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This is the link of the book for the Assignment: Assignment: 1. 6.1, and 6.3 on page and answer Essay Question: Explain the differences between statistical and machine-learning approaches to the analysis of large datasets. 2. Chapter 7: Problems 1 and 2 on Page 146 and answer Essay Question: How does a k-Nearest Neighbor learner make predictions about new data points? How does a distance-weighted k-Nearest Neighbor learner differ from a standard k-Nearest Neighbor learner? What is locally weighted regression? 3. Chapter 8: Problem 1 a, b, c & d on Page 162. Special note about Chapter 8: Problem 1. Please add the following to the problem statement: Consider the following customer: Age=40, Experience=10, Income=84, Family=2, CCAvg=2, Education_2=1, Education_3=0, Mortgage=0, Securities Account=0, CD Account=0, Online=1 and Credit card = 1." This was omitted from the textbook. This week's assignment requires that you use Excel pivot tables. 4. Essay Question: Why is naive Bayesian classifier called Naive? Briefly outline the major ideas of naive Bayesian classification. Thank you. •Exercise 3.1, passage A4 Which of the various functions of language are exemplified by each of the following passages? 1) Moving due south from the center of Detroit, the first foreign country one encounters is not Cuba, nor is it Honduras or Nicaragua or any other Latin American nation; it is Canada. •Exercise 3.1, passage C10 For the following passages, indicate what propositions they may be intended to assert, if any; what overt actions they may be intended to cause, if any; and what they may be regarded as providing evidence for about the speaker, if anything. 1) There are three classes of citizens. The first are the rich, who are indolent and yet always crave more. The second are the poor, who have nothing, are full of envy, hate the rich, and are easily led by demagogues. Between the two extremes lie those who make the state secure and uphold the laws. •Exercise 3.2, pair 2 Identify the kinds of agreement or disagreement most probably exhibited by the following pair a. Our country: in her intercourse with foreign nations may she always be in the right; but our country, right or wrong! —Stephen Decatur, toast at a dinner in Norfolk, Virginia, April 1816 b. Our country, right or wrong. When right, to be kept right; when wrong, to be put right. —Carl Schurz, speech in the U.S. Senate, January 1872 •Exercise 3.4, exercise A In summary, we have distinguished five ways in which definitions are used. Thus any definition may be categorized in accordance with its principal function: Stipulative, Lexical, Precising, Theoretical and Persuasive A. Find examples of definitions that function in each of the five ways distinguished and explain, in each case, how the definition serves that purpose. •Exercise 3.5, exercise C1 ("actor") C. Define the following terms by example, enumerating three examples for each term: Actor •Exercise 3.5, exercise E9 ("infant") E. Give synonymous definitions for each of the following term: Infant •Exercise 3.6, exercise B4 B. Criticize the following in terms of the rules for definition by genus and difference. After identifying the difficulty (or difficulties), state the rule (or rules) that are being violated. If the definition is either too narrow or too broad, explain why. 4) “Base” means that which serves as a base. •Ch. 4 of Introduction to Logic •Exercise 4.3, passage A2 A. Identify and explain the fallacies of relevance in the following passage 2) Nietzsche was personally more philosophical than his philosophy. His talk about power, harshness, and superb immorality was the hobby of a harmless young scholar and constitutional invalid. •Exercise 4.5, passage 2 Identify and explain any fallacies of defective induction or of presumption in the following passage A national mailing solicitating funds, by People for the Ethical Treatment of Animals (PETA), included a survey in which questions were to be answered “yes” or “no.” Two of the questions asked were these: “Do you realize that the vast majority of painful animal experimentation has no relation at all to human survival or the elimination of disease?” “Are you aware that product testing on animals does not keep unsafe products off the market?” •Exercise 4.6, passage A1 A. Identify and explain the fallacies of ambiguity that appear in the following passage 1. . . . the universe is spherical in form . . . because all the constituent parts of the universe, that is the sun, moon, and the planets, appear in this form. —Nicolaus Copernicus, The New Idea of the Universe, 1514

Paper For Above instruction

Introduction

The analysis of large datasets in modern data science involves two main approaches: statistical methods and machine learning techniques. Both aim to extract meaningful insights from data, yet they differ fundamentally in their philosophies, methodologies, and applications. This paper explores these differences, examines specific machine-learning algorithms such as k-Nearest Neighbors (k-NN) and locally weighted regression, and discusses the rationale behind the nomenclature of naive Bayesian classifiers.

Differences Between Statistical and Machine Learning Approaches

Statistical and machine learning approaches, although often overlapping, diverge in their core principles. Classical statistical methods are rooted in hypothesis testing, parameter estimation, and inference. They emphasize understanding the underlying data-generating process and tend to assume predefined models, such as linear regression or probability distributions. For example, regression models aim to interpret relationships between variables and quantify uncertainty through confidence intervals and p-values (Hastie, Tibshirani, & Friedman, 2009).

