Implicit Bayes Adaptation: A Collaborative Transport Approach

The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability distributions by some optimal metric, has been creatively exploited and shown to hold promise for many real-world data challenges. In a related theme in the present work, we posit that domain adaptation robustness is rooted in the intrinsic (latent) representations of the respective data, which are inherently lying in a non-linear submanifold embedded in a higher dimensional Euclidean space. We account for the geometric properties by refining the $l^2$ Euclidean metric to better reflect the geodesic distance between two distinct representations. We integrate a metric correction term as well as a prior cluster structure in the source data of the OT-driven adaptation. We show that this is tantamount to an implicit Bayesian framework, which we demonstrate to be viable for a more robust and better-performing approach to domain adaptation. Substantiating experiments are also included for validation purposes.

Refining Self-Supervised Learning in Imaging: Beyond Linear Metric

We introduce in this paper a new statistical perspective, exploiting the Jaccard similarity metric, as a measure-based metric to effectively invoke non-linear features in the loss of self-supervised contrastive learning. Specifically, our proposed metric may be interpreted as a dependence measure between two adapted projections learned from the so-called latent representations. This is in contrast to the cosine similarity measure in the conventional contrastive learning model, which accounts for correlation information. To the best of our knowledge, this effectively non-linearly fused information embedded in the Jaccard similarity, is novel to self-supervision learning with promising results. The proposed approach is compared to two state-of-the-art self-supervised contrastive learning methods on three image datasets. We not only demonstrate its amenable applicability in current ML problems, but also its improved performance and training efficiency.

Query Answering via Decentralized Search

Expert networks are formed by a group of expert-professionals with different specialties to collaboratively resolve specific queries posted to the network. In such networks, when a query reaches an expert who does not have sufficient expertise, this query needs to be routed to other experts for further processing until it is completely solved; therefore, query answering efficiency is sensitive to the underlying query routing mechanism being used. Among all possible query routing mechanisms, decentralized search, operating purely on each expert's local information without any knowledge of network global structure, represents the most basic and scalable routing mechanism, which is applicable to any network scenarios even in dynamic networks. However, there is still a lack of fundamental understanding of the efficiency of decentralized search in expert networks. In this regard, we investigate decentralized search by quantifying its performance under a variety of network settings. Our key findings reveal the existence of network conditions, under which decentralized search can achieve significantly short query routing paths (i.e., between $O(\log n)$ and $O(\log^2 n)$ hops, $n$: total number of experts in the network). Based on such theoretical foundation, we further study how the unique properties of decentralized search in expert networks is related to the anecdotal small-world phenomenon. In addition, we demonstrate that decentralized search is robust against estimation errors introduced by misinterpreting the required expertise levels. To the best of our knowledge, this is the first work studying fundamental behaviors of decentralized search in expert networks. The developed performance bounds, confirmed by real datasets, are able to assist in predicting network performance and designing complex expert networks.