Equation discovery provides a grey-box approach to system identification by uncovering governing dynamics directly from observed data. However, a persistent challenge lies in ensuring that identified models generalise across operating conditions rather than over-fitting to specific datasets. This work investigates this issue by applying a Bayesian relevance vector machine (RVM) within a multi-task learning (MTL) framework for simultaneous parameter identification across multiple datasets. In this formulation, responses from the same structure under different excitation levels are treated as related tasks that share model parameters but retain task-specific noise characteristics. A simulated single degree-of-freedom oscillator with linear and cubic stiffness provided the case study, with datasets generated under three excitation regimes. Standard single-task RVM models were able to reproduce system responses but often failed to recover the true governing terms when excitations insufficiently stimulated non-linear dynamics. By contrast, the MTL-RVM combined information across tasks, improving parameter recovery for weakly and moderately excited datasets, while maintaining strong performance under high excitation. These findings demonstrate that multi-task Bayesian inference can mitigate over-fitting and promote generalisation in equation discovery. The approach is particularly relevant to structural health monitoring, where varying load conditions reveal complementary aspects of system physics.

They currently serve the majority of fiber broadband subscribers worldwide and an ongoing demand for bandwidth has led to recent standardization efforts that enabled 50 Gb/s line rate transmission [1], while the research community is investigating the technologies that will enable PONs beyond 100 Gb/s [2]. One possibility for achieving 100 Gb/s is the use of higher-order modulation formats in intensity-modulation and direct-detection (IM/DD) links. However, this comes at the cost of an increased signal-to-noise ratio (SNR) requirement and lower tolerance to non-linearities in the channel. In a PON, the semiconductor optical amplifiers (SOAs) used to improve the receiver sensitivity suffer from non-linear gain saturation and the electro-absorption modulator (EAM) responsible for modulating the intensity of the optical signal has a non-linear transfer function.

Since PONs are primarily used for fiber-to-the-home (FTTH), the end-user transceivers must be cheap and power efficient while covering the increasing demand of data rates. For this reasons, they typically rely on intensity-modulation and direct-detection (IM/DD) of the optical signal. Current research is focusing on data rates beyond recent 50G-PON standardization efforts [1], i.e., towards PONs which are capable of delivering 100 Gbit/s [2]. Since cost-effective hardware hinders increasing the symbol rate, the focus shifts towards higherorder modulation formats such as 4-ary pulse amplitude modulation (PAM4). However, compared to conventional on-off-keying (OOK), which is used until 50G-PON, multi-level modulation formats are more prone to nonlinerities and, due to its reduced signal-to-noise ratio (SNR) tolerance, require optical amplification. The utilized low-cost semiconductor optical amplifiers (SOA) distort the signal at high received optical power (ROP) due to nonlinear gain saturation, which reduces the dynamic range [3].

Abstract. Brain computer interface (BCI) systems are developed in the biomedical engineering fields to increase the quality of life among patients with paralysis and neurological conditions. The development of a six class BCI controller to operate a semi-autonomous mobile robotic arm is presented. The controller uses the following mental tasks: imagined left/right hand squeeze, imagined left/right foot tap, rest, and a physical jaw clench. To design a controller, the locations of active electrodes are verified, and an appropriate machine learning algorithm is determined. Three subjects, ages ranging between 22 and 27, participated in five sessions of motor imagery experiments to record their brainwaves. These recordings were analyzed using event related potential (ERP) plots and topographical maps to determine active electrodes. bcilab was used to train two, three, five, and six class BCI controllers using linear discriminant analysis (LDA) and relevance vector machine (RVM) machine learning methods. The subjects' data were used to compare the two-method's performance in terms of error rate percentage. While a two class BCI controller showed the same accuracy for both methods, the three and five class BCI controllers showed the RVM approach having a higher accuracy than the LDA approach. For the five-class controller, error rate percentage was 33.3% for LDA and 29.2% for RVM. The six class BCI controller error rate percentage for both LDA and RVM was 34.5%. While the percentage values are the same, RVM was chosen as the desired machine learning algorithm based on the trend seen in the three and five class controller performances.

Sparse Bayesian Learning (SBL) constructs an extremely sparse probabilistic model with very competitive generalization. However, SBL needs to invert a big covariance matrix with complexity O(M^3 ) (M: feature size) for updating the regularization priors, making it difficult for practical use. There are three issues in SBL: 1) Inverting the covariance matrix may obtain singular solutions in some cases, which hinders SBL from convergence; 2) Poor scalability to problems with high dimensional feature space or large data size; 3) SBL easily suffers from memory overflow for large-scale data. This paper addresses these issues with a newly proposed diagonal Quasi-Newton (DQN) method for SBL called DQN-SBL where the inversion of big covariance matrix is ignored so that the complexity and memory storage are reduced to O(M). The DQN-SBL is thoroughly evaluated on non-linear classifiers and linear feature selection using various benchmark datasets of different sizes. Experimental results verify that DQN-SBL receives competitive generalization with a very sparse model and scales well to large-scale problems.

The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and interpretability via uncertainty analysis. This article introduces and discusses two methods which straddle the areas of probabilistic Bayesian schemes and kernel methods for regression: Gaussian Processes and Relevance Vector Machines. Our focus is on developing a common framework with which to view these methods, via intermediate methods a probabilistic version of the well-known kernel ridge regression, and drawing connections among them, via dual formulations, and discussion of their application in the context of major tasks: regression, smoothing, interpolation, and filtering. Overall, we provide understanding of the mathematical concepts behind these models, and we summarize and discuss in depth different interpretations and highlight the relationship to other methods, such as linear kernel smoothers, Kalman filtering and Fourier approximations. Throughout, we provide numerous figures to promote understanding, and we make numerous recommendations to practitioners. Benefits and drawbacks of the different techniques are highlighted. To our knowledge, this is the most in-depth study of its kind to date focused on these two methods, and will be relevant to theoretical understanding and practitioners throughout the domains of data-science, signal processing, machine learning, and artificial intelligence in general.

Reverse Vending Machines (RVMs) are a proven instrument for facilitating closed-loop plastic packaging recycling. A good customer experience at the RVM is crucial for a further proliferation of this technology. Bin full events are the major reason for Reverse Vending Machine (RVM) downtime at the world leader in the RVM market. The paper at hand develops and evaluates an approach based on machine learning and statistical approximation to foresee bin full events and, thus increase uptime of RVMs. Our approach relies on forecasting the hourly time series of returned beverage containers at a given RVM. We contribute by developing and evaluating an approach for hourly forecasts in a retail setting - this combination of application domain and forecast granularity is novel. A trace-driven simulation confirms that the forecasting-based approach leads to less downtime and costs than naive emptying strategies.

This study combines two different learning paradigms, k-nearest neighbor (k-NN) rule, as memory-based learning paradigm and relevance vector machines (RVM), as statistical learning paradigm. This combination is performed in kernel space and is called k-relevance vector (k-RV). The purpose is to improve the performance of k-NN rule. The proposed model significantly prunes irrelevant attributes. We also introduced a new parameter, responsible for early stopping of iterations in RVM. We show that the new parameter improves the classification accuracy of k-RV. Intensive experiments are conducted on several classification datasets from University of California Irvine (UCI) repository and two real datasets from computer vision domain. The performance of k-RV is highly competitive compared to a few state-of-the-arts in terms of classification accuracy.