Exercises in Machine Learning

This book contains 75+ exercises

Download, read, and practice:
arxiv.org/pdf/2206.13446

GitHub Repo: https://github.com/michaelgutmann/ml-pen-and-paper-exercises

#DataAnalytics #Python #SQL #RProgramming #DataScience #MachineLearning #DeepLearning #Statistics #DataVisualization #PowerBI #Tableau #LinearRegression #Probability #DataWrangling #Excel #AI #ArtificialIntelligence #BigData #DataAnalysis #NeuralNetworks #GAN #LearnDataScience #LLM #RAG #Mathematics #PythonProgramming  #Keras

https://t.iss.one/CodeProgrammer ✅

Topic: Python SciPy – From Easy to Top: Part 5 of 6: Working with SciPy Statistics

---

1. Introduction to `scipy.stats`

• The scipy.stats module contains a large number of probability distributions and statistical functions.
• You can perform tasks like descriptive statistics, hypothesis testing, sampling, and fitting distributions.

---

2. Descriptive Statistics

Use these functions to summarize and describe data characteristics:

from scipy import stats
import numpy as np

data = [2, 4, 4, 4, 5, 5, 7, 9]

mean = np.mean(data)
median = np.median(data)
mode = stats.mode(data, keepdims=True)
std_dev = np.std(data)

print("Mean:", mean)
print("Median:", median)
print("Mode:", mode.mode[0])
print("Standard Deviation:", std_dev)

---

3. Probability Distributions

SciPy has built-in continuous and discrete distributions such as normal, binomial, Poisson, etc.

Normal Distribution Example

from scipy.stats import norm

# PDF at x = 0
print("PDF at 0:", norm.pdf(0, loc=0, scale=1))

# CDF at x = 1
print("CDF at 1:", norm.cdf(1, loc=0, scale=1))

# Generate 5 random numbers
samples = norm.rvs(loc=0, scale=1, size=5)
print("Random Samples:", samples)

---

4. Hypothesis Testing

One-sample t-test – test if the mean of a sample is equal to a known value:

sample = [5.1, 5.3, 5.5, 5.7, 5.9]
t_stat, p_val = stats.ttest_1samp(sample, popmean=5.0)

print("T-statistic:", t_stat)
print("P-value:", p_val)

Interpretation: If the p-value is less than 0.05, reject the null hypothesis.

---

5. Two-sample t-test

Test if two samples come from populations with equal means:

group1 = [20, 22, 19, 24, 25]
group2 = [28, 27, 26, 30, 31]

t_stat, p_val = stats.ttest_ind(group1, group2)

print("T-statistic:", t_stat)
print("P-value:", p_val)

---

6. Chi-Square Test for Independence

Use to test independence between two categorical variables:

# Example contingency table
data = [[10, 20], [20, 40]]
chi2, p, dof, expected = stats.chi2_contingency(data)

print("Chi-square statistic:", chi2)
print("P-value:", p)

---

7. Correlation and Covariance

Measure linear relationship between variables:

x = [1, 2, 3, 4, 5]
y = [2, 4, 6, 8, 10]

corr, _ = stats.pearsonr(x, y)
print("Pearson Correlation Coefficient:", corr)

Covariance:

cov_matrix = np.cov(x, y)
print("Covariance Matrix:\n", cov_matrix)

---

8. Fitting Distributions to Data

You can fit a distribution to real-world data:

data = np.random.normal(loc=50, scale=10, size=1000)
params = norm.fit(data)  # returns mean and std dev

print("Fitted mean:", params[0])
print("Fitted std dev:", params[1])

---

9. Sampling from Distributions

Generate random numbers from different distributions:

# Binomial distribution
samples = stats.binom.rvs(n=10, p=0.5, size=10)
print("Binomial Samples:", samples)

# Poisson distribution
samples = stats.poisson.rvs(mu=3, size=10)
print("Poisson Samples:", samples)

---

10. Summary

• scipy.stats is a powerful tool for statistical analysis.
• You can compute summaries, perform tests, model distributions, and generate random samples.

---

Exercise

• Generate 1000 samples from a normal distribution and compute mean, median, std, and mode.
• Test if a sample has a mean significantly different from 5.
• Fit a normal distribution to your own dataset and plot the histogram with the fitted PDF curve.

---

#Python #SciPy #Statistics #HypothesisTesting #DataAnalysis

https://t.iss.one/DataScienceM

💡 SciPy: Scientific Computing in Python

SciPy is a fundamental library for scientific and technical computing in Python. Built on NumPy, it provides a wide range of user-friendly and efficient numerical routines for tasks like optimization, integration, linear algebra, and statistics.

import numpy as np
from scipy.optimize import minimize

# Define a function to minimize: f(x) = (x - 3)^2
def f(x):
    return (x - 3)**2

# Find the minimum of the function with an initial guess
res = minimize(f, x0=0)

print(f"Minimum found at x = {res.x[0]:.4f}")
# Output:
# Minimum found at x = 3.0000

