We prove the polynomial convergence rate of the average of the sequence which is explicitly determined only by the regularity of the initial state, Theorem 1 and 2. For convergence of the second moment, under a condition on the regularity of the random distribution (Assumption (A)), the convergence rate remains the same, Theorem 3. In another words, under (A), the regularity of the random sequence only affects the coefficient not the order of the polynomial convergence. Additionally we demonstrate almost sure convergence of the sequence, Theorem 4.

Learning Electronic Health Records (EHRs) representation is a preeminent yet under-discovered research topic. It benefits various clinical decision support applications, e.g., medication outcome prediction or patient similarity search. Current approaches focus on task-specific label supervision on vectorized sequential EHR, which is not applicable to large-scale unsupervised scenarios. Recently, contrastive learning shows great success on self-supervised representation learning problems. However, complex temporality often degrades the performance. We propose Graph Kernel Infomax, a self-supervised graph kernel learning approach on the graphical representation of EHR, to overcome the previous problems. Unlike the state-of-the-art, we do not change the graph structure to construct augmented views. Instead, we use Kernel Subspace Augmentation to embed nodes into two geometrically different manifold views. The entire framework is trained by contrasting nodes and graph representations on those two manifold views through the commonly used contrastive objectives. Empirically, using publicly available benchmark EHR datasets, our approach yields performance on clinical downstream tasks that exceeds the state-of-the-art. Theoretically, the variation on distance metrics naturally creates different views as data augmentation without changing graph structures.

Continual relation extraction (CRE) requires the model to continually learn new relations from class-incremental data streams. In this paper, we propose a Frustratingly easy but Effective Approach (FEA) method with two learning stages for CRE: 1) Fast Adaption (FA) warms up the model with only new data. 2) Balanced Tuning (BT) finetunes the model on the balanced memory data. Despite its simplicity, FEA achieves comparable (on TACRED or superior (on FewRel) performance compared with the state-of-the-art baselines. With careful examinations, we find that the data imbalance between new and old relations leads to a skewed decision boundary in the head classifiers over the pretrained encoders, thus hurting the overall performance. In FEA, the FA stage unleashes the potential of memory data for the subsequent finetuning, while the BT stage helps establish a more balanced decision boundary. With a unified view, we find that two strong CRE baselines can be subsumed into the proposed training pipeline. The success of FEA also provides actionable insights and suggestions for future model designing in CRE.

Over the past few years, graph representation learning (GRL) has been a powerful strategy for analyzing graph-structured data. Recently, GRL methods have shown promising results by adopting self-supervised learning methods developed for learning representations of images. Despite their success, existing GRL methods tend to overlook an inherent distinction between images and graphs, i.e., images are assumed to be independently and identically distributed, whereas graphs exhibit relational information among data instances, i.e., nodes. To fully benefit from the relational information inherent in the graph-structured data, we propose a novel GRL method, called RGRL, that learns from the relational information generated from the graph itself. RGRL learns node representations such that the relationship among nodes is invariant to augmentations, i.e., augmentation-invariant relationship, which allows the node representations to vary as long as the relationship among the nodes is preserved. By considering the relationship among nodes in both global and local perspectives, RGRL overcomes limitations of previous contrastive and non-contrastive methods, and achieves the best of both worlds. Extensive experiments on fourteen benchmark datasets over various downstream tasks demonstrate the superiority of RGRL over state-of-the-art baselines. The source code for RGRL is available at https://github.com/Namkyeong/RGRL.

The use of models, even if efficient, must be accompanied by an understanding at all levels of the process that transforms data (upstream and downstream). Thus, needs increase to define the relationships between individual data and the choice that an algorithm could make based on its analysis (e.g. the recommendation of one product or one promotional offer, or an insurance rate representative of the risk). Model users must ensure that models do not discriminate and that it is also possible to explain their results. This paper introduces the importance of model interpretation and tackles the notion of model transparency. Within an insurance context, it specifically illustrates how some tools can be used to enforce the control of actuarial models that can nowadays leverage on machine learning. On a simple example of loss frequency estimation in car insurance, we show the interest of some interpretability methods to adapt explanation to the target audience.

