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Show new changes starting from 21:39, 26 September 2024
 
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22 September 2024

 N    07:39  数据科学基础 (Fall 2024)/Volume of Hamming balls‎‎ 2 changes history +2,803‎ [Etone‎ (2×)]
     
07:39 (cur | prev) −3,786‎ Etone talk contribs
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07:39 (cur | prev) +6,589‎ Etone talk contribs (Created page with "在求解抛掷公平硬币（fair coin）的尾概率时，我们经常会需要分析如下二项式系数求和： :<math>\sum_{k=0}^r{n\choose k}</math>，对于某个<math>1\le r\le n</math> 这其实等价与求一个 <math>n</math> 维汉明空间中半径为 <math>r</math> 的球的体积。 :{|border="2" width="100%" cellspacing="4" cellpadding="3" rules="all" style="margin:1em 1em 1em 0; border:solid 1px #AAAAAA; border-collapse:collapse;empty-cells:show;" | :'...")
     07:38  数据科学基础 (Fall 2024)‎‎ 3 changes history +217‎ [Etone‎ (3×)]
     
07:38 (cur | prev) −24‎ Etone talk contribs (→‎Lectures)
     
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07:14 (cur | prev) +131‎ Etone talk contribs (→‎Lectures)

20 September 2024

      01:16  数据科学基础 (Fall 2024)/Problem Set 1‎‎ 3 changes history +240‎ [Liumingmou‎ (3×)]
     
01:16 (cur | prev) +66‎ Liumingmou talk contribs
     
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19 September 2024

     17:26  数据科学基础 (Fall 2024)‎ diffhist +222‎ Liumingmou talk contribs (→‎Assignments)
N    17:18  数据科学基础 (Fall 2024)/Problem Set 1‎‎ 6 changes history +12,716‎ [Liumingmou‎ (6×)]
     
17:18 (cur | prev) +10‎ Liumingmou talk contribs
     
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14:51 (cur | prev) +2,337‎ Liumingmou talk contribs (Created page with "*每道题目的解答都要有完整的解题过程，中英文不限。 *我们推荐大家使用LaTeX, markdown等对作业进行排版。 <h2 id="problem-1">Problem 1 (Probability space)</h2> <ul> <li>[<strong>De Morgan’s Laws</strong>] Let <math>\{A_i\}</math> be a collection of sets. Prove <math>\left(\bigcup_iA_i\right)^c=\bigcap_iA_i^c</math>.</li> <li>[<strong><math>\sigma</math>-algebra</strong>] Let <math>A</math> and <math>B</math> belong to some <math>\s...")
N    11:32  高级算法 (Fall 2024)/Conditional expectations‎ diffhist +10,715‎ Etone talk contribs (Created page with "= Conditional Expectations = The '''conditional expectation''' of a random variable <math>Y</math> with respect to an event <math>\mathcal{E}</math> is defined by :<math> \mathbf{E}[Y\mid \mathcal{E}]=\sum_{y}y\Pr[Y=y\mid\mathcal{E}]. </math> In particular, if the event <math>\mathcal{E}</math> is <math>X=a</math>, the conditional expectation :<math> \mathbf{E}[Y\mid X=a] </math> defines a function :<math> f(a)=\mathbf{E}[Y\mid X=a]. </math> Thus, <math>\mathbf{E}[Y\mid...")
N    11:31  高级算法 (Fall 2024)/Concentration of measure‎ diffhist +41,013‎ Etone talk contribs (Created page with "=Chernoff Bound= Suppose that we have a fair coin. If we toss it once, then the outcome is completely unpredictable. But if we toss it, say for 1000 times, then the number of HEADs is very likely to be around 500. This phenomenon, as illustrated in the following figure, is called the '''concentration''' of measure. The Chernoff bound is an inequality that characterizes the concentration phenomenon for the sum of independent trials. File:Coinflip.png|border|450px|cent...")
     11:30  高级算法 (Fall 2024)‎ diffhist +229‎ Etone talk contribs (→‎Lecture Notes)

