查看更多>>摘要：MLR（Modal Linear Regression，最頻値線形回帰）は，出力の最頻値が説明変数の線形予測子で表されるというモデルに基づく回帰手法である．線形回帰と異なり，パラメトリックな分布の仮定がないという意味で制約が緩いことが，MLRの特徴の1つである．一方，パラメトリックな分布の仮定がないことが，MLRを情報幾何学の枠組みで捉える際のモデル多様体，データ多様体の構成を非自明にする．本稿では，MLRを情報幾何学の枠組みで捉えるにあたり，一般に経験分布を構成するために用いる観測データを，モデル多様体を構成するために用いることを提案する．またMEMアルゴリズムの考察を通じて，MLRにおける誤差分布の最頻値の仮定を用いた経験分布の構成方法を提案する．本稿のモデル多様体，データ多様体におけるemアルゴリズムが，MLRをEMアルゴリズムの枠組みで捉えた際のE-Step，M-Stepの計算と等しくなるという結果を得た．
查看更多>>摘要：For parametric models of Markov sources, we prove that the notion of asymptotic exponential family is equivalent to the notion of exponential family of Markov kernels. The former was introduced by Takeuchi and Barron (1998) for families of general stochastic processes, inspired by the exponential family of Markov chains discovered by Ito and Amari (1988), while the latter was introduced by Nakagawa and Kanaya (1993) for one-dimensional families of Markov sources based on the discussion by Ito and Amari (1988) and later the general form was established by Nagaoka (2005). The discussion in this report is some refinement of works of Takeuchi and Nagaoka (2017).
查看更多>>摘要：In this study, we extract intra-week and intra-day activity patterns based on hourly step-count data recorded using an activity meter. The step-count measured each hour over the week is considered to be a bag of words and is applied to a hierarchical topic model with intra-day activity patterns as sub-topics and intra-week activity patterns as super-topics. Using the extracted patterns, we then analyze the dynamic relations between intra-week activities and body weight changes.
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