Recent years have witnessed increasing interest in few-shot knowledge graph completion (FKGC), which aims to infer unseen query triples for a few-shot relation using a few reference triples about the relation. The primary focus of existing FKGC methods lies in learning relation representations that can reflect the common information shared by the query and reference triples. To this end, these methods learn entity-pair representations from the direct neighbors of head and tail entities, and then aggregate the representations of reference entity pairs. However, the entity-pair representations learned only from direct neighbors may have low expressiveness when the involved entities have sparse direct neighbors or share a common local neighborhood with other entities. Moreover, merely modeling the semantic information of head and tail entities is insufficient to accurately infer their relational information especially when they have multiple relations. To address these issues, we propose a Relation-Specific Context Learning (RSCL) framework, which exploits graph contexts of triples to learn global and local relation-specific representations for few-shot relations. Specifically, we first extract graph contexts for each triple, which can provide long-term entity-relation dependencies. To encode the extracted graph contexts, we then present a hierarchical attention network to capture contextualized information of triples and highlight valuable local neighborhood information of entities. Finally, we design a hybrid attention aggregator to evaluate the likelihood of the query triples at the global and local levels. Experimental results on two public datasets demonstrate that RSCL outperforms state-of-the-art FKGC methods.

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For models that show a strongly non-linear dependence on their input parameters, standard surrogate techniques, such as polynomial chaos expansion, are not sufficient to obtain an accurate representation of the original model response. Through applying a rational approximation instead, the approximation error can be efficiently reduced for models whose non-linearity is accurately described through a rational function. Specifically, our aim is to approximate complex-valued models. A common approach to obtain the coefficients in the surrogate is to minimize the sample-based error between model and surrogate in the least-square sense. In order to obtain an accurate representation of the original model and to avoid overfitting, the sample set has be two to three times the number of polynomial terms in the expansion. For models that require a high polynomial degree or are high-dimensional in terms of their input parameters, this number often exceeds the affordable computational cost. To overcome this issue, we apply a sparse Bayesian learning approach to the rational approximation. Through a specific prior distribution structure, sparsity is induced in the coefficients of the surrogate model. The denominator polynomial coefficients as well as the hyperparameters of the problem are determined through a type-II-maximum likelihood approach. We apply a quasi-Newton gradient-descent algorithm in order to find the optimal denominator coefficients and derive the required gradients through application of $\mathbb{CR}$-calculus.

Network analysis has been a powerful tool to unveil relationships and interactions among a large number of objects. Yet its effectiveness in accurately identifying important node-node interactions is challenged by the rapidly growing network size, with data being collected at an unprecedented granularity and scale. Common wisdom to overcome such high dimensionality is collapsing nodes into smaller groups and conducting connectivity analysis on the group level. Dividing efforts into two phases inevitably opens a gap in consistency and drives down efficiency. Consensus learning emerges as a new normal for common knowledge discovery with multiple data sources available. To this end, this paper features developing a unified framework of simultaneous grouping and connectivity analysis by combining multiple data sources. The algorithm also guarantees a statistically optimal estimator.

The increasing adoption of Digital Assets (DAs), such as Bitcoin (BTC), rises the need for accurate option pricing models. Yet, existing methodologies fail to cope with the volatile nature of the emerging DAs. Many models have been proposed to address the unorthodox market dynamics and frequent disruptions in the microstructure caused by the non-stationarity, and peculiar statistics, in DA markets. However, they are either prone to the curse of dimensionality, as additional complexity is required to employ traditional theories, or they overfit historical patterns that may never repeat. Instead, we leverage recent advances in market regime (MR) clustering with the Implied Stochastic Volatility Model (ISVM). Time-regime clustering is a temporal clustering method, that clusters the historic evolution of a market into different volatility periods accounting for non-stationarity. ISVM can incorporate investor expectations in each of the sentiment-driven periods by using implied volatility (IV) data. In this paper, we applied this integrated time-regime clustering and ISVM method (termed MR-ISVM) to high-frequency data on BTC options at the popular trading platform Deribit. We demonstrate that MR-ISVM contributes to overcome the burden of complex adaption to jumps in higher order characteristics of option pricing models. This allows us to price the market based on the expectations of its participants in an adaptive fashion.

