The graph invariant EPT-sum has cropped up in several unrelated fields in later years: As an objective function for hierarchical clustering, as a more fine-grained version of the classical edge ranking problem, and, specifically when the input is a vertex-weighted tree, as a measure of average/expected search length in a partially ordered set. The EPT-sum of a graph $G$ is defined as the minimum sum of the depth of every leaf in an edge partition tree (EPT), a rooted tree where leaves correspond to vertices in $G$ and internal nodes correspond to edges in $G$. A simple algorithm that approximates EPT-sum on trees is given by recursively choosing the most balanced edge in the input tree $G$ to build an EPT of $G$. Due to its fast runtime, this balanced cut algorithm is used in practice. In this paper, we show that the balanced cut algorithm gives a 1.5-approximation of EPT-sum on trees, which amounts to a tight analysis and answers a question posed by Cicalese et al. in 2014.
相關內容
Communication robots have the potential to contribute to effective human-XAI interaction as an interface that goes beyond textual or graphical explanations. One of their strengths is that they can use physical and vocal expressions to add detailed nuances to explanations. However, it is not clear how a robot can apply such expressions, or in particular, how we can develop a strategy to adaptively use such expressions depending on the task and user in dynamic interactions. To address this question, this paper proposes DynEmph, a method for a communication robot to decide where to emphasize XAI-generated explanations with physical expressions. It predicts the effect of emphasizing certain points on a user and aims to minimize the expected difference between predicted user decisions and AI-suggested ones. DynEmph features a strategy for deciding where to emphasize in a data-driven manner, relieving engineers from the need to manually design a strategy. We further conducted experiments to investigate how emphasis selection strategies affect the performance of user decisions. The results suggest that, while a naive strategy (emphasizing explanations for an AI's most probable class) does not necessarily work better, DynEmph effectively guides users to better decisions under the condition that the performance of the AI suggestion is high.
Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-smooth Riesz kernels show a rich structure as singular measures can become absolutely continuous ones and conversely. In this paper we contribute to the understanding of such flows. We propose to approximate the backward scheme of Jordan, Kinderlehrer and Otto for computing such Wasserstein gradient flows as well as a forward scheme for so-called Wasserstein steepest descent flows by neural networks (NNs). Since we cannot restrict ourselves to absolutely continuous measures, we have to deal with transport plans and velocity plans instead of usual transport maps and velocity fields. Indeed, we approximate the disintegration of both plans by generative NNs which are learned with respect to appropriate loss functions. In order to evaluate the quality of both neural schemes, we benchmark them on the interaction energy. Here we provide analytic formulas for Wasserstein schemes starting at a Dirac measure and show their convergence as the time step size tends to zero. Finally, we illustrate our neural MMD flows by numerical examples.
Earth observation (EO) applications involving complex and heterogeneous data sources are commonly approached with machine learning models. However, there is a common assumption that data sources will be persistently available. Different situations could affect the availability of EO sources, like noise, clouds, or satellite mission failures. In this work, we assess the impact of missing temporal and static EO sources in trained models across four datasets with classification and regression tasks. We compare the predictive quality of different methods and find that some are naturally more robust to missing data. The Ensemble strategy, in particular, achieves a prediction robustness up to 100%. We evidence that missing scenarios are significantly more challenging in regression than classification tasks. Finally, we find that the optical view is the most critical view when it is missing individually.
Visual simultaneous localization and mapping (VSLAM) has broad applications, with state-of-the-art methods leveraging deep neural networks for better robustness and applicability. However, there is a lack of research in fusing these learning-based methods with multi-sensor information, which could be indispensable to push related applications to large-scale and complex scenarios. In this paper, we tightly integrate the trainable deep dense bundle adjustment (DBA) with multi-sensor information through a factor graph. In the framework, recurrent optical flow and DBA are performed among sequential images. The Hessian information derived from DBA is fed into a generic factor graph for multi-sensor fusion, which employs a sliding window and supports probabilistic marginalization. A pipeline for visual-inertial integration is firstly developed, which provides the minimum ability of metric-scale localization and mapping. Furthermore, other sensors (e.g., global navigation satellite system) are integrated for driftless and geo-referencing functionality. Extensive tests are conducted on both public datasets and self-collected datasets. The results validate the superior localization performance of our approach, which enables real-time dense mapping in large-scale environments. The code has been made open-source (//github.com/GREAT-WHU/DBA-Fusion).
