数据科学精要：理论、模型与算法探索

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"数据科学：理论、模型、算法与分析 / Data Science：Theories, Models, Algorithms…" 是一本由 Santa Clara 大学商学院金融与数据科学教授 Sanjiv Ranjan Das 编写的开源eBook，涵盖了广泛的IT领域知识，包括机器学习、深度学习、数据科学、数据分析、大数据、编程语言（如Keras、TensorFlow、PyTorch）以及强化学习等。本书是Das教授为其课程《Machine Learning with R》准备的课堂笔记，旨在提供一个全面的学习资源。书中涉及的知识点： 1. **数据科学的艺术**：这部分可能涵盖数据科学的基本理念、方法论及其在现实世界中的应用，强调数据驱动决策的重要性。 2. **数学基础**：这是学习数据科学的基础，可能包括概率论、统计学、线性代数、微积分等核心概念，这些都是理解和构建模型的基石。 3. **R语言建模**：R是一种广泛用于数据科学的编程语言，书中会讲解如何使用R进行数据处理、建模和可视化。 4. **数据处理与其他**：这部分可能包含数据清洗、预处理、特征工程和数据集成的技巧。 5. **马科维茨优化**：这是投资组合管理中的一个概念，可能讲解如何通过最小化风险来构建最优投资组合。 6. **贝叶斯定理**：一种基于先验知识更新概率的方法，在机器学习中常用于构建贝叶斯网络和朴素贝叶斯分类器。 7. **自然语言处理**：可能涵盖文本挖掘、情感分析和NLP技术，用于从新闻和其他文本中提取信息。 8. **巴斯模型**：一种经济模型，用于描述资产价格的随机变动，对理解金融市场有重要意义。 9. **判别和因子分析**：数据降维技术，用于发现隐藏的结构和减少复杂性。 10. **拍卖理论**：涉及经济学中的竞标策略和市场设计，可能讲解如何分析拍卖机制。 11. **有限因变量的截断和估计**：在统计学中，可能讨论如何处理具有截断或受限范围的数据。 12. **傅里叶分析**：用于将信号分解为不同频率的成分，常见于图像处理和信号处理中。 13. **网络理论**：探讨复杂网络的结构、动力学和分析方法，如社交网络分析。 14. **神经网络**：深度学习的核心，介绍神经网络的结构、训练过程和应用。 15. **聚类分析和预测树**：无监督学习方法，如K-means聚类，以及监督学习的决策树模型。这本eBook通过开源的形式，为读者提供了丰富的学习资源，涵盖了数据科学的多个重要方面，无论对于初学者还是有经验的专业人士，都是一个宝贵的自学工具。

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7.1 The data and algorithms pyramids. Depicts the inverse relationship between data vol-

ume and algorithmic complexity. 169

7.2 Quantity of hourly postings on message boards after selected news releases. Source:

Das, Martinez-Jerez and Tufano (2005). 171

7.3 Subjective evaluation of content of post-news release postings on message boards. The

content is divided into opinions, facts, and questions. Source: Das, Martinez-Jerez and

Tufano (2005). 172

7.4 Frequency of posting by message board participants. 173

7.5 Frequency of posting by day of week by message board participants. 173

7.6 Frequency of posting by segment of day by message board participants. We show the

average number of messages per day in the top panel and the average number of char-

acters per message in the bottom panel. 174

7.7 Example of application of word cloud to the bio data extracted from the web and stored

in a Corpus. 181

7.8 Plot of stock series (upper graph) versus sentiment series (lower graph). The correla-

tion between the series is high. The plot is based on messages from Yahoo! Finance and

is for a single twenty-four hour period. 211

7.9 Phase-lag analysis. The left-side shows the eight canonical graph patterns that are de-

rived from arrangements of the start, end, high, and low points of a time series. The right-

side shows the leads and lags of patterns of the stock series versus the sentiment series.

A positive value means that the stock series leads the sentiment series. 214

8.1 Actual versus Bass model predictions for VCRs. 228

8.2 Actual versus Bass model predictions for answering machines. 229

8.3 Example of the adoption rate: m = 100, 000, p = 0.01 and q = 0.2. 231

8.4 Example of the adoption rate: m = 100, 000, p = 0.01 and q = 0.2. 232

8.5 Computing the Bass model integral using WolframAlpha. 234

8.6 Bass model forecast of Apple Inc’s quarterly sales. The current sales are

also overlaid in the plot. 237

8.7 Empirical adoption rates and parameters from the Bass paper. 237

8.8 Increase in peak time with q ↑ 240

10.1 Probability density function for the Beta (a = 2, b = 4) distribution. 271

10.2 Revenue in the DPA and UPA auctions. 273

10.3 Treasury auction markups. 274

10.4 Bid-Ask Spread in the Auction. 275

13.1 Comparison of random and scale-free graphs. From Barabasi, Albert-Laszlo., and Eric

Bonabeau (2003). “Scale-Free Networks,” Scientiﬁc American May, 50–59. 323

13.2 Microsoft academic search tool for co-authorship networks. See: http://academic.research.microsoft.com/.

The top chart shows co-authors, the middle one shows citations, and the last one shows

my Erdos number, i.e., the number of hops needed to be connected to Paul Erdos via

my co-authors. My Erdos number is 3. Interestingly, I am a Finance academic, but my

shortest path to Erdos is through Computer Science co-authors, another ﬁeld in which