Roughly 10% of data was identified as outliers and all the observations introduced were correctly classified as outliers. Them, we can quickly visualize the inliers compared to outliers to see the remaining 26 observations flagged as outliers. Figure 5 shows that the observations located farthest from the hypothetical best-fit line of the original data are considered outliers. The last of the robust regression algorithms available in scikit-learn is the Theil-Sen regression. It is a non-parametric regression method, which means that it makes no assumption about the underlying data distribution. In short, it involves fitting multiple regression models on subsets of the training data and then aggregating the coefficients at the last step.

Six: All of this has happened before. Baltar: But the question remains, does all of this have to happen again? Six: This time I bet no. Baltar: You know, I've never known you to play the optimist. Let a complex system repeat itself long enough and eventually something surprising might occur.

This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert Spaces (RKHS), to solve the problem of approximating a regular target function given observations of it, i.e. supervised learning. A first class of algorithms is kernel flow, which was introduced in the context of classification in machine learning. It can be seen as a cross-validation procedure whereby a "best" kernel is selected such that the loss of accuracy incurred by removing some part of the dataset (typically half of it) is minimized. A second class of algorithms is called spectral kernel ridge regression, and aims at selecting a "best" kernel such that the norm of the function to be approximated is minimal in the associated RKHS. Within Mercer's theorem framework, we obtain an explicit construction of that "best" kernel in terms of the main features of the target function. Both approaches of learning kernels from data are illustrated by numerical examples on synthetic test functions, and on a classical test case in turbulence modeling validation for transonic flows about a two-dimensional airfoil.

Stochastic graph neural networks (SGNNs) are information processing architectures that learn representations from data over random graphs. SGNNs are trained with respect to the expected performance, which comes with no guarantee about deviations of particular output realizations around the optimal expectation. To overcome this issue, we propose a variance-constrained optimization problem for SGNNs, balancing the expected performance and the stochastic deviation. An alternating primal-dual learning procedure is undertaken that solves the problem by updating the SGNN parameters with gradient descent and the dual variable with gradient ascent. To characterize the explicit effect of the variance-constrained learning, we conduct a theoretical analysis on the variance of the SGNN output and identify a trade-off between the stochastic robustness and the discrimination power. We further analyze the duality gap of the variance-constrained optimization problem and the converging behavior of the primal-dual learning procedure. The former indicates the optimality loss induced by the dual transformation and the latter characterizes the limiting error of the iterative algorithm, both of which guarantee the performance of the variance-constrained learning. Through numerical simulations, we corroborate our theoretical findings and observe a strong expected performance with a controllable standard deviation.

Softwarization, programmable network control and the use of all-encompassing controllers acting at different timescales are heralded as the key drivers for the evolution to next-generation cellular networks. These technologies have fostered newly designed intelligent data-driven solutions for managing large sets of diverse cellular functionalities, basically impossible to implement in traditionally closed cellular architectures. Despite the evident interest of industry on Artificial Intelligence (AI) and Machine Learning (ML) solutions for closed-loop control of the Radio Access Network (RAN), and several research works in the field, their design is far from mainstream, and it is still a sophisticated and often overlooked operation. In this paper, we discuss how to design AI/ML solutions for the intelligent closed-loop control of the Open RAN, providing guidelines and insights based on exemplary solutions with high-performance record. We then show how to embed these solutions into xApps instantiated on the O-RAN near-real-time RAN Intelligent Controller (RIC) through OpenRAN Gym, the first publicly available toolbox for data-driven O-RAN experimentation at scale. We showcase a use case of an xApp developed with OpenRAN Gym and tested on a cellular network with 7 base stations and 42 users deployed on the Colosseum wireless network emulator. Our demonstration shows the high degree of flexibility of the OpenRAN Gym-based xApp development environment, which is independent of deployment scenarios and traffic demand.