Cross-modal retrieval (CMR) aims to establish interaction between different modalities, among which supervised CMR is emerging due to its flexibility in learning semantic category discrimination. Despite the remarkable performance of previous supervised CMR methods, much of their success can be attributed to the well-annotated data. However, even for unimodal data, precise annotation is expensive and time-consuming, and it becomes more challenging with the multimodal scenario. In practice, massive multimodal data are collected from the Internet with coarse annotation, which inevitably introduces noisy labels. Training with such misleading labels would bring two key challenges -- enforcing the multimodal samples to \emph{align incorrect semantics} and \emph{widen the heterogeneous gap}, resulting in poor retrieval performance. To tackle these challenges, this work proposes UOT-RCL, a Unified framework based on Optimal Transport (OT) for Robust Cross-modal Retrieval. First, we propose a semantic alignment based on partial OT to progressively correct the noisy labels, where a novel cross-modal consistent cost function is designed to blend different modalities and provide precise transport cost. Second, to narrow the discrepancy in multi-modal data, an OT-based relation alignment is proposed to infer the semantic-level cross-modal matching. Both of these two components leverage the inherent correlation among multi-modal data to facilitate effective cost function. The experiments on three widely-used cross-modal retrieval datasets demonstrate that our UOT-RCL surpasses the state-of-the-art approaches and significantly improves the robustness against noisy labels.
Data consisting of a graph with a function mapping into $\R^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such objects is required in a data analysis pipeline, leading to a need for distances between them. In this work, we study the interleaving distance on discretization of these objects, $\R^d$-mapper graphs, where functor representations of the data can be compared by finding pairs of natural transformations between them. However, in many cases, computation of the interleaving distance is NP-hard. For this reason, we take inspiration from recent work by Robinson to find quality measures for families of maps that do not rise to the level of a natural transformation, called assignments. We then endow the functor images with the extra structure of a metric space and define a loss function which measures how far an assignment is from making the required diagrams of an interleaving commute. Finally we show that the computation of the loss function is polynomial with a given assignment. We believe this idea is both powerful and translatable, with the potential to provide approximations and bounds on interleavings in a broad array of contexts.
Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the samples these models generate? This work aims to provide an accessible entry point to understanding popular notions of statistical distances, requiring only foundational knowledge in mathematics and statistics. We focus on four commonly used notions of statistical distances representing different methodologies: Using low-dimensional projections (Sliced-Wasserstein; SW), obtaining a distance using classifiers (Classifier Two-Sample Tests; C2ST), using embeddings through kernels (Maximum Mean Discrepancy; MMD), or neural networks (Fr\'echet Inception Distance; FID). We highlight the intuition behind each distance and explain their merits, scalability, complexity, and pitfalls. To demonstrate how these distances are used in practice, we evaluate generative models from different scientific domains, namely a model of decision making and a model generating medical images. We showcase that distinct distances can give different results on similar data. Through this guide, we aim to help researchers to use, interpret, and evaluate statistical distances for generative models in science.
Named entity recognition (NER) is the task to identify text spans that mention named entities, and to classify them into predefined categories such as person, location, organization etc. NER serves as the basis for a variety of natural language applications such as question answering, text summarization, and machine translation. Although early NER systems are successful in producing decent recognition accuracy, they often require much human effort in carefully designing rules or features. In recent years, deep learning, empowered by continuous real-valued vector representations and semantic composition through nonlinear processing, has been employed in NER systems, yielding stat-of-the-art performance. In this paper, we provide a comprehensive review on existing deep learning techniques for NER. We first introduce NER resources, including tagged NER corpora and off-the-shelf NER tools. Then, we systematically categorize existing works based on a taxonomy along three axes: distributed representations for input, context encoder, and tag decoder. Next, we survey the most representative methods for recent applied techniques of deep learning in new NER problem settings and applications. Finally, we present readers with the challenges faced by NER systems and outline future directions in this area.
Neural machine translation (NMT) is a deep learning based approach for machine translation, which yields the state-of-the-art translation performance in scenarios where large-scale parallel corpora are available. Although the high-quality and domain-specific translation is crucial in the real world, domain-specific corpora are usually scarce or nonexistent, and thus vanilla NMT performs poorly in such scenarios. Domain adaptation that leverages both out-of-domain parallel corpora as well as monolingual corpora for in-domain translation, is very important for domain-specific translation. In this paper, we give a comprehensive survey of the state-of-the-art domain adaptation techniques for NMT.
Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural network component that allows robust counting from object proposals. Experiments on a toy task show the effectiveness of this component and we obtain state-of-the-art accuracy on the number category of the VQA v2 dataset without negatively affecting other categories, even outperforming ensemble models with our single model. On a difficult balanced pair metric, the component gives a substantial improvement in counting over a strong baseline by 6.6%.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191