• Optimization: scipy.optimize.minimize is used to find the minimum value of a function.
• We provide the function (f) and an initial guess (x0=0).
• The result object (res) contains the solution in the .x attribute.

from scipy.integrate import quad

# Define the function to integrate: f(x) = sin(x)
def integrand(x):
    return np.sin(x)

# Integrate sin(x) from 0 to pi
result, error = quad(integrand, 0, np.pi)

print(f"Integral result: {result:.4f}")
print(f"Estimated error: {error:.2e}")
# Output:
# Integral result: 2.0000
# Estimated error: 2.22e-14

• Numerical Integration: scipy.integrate.quad calculates the definite integral of a function over a given interval.
• It returns a tuple containing the integral result and an estimate of the absolute error.

from scipy.linalg import solve

# Solve the linear system Ax = b
# 3x + 2y = 12
#  x -  y = 1

A = np.array([[3, 2], [1, -1]])
b = np.array([12, 1])

solution = solve(A, b)
print(f"Solution (x, y): {solution}")
# Output:
# Solution (x, y): [2.8 1.8]

• Linear Algebra: scipy.linalg provides more advanced linear algebra routines than NumPy.
• solve(A, b) efficiently finds the solution vector x for a system of linear equations defined by a matrix A and a vector b.

from scipy import stats

# Create two independent samples
sample1 = np.random.normal(loc=5, scale=2, size=100)
sample2 = np.random.normal(loc=5.5, scale=2, size=100)

# Perform an independent t-test
t_stat, p_value = stats.ttest_ind(sample1, sample2)

print(f"T-statistic: {t_stat:.4f}")
print(f"P-value: {p_value:.4f}")
# Output (will vary):
# T-statistic: -1.7432
# P-value: 0.0829

• Statistics: scipy.stats is a powerful module for statistical analysis.
• ttest_ind calculates the T-test for the means of two independent samples.
• The p-value helps determine if the difference between sample means is statistically significant (a low p-value, e.g., < 0.05, suggests it is).

#SciPy #Python #DataScience #ScientificComputing #Statistics

━━━━━━━━━━━━━━━
By: @DataScienceM ✨

Age
count   5.000000
mean   30.000000
std     6.363961
min    22.000000
25%    26.000000
50%    29.000000
75%    35.000000
max    38.000000

---

10. df.columns
Returns the column labels of the DataFrame.

import pandas as pd
df = pd.DataFrame({'Name': [], 'Age': [], 'City': []})
print(df.columns)

Index(['Name', 'Age', 'City'], dtype='object')

---

11. df.dtypes
Returns the data type of each column.

import pandas as pd
df = pd.DataFrame({'Name': ['Alice'], 'Age': [25], 'Salary': [75000.50]})
print(df.dtypes)

Name       object
Age         int64
Salary    float64
dtype: object

---

12. Selecting a Column
Select a single column, which returns a Pandas Series.

import pandas as pd
data = {'Name': ['Alice', 'Bob'], 'Age': [25, 30]}
df = pd.DataFrame(data)
ages = df['Age']
print(ages)

0    25
1    30
Name: Age, dtype: int64

#DataSelection #Indexing #Statistics

---

13. df.loc[]
Access a group of rows and columns by label(s) or a boolean array.

import pandas as pd
data = {'Age': [25, 30, 35], 'City': ['NY', 'LA', 'CH']}
df = pd.DataFrame(data, index=['Alice', 'Bob', 'Charlie'])
print(df.loc['Bob'])

Age     30
City    LA
Name: Bob, dtype: object

---

14. df.iloc[]
Access a group of rows and columns by integer position(s).

import pandas as pd
data = {'Age': [25, 30, 35], 'City': ['NY', 'LA', 'CH']}
df = pd.DataFrame(data, index=['Alice', 'Bob', 'Charlie'])
print(df.iloc[1]) # Get the second row (index 1)

Age     30
City    LA
Name: Bob, dtype: object

---

15. df.isnull()
Returns a DataFrame of the same shape with boolean values indicating if a value is missing (NaN).

import pandas as pd
import numpy as np
df = pd.DataFrame({'A': [1, np.nan], 'B': [3, 4]})
print(df.isnull())

A      B
0  False  False
1   True  False

---

16. df.dropna()
Removes missing values.

import pandas as pd
import numpy as np
df = pd.DataFrame({'A': [1, np.nan, 3], 'B': [4, 5, 6]})
cleaned_df = df.dropna()
print(cleaned_df)

A  B
0  1.0  4
2  3.0  6

#DataCleaning #MissingData

---

17. df.fillna()
Fills missing (NaN) values with a specified value or method.

import pandas as pd
import numpy as np
df = pd.DataFrame({'Score': [90, 85, np.nan, 92]})
filled_df = df.fillna(0)
print(filled_df)

Score
0   90.0
1   85.0
2    0.0
3   92.0

---

18. df.drop_duplicates()
Removes duplicate rows from the DataFrame.

import pandas as pd
data = {'Name': ['Alice', 'Bob', 'Alice'], 'Age': [25, 30, 25]}
df = pd.DataFrame(data)
unique_df = df.drop_duplicates()
print(unique_df)

Name  Age
0  Alice   25
1    Bob   30

---

19. df.rename()
Alters axes labels (e.g., column names).

import pandas as pd
df = pd.DataFrame({'A': [1], 'B': [2]})
renamed_df = df.rename(columns={'A': 'Column_A', 'B': 'Column_B'})
print(renamed_df)

Column_A  Column_B
0         1         2

---

20. series.value_counts()
Returns a Series containing counts of unique values.

