統計と最適化

- 確率変数と確率分布，確率分布の性質を表す指標/Random variables, probability distributions, and indices representing properties of probability distributions - 同時確率，条件付き確率/Joint probability, conditional probability - 離散型確率分布，連続型確率分布/Discrete probability distributions, continuous probability distributions - 任意の確率分布に従う標本の生成/Sampling from arbitrary probability distributions - 確率不等式/Probabilistic inequalities - 大数の法則と中心極限定理/Law of large numbers and central limit theorem - 重複対数の法則，仮説検定/Law of the iterated logarithm, hypothesis testing - 行列，微分積分，凸集合，凸関数/Matrices, differential and integral calculus, convex sets, convex functions - 制約なし最適化/Unconstrained optimization - 等式制約付き最適化/Equality constrained optimization - 不等式制約付き最適化/Inequality constrained optimization - 確率的最適化/Stochastic optimization - 自動微分/Automatic differentiation - 共役勾配法/Conjugate gradient method

講義を中心に進める / Mainly through lectures

レポートと試験による By reports and exams

杉山 将：機械学習のための確率と統計, 講談社, 2015. 金森 敬文, 鈴木 大慈, 竹内 一郎, 佐藤 一誠: 機械学習のための連続最適化，講談社, 2016. / Masashi Sugiyama: Introduction to Statistical Machine Learning, Morgan Kaufmann, 2015. Ian Goodfellow, Yoshua Bengio, and Aaron Courville: Deep Learning, MIT Press, 2016.

杉山 将（編）：機械学習プロフェッショナルシリーズ，講談社 / Trevor Hastie, Robert Tibshirani, and Jerome Friedman: The Elements of Statistical Learning:---Data Mining, Inference, and Prediction, 2nd Edition, Springer, 2009. Christopher M. Bishop: Pattern Recognition and Machine Learning, 2nd Edition, Springer, 2016.

講義スライドを講義前に公開するので，事前に目を通しておくこと． また，教科書・参考書の該当部分を講義前に予習しておくことを勧める． / The lecture slides will be made available before the lecture, so please read through them beforehand. It is also recommended that the students study the relevant parts of the textbooks and reference books before the lecture.