近傍法における距離・類似度尺度のデータ中心化 －ハブネスの軽減－

Open House, ISM in Tachikawa, 2015.6.19統計数理研究所オープンハウス（立川）、H27.6.19ポスター発

Ridge Regression, Hubness, and Zero-Shot Learning

This paper discusses the effect of hubness in zero-shot learning, when ridge regression is used to find a mapping between the example space to the label space. Contrary to the existing approach, which attempts to find a mapping from the example space to the label space, we show that mapping labels into the example space is desirable to suppress the emergence of hubs in the subsequent nearest neighbor search step. Assuming a simple data model, we prove that the proposed approach indeed reduces hubness. This was verified empirically on the tasks of bilingual lexicon extraction and image labeling: hubness was reduced with both of these tasks and the accuracy was improved accordingly.Comment: To be presented at ECML/PKDD 201

Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)

Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a graph is scale-free, and prove a series of results that recover many of the claimed properties while suggesting the potential for a rich and interesting theory. With this definition, scale-free (or its opposite, scale-rich) is closely related to other structural graph properties such as various notions of self-similarity (or respectively, self-dissimilarity). Scale-free graphs are also shown to be the likely outcome of random construction processes, consistent with the heuristic definitions implicit in existing random graph approaches. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the scale-free literature, and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet Mathematics (2005

Balance Act: Mitigating Hubness in Cross-Modal Retrieval with Query and Gallery Banks

In this work, we present a post-processing solution to address the hubness problem in cross-modal retrieval, a phenomenon where a small number of gallery data points are frequently retrieved, resulting in a decline in retrieval performance. We first theoretically demonstrate the necessity of incorporating both the gallery and query data for addressing hubness as hubs always exhibit high similarity with gallery and query data. Second, building on our theoretical results, we propose a novel framework, Dual Bank Normalization (DBNorm). While previous work has attempted to alleviate hubness by only utilizing the query samples, DBNorm leverages two banks constructed from the query and gallery samples to reduce the occurrence of hubs during inference. Next, to complement DBNorm, we introduce two novel methods, dual inverted softmax and dual dynamic inverted softmax, for normalizing similarity based on the two banks. Specifically, our proposed methods reduce the similarity between hubs and queries while improving the similarity between non-hubs and queries. Finally, we present extensive experimental results on diverse language-grounded benchmarks, including text-image, text-video, and text-audio, demonstrating the superior performance of our approaches compared to previous methods in addressing hubness and boosting retrieval performance. Our code is available at https://github.com/yimuwangcs/Better_Cross_Modal_Retrieval.Comment: Accepted by EMNLP 202

On the Selection of Anchors and Targets for Video Hyperlinking

A problem not well understood in video hyperlinking is what qualifies a fragment as an anchor or target. Ideally, anchors provide good starting points for navigation, and targets supplement anchors with additional details while not distracting users with irrelevant, false and redundant information. The problem is not trivial for intertwining relationship between data characteristics and user expectation. Imagine that in a large dataset, there are clusters of fragments spreading over the feature space. The nature of each cluster can be described by its size (implying popularity) and structure (implying complexity). A principle way of hyperlinking can be carried out by picking centers of clusters as anchors and from there reach out to targets within or outside of clusters with consideration of neighborhood complexity. The question is which fragments should be selected either as anchors or targets, in one way to reflect the rich content of a dataset, and meanwhile to minimize the risk of frustrating user experience. This paper provides some insights to this question from the perspective of hubness and local intrinsic dimensionality, which are two statistical properties in assessing the popularity and complexity of data space. Based these properties, two novel algorithms are proposed for low-risk automatic selection of anchors and targets.Comment: ACM International Conference on Multimedia Retrieval (ICMR), 2017. (Oral

Nonparametric Bayes Modeling of Populations of Networks

Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can flexibly characterize the probabilistic generative mechanism underlying these network-valued data. Available models for a single network are not designed specifically for inference on the entire probability mass function of a network-valued random variable and therefore lack flexibility in characterizing the distribution of relevant topological structures. We propose a flexible Bayesian nonparametric approach for modeling the population distribution of network-valued data. The joint distribution of the edges is defined via a mixture model which reduces dimensionality and efficiently incorporates network information within each mixture component by leveraging latent space representations. The formulation leads to an efficient Gibbs sampler and provides simple and coherent strategies for inference and goodness-of-fit assessments. We provide theoretical results on the flexibility of our model and illustrate improved performance --- compared to state-of-the-art models --- in simulations and application to human brain networks