framework achieves accurate, data-efficient predictions and outperforms two-step kernel-based baselines, particularly in scarce-data regimes, while preserving the conservation properties of Hamiltonian dynamics. Moreover, our methodology provides theoretical a priori error estimates, ensuring reliability of the learned models. We also provide a more general, problem-agnostic numerical framework that goes beyond Hamiltonian systems and can be used for data-driven learning of arbitrary dynamical systems.

Traditional neural networks (multi-layer perceptrons) have become an important tool in data science due to their success across a wide range of tasks. However, their performance is sometimes unsatisfactory, and they often require a large number of parameters, primarily due to their reliance on the linear combination structure. Meanwhile, additive regression has been a popular alternative to linear regression in statistics. In this work, we introduce novel deep neural networks that incorporate the idea of additive regression. Our neural networks share architectural similarities with Kolmogorov-Arnold networks but are based on simpler yet flexible activation and basis functions. Additionally, we introduce several hybrid neural networks that combine this architecture with that of traditional neural networks. We derive their universal approximation properties and demonstrate their effectiveness through simulation studies and a real-data application. The numerical results indicate that our neural networks generally achieve better performance than traditional neural networks while using fewer parameters.

The increasing concerns of knowledge transfer and data privacy challenge the traditional gather-and-analyse paradigm in networks. Specifically, the intelligent orchestration of Virtual Network Functions (VNFs) requires understanding and profiling the resource consumption. However, profiling all kinds of VNFs is time-consuming. It is important to consider transferring the well-profiled VNF knowledge to other lack-profiled VNF types while keeping data private. To this end, this paper proposes a Federated Transfer Component Analysis (FTCA) method between the source and target VNFs. FTCA first trains Generative Adversarial Networks (GANs) based on the source VNF profiling data, and the trained GANs model is sent to the target VNF domain. Then, FTCA realizes federated domain adaptation by using the generated source VNF data and less target VNF profiling data, while keeping the raw data locally. Experiments show that the proposed FTCA can effectively predict the required resources for the target VNF. Specifically, the RMSE index of the regression model decreases by 38.5% and the R-squared metric advances up to 68.6%.

In cancer research, overall survival and progression free survival are often analyzed with the Cox model. To estimate accurately the parameters in the model, sufficient data and, more importantly, sufficient events need to be observed. In practice, this is often a problem. Merging data sets from different medical centers may help, but this is not always possible due to strict privacy legislation and logistic difficulties. Recently, the Bayesian Federated Inference (BFI) strategy for generalized linear models was proposed. With this strategy the statistical analyses are performed in the local centers where the data were collected (or stored) and only the inference results are combined to a single estimated model; merging data is not necessary. The BFI methodology aims to compute from the separate inference results in the local centers what would have been obtained if the analysis had been based on the merged data sets. In this paper we generalize the BFI methodology as initially developed for generalized linear models to survival models. Simulation studies and real data analyses show excellent performance; i.e., the results obtained with the BFI methodology are very similar to the results obtained by analyzing the merged data. An R package for doing the analyses is available.

The aim of this study is to look at predicting whether a person will complete a drug and alcohol rehabilitation program and the number of times a person attends. The study is based on demographic data obtained from Substance Abuse and Mental Health Services Administration (SAMHSA) from both admissions and discharge data from drug and alcohol rehabilitation centers in Oklahoma. Demographic data is highly categorical which led to binary encoding being used and various fairness measures being utilized to mitigate bias of nine demographic variables. Kernel methods such as linear, polynomial, sigmoid, and radial basis functions were compared using support vector machines at various parameter ranges to find the optimal values. These were then compared to methods such as decision trees, random forests, and neural networks. Synthetic Minority Oversampling Technique Nominal (SMOTEN) for categorical data was used to balance the data with imputation for missing data. The nine bias variables were then intersectionalized to mitigate bias and the dual and triple interactions were integrated to use the probabilities to look at worst case ratio fairness mitigation. Disparate Impact, Statistical Parity difference, Conditional Statistical Parity Ratio, Demographic Parity, Demographic Parity Ratio, Equalized Odds, Equalized Odds Ratio, Equal Opportunity, and Equalized Opportunity Ratio were all explored at both the binary and multiclass scenarios.

The representation space of neural models for textual data emerges in an unsupervised manner during training. Understanding how those representations encode human-interpretable concepts is a fundamental problem. One prominent approach for the identification of concepts in neural representations is searching for a linear subspace whose erasure prevents the prediction of the concept from the representations. However, while many linear erasure algorithms are tractable and interpretable, neural networks do not necessarily represent concepts in a linear manner. To identify non-linearly encoded concepts, we propose a kernelization of a linear minimax game for concept erasure. We demonstrate that it is possible to prevent specific non-linear adversaries from predicting the concept. However, the protection does not transfer to different nonlinear adversaries. Therefore, exhaustively erasing a non-linearly encoded concept remains an open problem.