J. Jon Ryu

J. Jon Ryu, Young-Han Kim

This paper presents how to perform minimax optimal classification, regression, and density estimation based on fixed-$k$ nearest neighbor (NN) searches. We consider a distributed learning scenario, in which a massive dataset is split into smaller groups, where the $k$-NNs are found for a query point with respect to each subset of data. We propose \emph{optimal} rules to aggregate the fixed-$k$-NN information for classification, regression, and density estimation that achieve minimax optimal rates for the respective problems. We show that the distributed algorithm with a fixed $k$ over a sufficiently large number of groups attains a minimax optimal error rate up to a multiplicative logarithmic factor under some regularity conditions. Roughly speaking, distributed $k$-NN rules with $M$ groups has a performance comparable to the standard $Θ(kM)$-NN rules even for fixed $k$.

J. Jon Ryu, Alankrita Bhatt, Young-Han Kim

A class of parameter-free online linear optimization algorithms is proposed that harnesses the structure of an adversarial sequence by adapting to some side information. These algorithms combine the reduction technique of Orabona and P{á}l (2016) for adapting coin betting algorithms for online linear optimization with universal compression techniques in information theory for incorporating sequential side information to coin betting. Concrete examples are studied in which the side information has a tree structure and consists of quantized values of the previous symbols of the adversarial sequence, including fixed-order and variable-order Markov cases. By modifying the context-tree weighting technique of Willems, Shtarkov, and Tjalkens (1995), the proposed algorithm is further refined to achieve the best performance over all adaptive algorithms with tree-structured side information of a given maximum order in a computationally efficient manner.

J. Jon Ryu, Yoojin Choi, Young-Han Kim et al.

A new bimodal generative model is proposed for generating conditional and joint samples, accompanied with a training method with learning a succinct bottleneck representation. The proposed model, dubbed as the variational Wyner model, is designed based on two classical problems in network information theory -- distributed simulation and channel synthesis -- in which Wyner's common information arises as the fundamental limit on the succinctness of the common representation. The model is trained by minimizing the symmetric Kullback--Leibler divergence between variational and model distributions with regularization terms for common information, reconstruction consistency, and latent space matching terms, which is carried out via an adversarial density ratio estimation technique. The utility of the proposed approach is demonstrated through experiments for joint and conditional generation with synthetic and real-world datasets, as well as a challenging zero-shot image retrieval task.