18 September 2024

     08:10  数据科学基础 (Fall 2024)‎ diffhist +2,264‎ Etone talk contribs (→‎Concepts)

16 September 2024

N    02:45  高级算法 (Fall 2024)/Basic deviation inequalities‎ diffhist +5,755‎ Etone talk contribs (Created page with "=Markov's Inequality= One of the most natural information about a random variable is its expectation, which is the first moment of the random variable. Markov's inequality draws a tail bound for a random variable from its expectation. {{Theorem |Theorem (Markov's Inequality)| :Let <math>X</math> be a random variable assuming only nonnegative values. Then, for all <math>t>0</math>, ::<math>\begin{align} \Pr[X\ge t]\le \frac{\mathbf{E}[X]}{t}. \end{align}</math> }} {{Proo...")
N    02:44  高级算法 (Fall 2024)/Limited independence‎ diffhist +15,812‎ Etone talk contribs (Created page with "= <math>k</math>-wise independence = Recall the definition of independence between events: {{Theorem |Definition (Independent events)| :Events <math>\mathcal{E}_1, \mathcal{E}_2, \ldots, \mathcal{E}_n</math> are '''mutually independent''' if, for any subset <math>I\subseteq\{1,2,\ldots,n\}</math>, ::<math>\begin{align} \Pr\left[\bigwedge_{i\in I}\mathcal{E}_i\right] &= \prod_{i\in I}\Pr[\mathcal{E}_i]. \end{align}</math> }} Similarly, we can define independence between...")
N    02:44  高级算法 (Fall 2024)/Hashing and Sketching‎ diffhist +49,238‎ Etone talk contribs (Created page with "=Balls into Bins= The following is the so-called balls into bins model. Consider throwing <math>m</math> balls into <math>n</math> bins uniformly and independently at random. This is equivalent to a random mapping <math>f:[m]\to[n]</math>. Needless to say, random mapping is an important random model and may have many applications in Computer Science, e.g. hashing. We are concerned with the following three questions regarding the balls into bins model: * birthday problem...")
     02:44  高级算法 (Fall 2024)‎ diffhist +304‎ Etone talk contribs (→‎Lecture Notes)

14 September 2024

     08:10  数据科学基础 (Fall 2024)‎ diffhist +33‎ Liumingmou talk contribs

12 September 2024

N    11:22  高级算法 (Fall 2024)/Finite Field Basics‎ diffhist +6,210‎ Etone talk contribs (Created page with "=Field= Let <math>S</math> be a set, '''closed''' under binary operations <math>+</math> (addition) and <math>\cdot</math> (multiplication). It gives us the following algebraic structures if the corresponding set of axioms are satisfied. {|class="wikitable" !colspan="7"|Structures !Axioms !Operations |- |rowspan="9" style="background-color:#ffffcc;text-align:center;"|'''''field''''' |rowspan="8" style="background-color:#ffffcc;text-align:center;"|'''''commutative<br>rin...")
N    11:21  高级算法 (Fall 2024)/Fingerprinting‎ diffhist +38,283‎ Etone talk contribs (Created page with "= Checking Matrix Multiplication= thumb|360px|right|The evolution of time complexity <math>O(n^{\omega})</math> for matrix multiplication. Let <math>\mathbb{F}</math> be a feild (you may think of it as the filed <math>\mathbb{Q}</math> of rational numbers, or the finite field <math>\mathbb{Z}_p</math> of integers modulo prime <math>p</math>). We suppose that each field operation (addition, subtraction, multiplication, division) has u...")
     11:21  高级算法 (Fall 2024)‎ diffhist +203‎ Etone talk contribs (→‎Lecture Notes)
     04:57  数据科学基础 (Fall 2024)‎ diffhist +157‎ Liumingmou talk contribs Tag: Visual edit: Switched

6 September 2024

      09:40  数据科学基础 (Fall 2024)‎‎ 2 changes history +161‎ [Liumingmou‎; Etone‎]
     
09:40 (cur | prev) +159‎ Etone talk contribs (→‎Lectures)
     
