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課程名稱 |
資料科學的數理統計基礎
Mathematical statistics for data science |
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開課學期 |
104-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
銀慶剛 |
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課號 |
MATH5013 |
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課程識別碼 |
221 U6700 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期五2,3,4(9:10~12:10) |
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上課地點 |
天數101 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1041MATH5013_ |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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課程概述 |
見課程第一週內容 |
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課程目標 |
Statistical analysis of complex or high-dimensional data often involves fundamental techniques in
statistics and probability. As a case in point, we note that concentration inequalities can be used to perform
variable screening in a high-dimensional regression model, in which the number of variables is much larger
than the number of observations. After the number of variables is reduced to a manageable size, one is allowed
to estimate unknown parameters using classical estimation methods, such as least squares estimates and
maximum likelihood estimates, and then conducts statistical inference with (or without) screening effects taken
into account. When data are serially dependent or the parameters of interest are related to the variance of the
data, asymptotic theory for martingales or quadratic forms becomes relevant. This course intends to equip
learners with updated knowledge of statistics and probability techniques required for analyzing complex and
high-dimensional data. Moreover, the student(s) will acquire solid background needed for courses like
Statistical Machine Learning for Data Science. |
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課程要求 |
待補 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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參考書目 |
見課程第一週內容 |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/18 |
Introduction and Finite Sample Theory I (起) |
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第2週 |
9/25 |
Finite Sample Theory II (起): Projection Theory and BLUE |
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第3週 |
10/02 |
Finite Sample Theory III (承): Multivariate Normal Distributions, Distributions of Quadratic and Linear Forms under Normality, F Tests and Wald Tests |
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第4週 |
10/09 |
National Holiday |
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第5週 |
10/16 |
Finite Sample Theory IV: T Tests, Interval Estimation, Prediction, Model Selection (承) |
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第6週 |
10/23 |
Large Sample Theory I (轉 1) |
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第7週 |
10/30 |
Large Sample Theory II (轉 1) |
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第8週 |
11/06 |
Large Sample Theory III (轉 1) |
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第9週 |
11/13 |
Midterm Exam |
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第10週 |
11/20 |
Maximum Likelihood Methods I (轉 2) |
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第11週 |
11/27 |
自主學習週 |
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第13週 |
12/11 |
Maximum Likelihood Methods III (轉 3) |
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第14週 |
12/18 |
High-Dimensional Models I (轉 3) |
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第15週 |
12/25 |
High-Dimensional Models II (轉 3) |
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第16週 |
1/01 |
National Holiday |
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第17週 |
1/08 |
Statistical Inference after High-Dimensional Methods (合) |
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第18週 |
1/15 |
Final Exam |
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