Eisuke Yamagata

Eisuke Yamagata, Shunsuke Ono

Sparse index tracking is a prominent passive portfolio management strategy that constructs a sparse portfolio to track a financial index. A sparse portfolio is preferable to a full portfolio in terms of reducing transaction costs and avoiding illiquid assets. To achieve portfolio sparsity, conventional studies have utilized $\ell_p$-norm regularizations as a continuous surrogate of the $\ell_0$-norm regularization. Although these formulations can construct sparse portfolios, their practical application is challenging due to the intricate and time-consuming process of tuning parameters to define the precise upper limit of assets in the portfolio. In this paper, we propose a new problem formulation of sparse index tracking using an $\ell_0$-norm constraint that enables easy control of the upper bound on the number of assets in the portfolio. Moreover, our approach offers a choice between constraints on portfolio and turnover sparsity, further reducing transaction costs by limiting asset updates at each rebalancing interval. Furthermore, we develop an efficient algorithm for solving this problem based on a primal-dual splitting method. Finally, we illustrate the effectiveness of the proposed method through experiments on the S&P500 and Russell3000 index datasets.

Hirokatsu Kataoka, Kazushige Okayasu, Asato Matsumoto et al.

Is it possible to use convolutional neural networks pre-trained without any natural images to assist natural image understanding? The paper proposes a novel concept, Formula-driven Supervised Learning. We automatically generate image patterns and their category labels by assigning fractals, which are based on a natural law existing in the background knowledge of the real world. Theoretically, the use of automatically generated images instead of natural images in the pre-training phase allows us to generate an infinite scale dataset of labeled images. Although the models pre-trained with the proposed Fractal DataBase (FractalDB), a database without natural images, does not necessarily outperform models pre-trained with human annotated datasets at all settings, we are able to partially surpass the accuracy of ImageNet/Places pre-trained models. The image representation with the proposed FractalDB captures a unique feature in the visualization of convolutional layers and attentions.

Nakamasa Inoue, Eisuke Yamagata, Hirokatsu Kataoka

We propose a novel network initialization method using Perlin noise for training image classification networks with a limited amount of data. Our main idea is to initialize the network parameters by solving an artificial noise classification problem, where the aim is to classify Perlin noise samples into their noise categories. Specifically, the proposed method consists of two steps. First, it generates Perlin noise samples with category labels defined based on noise complexity. Second, it solves a classification problem, in which network parameters are optimized to classify the generated noise samples. This method produces a reasonable set of initial weights (filters) for image classification. To the best of our knowledge, this is the first work to initialize networks by solving an artificial optimization problem without using any real-world images. Our experiments show that the proposed method outperforms conventional initialization methods on four image classification datasets.