04:59 (cur | prev) +2‎ Liumingmou talk contribs

5 September 2024

      08:55  数据科学基础 (Fall 2024)‎‎ 2 changes history −43‎ [Liumingmou‎ (2×)]
     
08:55 (cur | prev) −14‎ Liumingmou talk contribs
     
08:55 (cur | prev) −29‎ Liumingmou talk contribs (→‎Course info)
     04:08  高级算法 (Fall 2024)‎‎ 2 changes history +53‎ [Etone‎ (2×)]
     
04:08 (cur | prev) 0‎ Etone talk contribs (→‎Lecture Notes)
     
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4 September 2024

     15:23  Main Page‎ diffhist −252‎ Liuexp talk contribs (→‎Home Pages for Courses and Seminars)

29 August 2024

      10:29  数据科学基础 (Fall 2024)‎‎ 3 changes history +52‎ [Liumingmou‎; Etone‎ (2×)]
     
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28 August 2024

N    23:02  数据科学基础 (Fall 2024)‎ diffhist +4,948‎ Liumingmou talk contribs (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>'''数据科学基础'''<br> Foundations of Data Science |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = '''尹一通''' |header3 = |label3 = Email |data3 = yinyt@nju.edu.cn |header4 = |l...")
     12:18  Main Page‎‎ 2 changes history +184‎ [Etone‎ (2×)]
     
12:18 (cur | prev) +109‎ Etone talk contribs
     
05:14 (cur | prev) +75‎ Etone talk contribs (→‎Home Pages for Courses and Seminars)
N    05:24  高级算法 (Fall 2024)/Probability Basics‎ diffhist +17,328‎ Etone talk contribs (Created page with "=Probability Space= The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one of the greatest mathematician of the 20th century, who advanced various very different fields of mathematics. {{Theorem|Definition (Probability Space)| A '''probability space''' is a triple <math>(\Omega,\Sigma,\Pr)</math>. *<math>\Omega</math> is a set, called the '''sample space'''. *<math>\Sigma\subseteq 2^{\Omega}</math> is the...")
N    05:24  高级算法 (Fall 2024)/Min Cut, Max Cut, and Spectral Cut‎ diffhist +50,059‎ Etone talk contribs (Created page with "= Graph Cut = Let <math>G(V, E)</math> be an undirected graph. A subset <math>C\subseteq E</math> of edges is a '''cut''' of graph <math>G</math> if <math>G</math> becomes ''disconnected'' after deleting all edges in <math>C</math>. Let <math>\{S,T\}</math> be a '''bipartition''' of <math>V</math> into nonempty subsets <math>S,T\subseteq V</math>, where <math>S\cap T=\emptyset</math> and <math>S\cup T=V</math>. A cut <math>C</math> is specified by this bipartition as...")
N    05:23  高级算法 (Fall 2024) / Course materials‎ diffhist +2,043‎ Etone talk contribs (Created page with "= Course textbooks = {|border="2" cellspacing="4" cellpadding="3" rules="all" style="margin:1em 1em 1em 0; border:solid 1px #AAAAAA; border-collapse:collapse;empty-cells:show;" |border|100px |width="100%"| :Rajeev Motwani and Prabhakar Raghavan. :'''''Randomized Algorithms'''''. :Cambridge University Press, 1995. |- |border|100px|| : Vijay Vazirani. :'''''Approximation Algorithms'''''. :S...")
N    05:22  高级算法 (Fall 2024)‎ diffhist +6,278‎ Etone talk contribs (Created page with "{{Infobox |name = Infobox |bodystyle = |title = <font size=3>高级算法 <br>Advanced Algorithms</font> |titlestyle = |image = |imagestyle = |caption = |captionstyle = |headerstyle = background:#ccf; |labelstyle = background:#ddf; |datastyle = |header1 =Instructor |label1 = |data1 = |header2 = |label2 = |data2 = '''尹一通''' |header3 = |label3 = Email |data3 = yinyt@nju.edu.cn |header4 = |label4= office...")
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