随机算法 7 Dimensionality Reduction
Lecturer: Iannis Goal of dimensionality reduction: represent a high dimensional data set in a lower dimensional space while preserving much of the important structure. PCA (principle component analysis): to maintain as much variance in the data as possible while reducing the dimensionality. The mapping of data from a high dimensional space to a low dimensional space is called an embedding. Johnson-Lindenstrauss Dimensionality Reduction Lecture notes by Allan Grønlund Main results of JL: any mmm ...
Fair Division 4 Alternatives to EFX
Objective: Investigate alternative fairness concepts for allocating indivisible items. Activities: Read and present the paper New Fairness Concepts for Allocating Indivisible Items by Ioannis et al. IJCAI2023 🍬Bonus: Methodology After reading some papers in fair division with indivisible items. I have come up with a naive 👓 methodology about research in this field. Definition of Fairness Notions: This initial phase entails defining various fairness notions and exploring how these concepts ca ...
丹麦语 DU 3.2 5 Venskab
Personlige egenskaber Han/hun er … flink/sød/venlig 好/甜/友好 stille og rolig 文静 hjælpsom 乐于助人 sjov 有趣的 aktiv 活跃，活泼 kreativ 有创造力的 kvik/intelligent 思维敏捷/聪明 interessant 有意思的 åben/udadvendt 放得开的/外向的 lidt stille 有点不爱说话 ærlig/til at stole på 诚实/可信 naturlig/ligetil 自然随和/直接 selvsikker 自信 god at snakker med 好说话 et positivt menneske 乐观的人 en god ven 好朋友 god til/ikke så god til … 擅长/不擅长 Han/hun har … et godt humør 心态好 humoristisk sans 幽默感 fuld fart på 雷厉风行 et stort hjerte 有颗大心脏，形容人处变不惊 Han/hun … kan god ...
数据挖掘 6 Spectral Theory and Clustering
This module introduces graph mining. Data points from networks, graphs, of connections. Purpose: extract patterns from graphs. 3 different areas of graph mining: Community detection: finding groups of nodes with similar characteristics. Link analysis: understanding which node is more important than others. Embedding: capturing similarities among nodes. Graph G=(V,E)G=(V,E)G=(V,E): a set of vertices VVV connected through edges E⊆V×VE\subseteq V\times VE⊆V×V. undirected & directed graph Grap ...
随机算法 6 Streaming Heavy Hitters
Lecture notes by Kasper. Review of Count Sketch This course: extends the results for count sketch algorithm (Lecture 5). Strict turnstile model, where we maintain estimates of some underlying frequency vector fff. The vector fff has coordinates indexed by integers in [U][U][U] for some universe size UUU. We receive updates one at a time. An update: (i,Δ)(i,\Delta)(i,Δ) and has the effect of updating fi←fi+Δf_i\gets f_i+\Deltafi←fi+Δ for i∈[U]i\in[U]i∈[U] and Δ∈{x}x=−MM\Delta\in\{x\}_{x=-M}^MΔ ...
Fair Division 3 Price of Fairness and MMS Property
Objective: Explore the concept of the Price of Fairness and Maximin Share (MMS) property. Activities: Read and present paper Optimal Bounds on the Price of Fairness for Indivisible Goods (2020) and Approximation Algorithms for Maximin Fair Division (2020). Paper on PoF Price of Fairness measures the worst-case loss of social welfare due to fairness constraints. This paper: Both EF1 and 12{1\over2}21-MMS guarantees has PoF O(n)O(\sqrt n)O(n), where nnn is number of agents. For 12{1\over2}21- ...
意大利语 A1 发音入门
入门阶段内容 元音 意大利语字母表 辅音 元音的发音 元音实在发音过程中气流通过口腔而不受阻碍发出的音 意大利语的元音： A, 啊 E, 诶 I, 衣 O, 喔 U, 屋 意大利语只需要拼读，无需音标👍优秀的正字法，赞一个 A: Casa, Mamma, Mare, Pane, Anche I: Vino, Mito, Cina, Piccolo, Birra U: Fumo, Scusa, Turno, Multa, Burro E: 作为单词的重音时，会有开口因和闭口音两种读法。 开口音为 [ɛ] Letto, Bene, Certo, Bello, Ecco, Problema 闭口音为 [e] Inglese, Vero, Stesso, Pesce, Me, Te ⚠️如果 E 并不作为单词的重音，默认为闭口音 O: 也会区分开口音和闭口音 开口音为 [ɔ] Porta, Uomo, Scuola, Però, Dirò 闭口音为 [o] Ora, Roma, Croce, Bisogno, Giorno, Colore ⚠️如 ...
丹麦语 DU 3.2 4 Humør og følelser
Ved du hvem der … 你知道谁…… Modul 2 考试的选题： Mit studie, Min sprogskole, Min praktik, Min bolig, Min fritidsaktivitet, Mit arbejde God fornøjelse. 玩的开心。 Hvad er der i vejen med dig? 你咋了？ Hvordan har du det? miste -r -de -t 丢失，失去 tegnebog -en …bøger …bøgerne 钱包 oplevelse -b -r -rne 经历 dumpe -r -de -t 挂科；倾倒 fejl -en - -ene 失误；错误 Humør/følelser Dansk Kinesisk Jeg er i godt humør 我心情好 Jeg er i dårligt humør 我心情不好 Jeg er glad 我高兴 Jeg er tilfreds 我满意 Jeg er lykkelig 我很高兴 Jeg er stolt 我自豪 ...
数据挖掘 5 Outlier Detection
Outlier detection as the task of finding anomalous points in data. Brief Introduction Outlier: definition depends on the application. “An object that deviates so much from the rest of the data as to arouse suspicion that it was generated by a different mechanism.” Noise VS outliers: Noise is a measuring error. Outlier is a point that belongs to the same distribution. Different types of outliers: Global outliers: Point that significantly deviate from the data set. Contextual outliers: Points de ...
随机算法 5 Streaming Algorithms for Frequency Estimation
Lecture notes adopted from UCB CS270 Streaming Algorithms: Frequent Items Streaming setting: Data stream x1,x2,⋯ ,xnx_1,x_2,\cdots,x_nx1,x2,⋯,xn with xi∈[m]x_i\in[m]xi∈[m]. The available memory is O(logcn)O(\log^cn)O(logcn). Sub-linear space. Algorithm: Approximates frequencies for the top kkk items. Deterministic Algorithm To estimate item frequencies fjf_jfj within an additive error of n/kn/kn/k using with O(klogn)O(k\log n)O(klogn) memory. （logn\log nlogn 这里指的是内存的比特数量。） Maintain set ...