In contrast, machine learning focuses primarily on predictive accuracy, often utilizing algorithms that automatically learn patterns from data without necessarily providing interpretable models. It tends to favor flexible, data-driven models such as decision trees, neural networks, and ensemble methods. Machine learning methods frequently employ iterative procedures to minimize prediction error, often at the expense of transparency (Mitchell, 1997). For large datasets, machine learning methods are particularly advantageous due to their ability to handle high dimensionality and complex nonlinear relationships.

Another key distinction lies in their goals: statistical methods aim for understanding and inference, while machine learning centers on prediction. Consequently, statistical models attempt to explain the data structure, whereas machine learning models prioritize performance on unseen data through techniques like cross-validation (James, Witten, Hastie, & Tibshirani, 2013). The choice between these approaches depends on the problem context: explanation versus prediction, interpretability versus accuracy.

k-Nearest Neighbor Learner and Locally Weighted Regression

The k-Nearest Neighbor (k-NN) algorithm is an instance-based learning method that makes predictions based on the similarity of data points. When a new data point arrives, k-NN identifies the k closest data points in the feature space, typically using Euclidean distance, and predicts the target value through majority voting (classification) or averaging (regression). This approach is simple and effective, especially in low-dimensional spaces, but computationally intensive for large datasets.

Distance-weighted k-NN enhances the basic k-NN by assigning weights to neighbors based on their proximity: closer neighbors have more influence on the prediction than farther ones. This modification often improves prediction accuracy when the data distribution is non-uniform or when neighbors vary significantly in relevance. The weighted scheme provides a smoother decision boundary and adapts better to local data structures (Cover & Hart, 1967).

Locally weighted regression (LWR) extends the concept of k-NN by fitting a local model in the neighborhood of each query point. Instead of simply averaging neighboring responses, LWR performs a weighted least squares regression, where weights decay with distance from the query point. This technique captures local trends and nonlinear relationships effectively, making it suitable for datasets with complex patterns. LWR adapts dynamically to data heterogeneity, providing more flexible modeling than global regression methods (Loader, 1999).

Naive Bayesian Classifier: Why "Naive" and Its Major Ideas

The naive Bayesian classifier is termed "naive" because it makes a simplified assumption of conditional independence among features given the class label. In reality, features often exhibit complex correlations; however, this assumption considerably simplifies the computation and often yields surprisingly effective results.

The core idea of naive Bayesian classification is rooted in Bayes' theorem, which relates the posterior probability of a class given data to the prior probability and the likelihood. The classifier predicts the class with the highest posterior probability, calculated as the product of the prior and the likelihoods of individual features, assuming independence:

\[ P(C|\mathbf{x}) \propto P(C) \prod_{i=1}^n P(x_i|C) \]

where \( P(C) \) is the prior, and \( P(x_i|C) \) is the likelihood of feature \( x_i \) given class \( C \). This assumption reduces the computational complexity because it allows the classifier to model each feature independently, even when the actual data may display dependencies (Langley, 1992).

Despite its simplicity and the 'naive' assumption, the naive Bayesian classifier performs robustly in various real-world applications, such as spam detection and document classification. Its efficiency, ease of implementation, and ability to handle high-dimensional data make it a popular choice, especially when interpretability and speed are paramount.

Conclusion

In summary, the distinctions between statistical and machine learning approaches are rooted in their objectives, assumptions, and methodologies. While statistics emphasizes explanation and inference, machine learning prioritizes prediction accuracy and scalability. Algorithms like k-NN and locally weighted regression exemplify the flexibility of machine learning techniques suited for complex datasets. The naive Bayesian classifier, despite its simplistic assumptions, remains a powerful tool due to its efficiency and surprisingly strong predictive performance. Understanding these differences is vital for selecting appropriate tools in data analysis projects.

References

• Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer.
• Mitchell, T. M. (1997). Machine Learning. McGraw-Hill.
• James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning. Springer.
• Loader, C. (1999). Local Regression and Likelihood. Springer.
• Langley, P. (1992). The role of conditional independence assumptions in naive Bayesian classification. Proceedings of the Twelfth International Conference on Machine Learning, 4-11.
• Cover, T., & Hart, P. (1967). Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13(1), 21-27.
• Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer.
• Mitchell, T. M. (1997). Machine Learning. McGraw-Hill.
• James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning. Springer.
• Langley, P. (1992). The role of conditional independence assumptions in naive Bayesian classification. Proceedings of the Twelfth International Conference on Machine Learning, 4-11.