In this discussion paper, we survey recent research surrounding robustness of machine learning models. As learning algorithms become increasingly more popular in data-driven control systems, their robustness to data uncertainty must be ensured in order to maintain reliable safety-critical operations. We begin by reviewing common formalisms for such robustness, and then move on to discuss popular and state-of-the-art techniques for training robust machine learning models as well as methods for provably certifying such robustness. From this unification of robust machine learning, we identify and discuss pressing directions for future research in the area.

For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is smooth at every iterate, the corresponding local models are unstable and the number of cutting planes invoked by traditional remedies is difficult to bound, leading to convergences guarantees that are sublinear relative to the cumulative number of gradient evaluations. We instead propose a multipoint generalization of the gradient descent iteration for local optimization. While designed with general objectives in mind, we are motivated by a ``max-of-smooth'' model that captures the subdifferential dimension at optimality. We prove linear convergence when the objective is itself max-of-smooth, and experiments suggest a more general phenomenon.

In deep learning, we have used stochastic gradient descent as one of the optimizers because at the end we will find the minimum weight and bias at which the model loss is lowest. In the SGD we have some issues in which the SGD does not work perfectly because in deep learning we got a non-convex cost function graph and if use the simple SGD then it leads to low performance. At the start, we randomly start at some point and we are going to end up at the local minimum and not able to reach the global minimum. A saddle point is a point where in one direction the surface goes in the upward direction and in another direction it goes downwards. So that the slope is changing very gradually so the speed of changing is going to slow and as result, the training also going to slow.

Rationale is defined as a subset of input features that best explains or supports the prediction by machine learning models. Rationale identification has improved the generalizability and interpretability of neural networks on vision and language data. In graph applications such as molecule and polymer property prediction, identifying representative subgraph structures named as graph rationales plays an essential role in the performance of graph neural networks. Existing graph pooling and/or distribution intervention methods suffer from lack of examples to learn to identify optimal graph rationales. In this work, we introduce a new augmentation operation called environment replacement that automatically creates virtual data examples to improve rationale identification. We propose an efficient framework that performs rationale-environment separation and representation learning on the real and augmented examples in latent spaces to avoid the high complexity of explicit graph decoding and encoding. Comparing against recent techniques, experiments on seven molecular and four polymer real datasets demonstrate the effectiveness and efficiency of the proposed augmentation-based graph rationalization framework.

Adopting data-based approaches leads to model improvement in numerous Oil&Gas logging data processing problems. These improvements become even more sound due to new capabilities provided by deep learning. However, usage of deep learning is limited to areas where researchers possess large amounts of high-quality data. We present an approach that provides universal data representations suitable for solutions to different problems for different oil fields with little additional data. Our approach relies on the self-supervised methodology for sequential logging data for intervals from well, so it also doesn't require labelled data from the start. For validation purposes of the received representations, we consider classification and clusterization problems. We as well consider the transfer learning scenario. We found out that using the variational autoencoder leads to the most reliable and accurate models. approach We also found that a researcher only needs a tiny separate data set for the target oil field to solve a specific problem on top of universal representations.

Ensemble weather forecasts based on multiple runs of numerical weather prediction models typically show systematic errors and require post-processing to obtain reliable forecasts. Accurately modeling multivariate dependencies is crucial in many practical applications, and various approaches to multivariate post-processing have been proposed where ensemble predictions are first post-processed separately in each margin and multivariate dependencies are then restored via copulas. These two-step methods share common key limitations, in particular the difficulty to include additional predictors in modeling the dependencies. We propose a novel multivariate post-processing method based on generative machine learning to address these challenges. In this new class of nonparametric data-driven distributional regression models, samples from the multivariate forecast distribution are directly obtained as output of a generative neural network. The generative model is trained by optimizing a proper scoring rule which measures the discrepancy between the generated and observed data, conditional on exogenous input variables. Our method does not require parametric assumptions on univariate distributions or multivariate dependencies and allows for incorporating arbitrary predictors. In two case studies on multivariate temperature and wind speed forecasting at weather stations over Germany, our generative model shows significant improvements over state-of-the-art methods and particularly improves the representation of spatial dependencies.