I dabble. 326

13.3 Depth-ﬁrst-search. 327

13.4 Depth-ﬁrst search on a simple graph generated from a paired node list. 329

13.5 Breadth-ﬁrst-search. 330

13.6 Strongly connected components. The upper graph shows the original network and the

lower one shows the compressed network comprising only the SCCs. The algorithm to

determine SCCs relies on two DFSs. Can you see a further SCC in the second graph?

There should not be one. 332

13.7 Finding connected components on a graph. 334

13.8 Dijkstra’s algorithm. 335

13.9 Network for computation of shortest path algorithm 336

13.10Plot using the Fruchterman-Rheingold and Circle layouts 338

13.11Plot of the Erdos-Renyi random graph 339

13.12Plot of the degree distribution of the Erdos-Renyi random graph 340

13.13Interbank lending networks by year. The top panel shows 2005, and the bottom panel

is for the years 2006-2009. 345

13.14Community versus centrality 354

13.15Banking network adjacency matrix and plot 357

13.16Centrality for the 15 banks. 359

13.17Risk Decompositions for the 15 banks. 361

13.18Risk Increments for the 15 banks. 363

13.19Criticality for the 15 banks. 364

13.20Spillover effects. 366

13.21How risk increases with connectivity of the network. 368

13.22How risk increases with connectivity of the network. 370

13.23Screens for selecting the relevant set of Indian FIs to construct the banking network. 372

13.24Screens for the Indian FIs banking network. The upper plot shows the entire network.

The lower plot shows the network when we mouse over the bank in the middle of the

plot. Red lines show that the bank is impacted by the other banks, and blue lines de-

pict that the bank impacts the others, in a Granger causal manner. 373

13.25Screens for systemic risk metrics of the Indian FIs banking network. The top plot shows

the current risk metrics, and the bottom plot shows the history from 2008. 374

13.26The Map of Science. 375

14.1 A feed-forward multilayer neural network. 380

14.2 The neural net for the infert data set with two perceptrons in a single hidden layer. 387

15.1 Plot of the ﬁnal outcome distribution for a digital portfolio with ﬁve assets of outcomes

{5, 8, 4, 2, 1} all of equal probability. 400

15.2 Plot of the ﬁnal outcome distribution for a digital portfolio with ﬁve assets of outcomes

{5, 8, 4, 2, 1} with unconditional probability of success of {0.1, 0.2, 0.1, 0.05, 0.15}, respecitvely.

403

15.3 Plot of the difference in distribution for a digital portfolio with ﬁve assets when ρ =

0.75 minus that when ρ = 0.25. We use outcomes {5, 8, 4, 2, 1} with unconditional prob-

ability of success of {0.1, 0.2, 0.1, 0.05, 0.15}, respecitvely. 405

15.4 Distribution functions for returns from Bernoulli investments as the number of invest-

ments (n) increases. Using the recursion technique we computed the probability dis-

tribution of the portfolio payoff for four values of n = {25, 50, 75, 100}. The distribu-

tion function is plotted in the left panel. There are 4 plots, one for each n, and if we look

at the bottom left of the plot, the leftmost line is for n = 100. The next line to the right

is for n = 75, and so on. The right panel plots the value of

100

(x) − G

(x)] dx

for all u ∈ (0, 1), and conﬁrms that it is always negative. The correlation parameter

is ρ = 0.25. 408

15.5 Distribution functions for returns from Bernoulli investments as the correlation param-

eter (ρ

) increases. Using the recursion technique we computed the probability distri-

bution of the portfolio payoff for four values of ρ = {0.09, 0.25, 0.49, 0.81} shown by

the black, red, green and blue lines respectively. The distribution function is plotted in

the left panel. The right panel plots the value of

ρ=0.09

(x) −G

ρ=0.81

(x)] dx for all

u ∈ (0, 1), and conﬁrms that it is always negative. 410

16.1 Bankroll evolution under the Kelly rule. The top plot follows the Kelly criterion, but

the other two deviate from it, by overbetting or underbetting the fraction given by Kelly.

The variables are: odds are 4 to 1, implying a house probability of p = 0.2, own prob-

ability of winning is p

∗

= 0.25. 419

16.2 See http://wizardofodds.com/gambling/house-edge/. The House Edge for various games.

The edge is the same as −f in our notation. The standard deviation is that of the bankroll

of $1 for one bet. 424

17.1 VC Style Clusters. 430

17.2 Two cluster example. 432

17.3 Five cluster example. 433

17.4 NCAA cluster example. 435

17.5 NCAA data, hierarchical cluster example. 437

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