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Linear arrangements of graphs are a well-known type of graph labeling and are found in many important computational problems, such as the Minimum Linear Arrangement Problem ($\texttt{minLA}$). A linear arrangement is usually defined as a permutation of the $n$ vertices of a graph. An intuitive geometric setting is that of vertices lying on consecutive integer positions in the real line, starting at 1; edges are often drawn as semicircles above the real line. In this paper we study the Maximum Linear Arrangement problem ($\texttt{MaxLA}$), the maximization variant of $\texttt{minLA}$. We devise a new characterization of maximum arrangements of general graphs, and prove that $\texttt{MaxLA}$ can be solved for cycle graphs in constant time, and for $k$-linear trees ($k\le2$) in time $O(n)$. We present two constrained variants of $\texttt{MaxLA}$ we call $\texttt{bipartite MaxLA}$ and $\texttt{1-thistle MaxLA}$. We prove that the former can be solved in time $O(n)$ for any bipartite graph; the latter, by an algorithm that typically runs in time $O(n^4)$ on unlabelled trees. The combination of the two variants has two promising characteristics. First, it solves $\texttt{MaxLA}$ for almost all trees consisting of a few tenths of nodes. Second, we prove that it constitutes a $3/2$-approximation algorithm for $\texttt{MaxLA}$ for trees. Furthermore, we conjecture that $\texttt{bipartite MaxLA}$ solves $\texttt{MaxLA}$ for at least $50\%$ of all free trees.

Distinguishing sources of predictive uncertainty is of crucial importance in the application of forecasting models across various domains. Despite the presence of a great variety of proposed uncertainty measures, there are no strict definitions to disentangle them. Furthermore, the relationship between different measures of uncertainty quantification remains somewhat unclear. In this work, we introduce a general framework, rooted in statistical reasoning, which not only allows the creation of new uncertainty measures but also clarifies their interrelations. Our approach leverages statistical risk to distinguish aleatoric and epistemic uncertainty components and utilizes proper scoring rules to quantify them. To make it practically tractable, we propose an idea to incorporate Bayesian reasoning into this framework and discuss the properties of the proposed approximation.

Disentangled latent spaces usually have better semantic separability and geometrical properties, which leads to better interpretability and more controllable data generation. While this has been well investigated in Computer Vision, in tasks such as image disentanglement, in the NLP domain sentence disentanglement is still comparatively under-investigated. Most previous work have concentrated on disentangling task-specific generative factors, such as sentiment, within the context of style transfer. In this work, we focus on a more general form of sentence disentanglement, targeting the localised modification and control of more general sentence semantic features. To achieve this, we contribute to a novel notion of sentence semantic disentanglement and introduce a flow-based invertible neural network (INN) mechanism integrated with a transformer-based language Autoencoder (AE) in order to deliver latent spaces with better separability properties. Experimental results demonstrate that the model can conform the distributed latent space into a better semantically disentangled sentence space, leading to improved language interpretability and controlled generation when compared to the recent state-of-the-art language VAE models.

Several applications in time series forecasting require predicting multiple steps ahead. Despite the vast amount of literature in the topic, both classical and recent deep learning based approaches have mostly focused on minimising performance averaged over the predicted window. We observe that this can lead to disparate distributions of errors across forecasting steps, especially for recent transformer architectures trained on popular forecasting benchmarks. That is, optimising performance on average can lead to undesirably large errors at specific time-steps. In this work, we present a Constrained Learning approach for long-term time series forecasting that aims to find the best model in terms of average performance that respects a user-defined upper bound on the loss at each time-step. We call our approach loss shaping constraints because it imposes constraints on the loss at each time step, and leverage recent duality results to show that despite its non-convexity, the resulting problem has a bounded duality gap. We propose a practical Primal-Dual algorithm to tackle it, and demonstrate that the proposed approach exhibits competitive average performance in time series forecasting benchmarks, while shaping the distribution of errors across the predicted window.

In research of manufacturing systems and autonomous robots, the term capability is used for a machine-interpretable specification of a system function. Approaches in this research area develop information models that capture all information relevant to interpret the requirements, effects and behavior of functions. These approaches are intended to overcome the heterogeneity resulting from the various types of processes and from the large number of different vendors. However, these models and associated methods do not offer solutions for automated process planning, i.e. finding a sequence of individual capabilities required to manufacture a certain product or to accomplish a mission using autonomous robots. Instead, this is a typical task for AI planning approaches, which unfortunately require a high effort to create the respective planning problem descriptions. In this paper, we present an approach that combines these two topics: Starting from a semantic capability model, an AI planning problem is automatically generated. The planning problem is encoded using Satisfiability Modulo Theories and uses an existing solver to find valid capability sequences including required parameter values. The approach also offers possibilities to integrate existing human expertise and to provide explanations for human operators in order to help understand planning decisions.

We consider the problem of finding an informative path through a graph, given initial and terminal nodes and a given maximum path length. We assume that a linear noise corrupted measurement is taken at each node of an underlying unknown vector that we wish to estimate. The informativeness is measured by the reduction in uncertainty in our estimate, evaluated using several metrics. We present a convex relaxation for this informative path planning problem, which we can readily solve to obtain a bound on the possible performance. We develop an approximate sequential method where the path is constructed segment by segment through dynamic programming. This involves solving an orienteering problem, with the node reward acting as a surrogate for informativeness, taking the first step, and then repeating the process. The method scales to very large problem instances and achieves performance not too far from the bound produced by the convex relaxation. We also demonstrate our method's ability to handle adaptive objectives, multimodal sensing, and multi-agent variations of the informative path planning problem.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.

Learning latent representations of nodes in graphs is an important and ubiquitous task with widespread applications such as link prediction, node classification, and graph visualization. Previous methods on graph representation learning mainly focus on static graphs, however, many real-world graphs are dynamic and evolve over time. In this paper, we present Dynamic Self-Attention Network (DySAT), a novel neural architecture that operates on dynamic graphs and learns node representations that capture both structural properties and temporal evolutionary patterns. Specifically, DySAT computes node representations by jointly employing self-attention layers along two dimensions: structural neighborhood and temporal dynamics. We conduct link prediction experiments on two classes of graphs: communication networks and bipartite rating networks. Our experimental results show that DySAT has a significant performance gain over several different state-of-the-art graph embedding baselines.

Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree of over-segmentation produced. It still remains a challenge to properly select such parameters for human-like perceptual grouping. In this work, we exploit the diversity of segments produced by different choices of parameters. We scan the segmentation parameter space and generate a collection of image segmentation hypotheses (from highly over-segmented to under-segmented). These are fed into a cost minimization framework that produces the final segmentation by selecting segments that: (1) better describe the natural contours of the image, and (2) are more stable and persistent among all the segmentation hypotheses. We compare our algorithm's performance with state-of-the-art algorithms, showing that we can achieve improved results. We also show that our framework is robust to the choice of segmentation kernel that produces the initial set of hypotheses.