Top 100 Data Analyst Interview Questions & Answers

#DataAnalysis #InterviewQuestions #SQL #Python #Statistics #CaseStudy #DataScience

Part 1: SQL Questions (Q1-30)

#1. What is the difference between DELETE, TRUNCATE, and DROP?
A:
• DELETE is a DML command that removes rows from a table based on a WHERE clause. It is slower as it logs each row deletion and can be rolled back.
• TRUNCATE is a DDL command that quickly removes all rows from a table. It is faster, cannot be rolled back, and resets table identity.
• DROP is a DDL command that removes the entire table, including its structure, data, and indexes.

#2. Select all unique departments from the employees table.
A: Use the DISTINCT keyword.

SELECT DISTINCT department
FROM employees;

#3. Find the top 5 highest-paid employees.
A: Use ORDER BY and LIMIT.

SELECT name, salary
FROM employees
ORDER BY salary DESC
LIMIT 5;

#4. What is the difference between WHERE and HAVING?
A:
• WHERE is used to filter records before any groupings are made (i.e., it operates on individual rows).
• HAVING is used to filter groups after aggregations (GROUP BY) have been performed.

-- Find departments with more than 10 employees
SELECT department, COUNT(employee_id)
FROM employees
GROUP BY department
HAVING COUNT(employee_id) > 10;

#5. What are the different types of SQL joins?
A:
• (INNER) JOIN: Returns records that have matching values in both tables.
• LEFT (OUTER) JOIN: Returns all records from the left table, and the matched records from the right table.
• RIGHT (OUTER) JOIN: Returns all records from the right table, and the matched records from the left table.
• FULL (OUTER) JOIN: Returns all records when there is a match in either the left or right table.
• SELF JOIN: A regular join, but the table is joined with itself.

#6. Write a query to find the second-highest salary.
A: Use OFFSET or a subquery.

-- Method 1: Using OFFSET
SELECT salary
FROM employees
ORDER BY salary DESC
LIMIT 1 OFFSET 1;

-- Method 2: Using a Subquery
SELECT MAX(salary)
FROM employees
WHERE salary < (SELECT MAX(salary) FROM employees);

#7. Find duplicate emails in a customers table.
A: Group by the email column and use HAVING to find groups with a count greater than 1.

SELECT email, COUNT(email)
FROM customers
GROUP BY email
HAVING COUNT(email) > 1;

#8. What is a primary key vs. a foreign key?
A:
• A Primary Key is a constraint that uniquely identifies each record in a table. It must contain unique values and cannot contain NULL values.
• A Foreign Key is a key used to link two tables together. It is a field (or collection of fields) in one table that refers to the Primary Key in another table.

#9. Explain Window Functions. Give an example.
A: Window functions perform a calculation across a set of table rows that are somehow related to the current row. Unlike aggregate functions, they do not collapse rows.

-- Rank employees by salary within each department
SELECT
    name,
    department,
    salary,
    RANK() OVER (PARTITION BY department ORDER BY salary DESC) as dept_rank
FROM employees;

#10. What is a CTE (Common Table Expression)?
A: A CTE is a temporary, named result set that you can reference within a SELECT, INSERT, UPDATE, or DELETE statement. It helps improve readability and break down complex queries.

• (Time: 90s) Simpson's Paradox occurs when:
a) A model performs well on training data but poorly on test data.
b) Two variables appear to be correlated, but the correlation is caused by a third variable.
c) A trend appears in several different groups of data but disappears or reverses when these groups are combined.
d) The mean, median, and mode of a distribution are all the same.

• (Time: 75s) When presenting your findings to non-technical stakeholders, you should focus on:
a) The complexity of your statistical models and the p-values.
b) The story the data tells, the business implications, and actionable recommendations.
c) The exact Python code and SQL queries you used.
d) Every single chart and table you produced during EDA.

• (Time: 75s) A survey about job satisfaction is only sent out via a corporate email newsletter. The results may suffer from what kind of bias?
a) Survivorship bias
b) Selection bias
c) Recall bias
d) Observer bias

• (Time: 90s) For which of the following machine learning algorithms is feature scaling (e.g., normalization or standardization) most critical?
a) Decision Trees and Random Forests.
b) K-Nearest Neighbors (KNN) and Support Vector Machines (SVM).
c) Naive Bayes.
d) All algorithms require feature scaling to the same degree.

• (Time: 90s) A Root Cause Analysis for a business problem primarily aims to:
a) Identify all correlations related to the problem.
b) Assign blame to the responsible team.
c) Build a model to predict when the problem will happen again.
d) Move beyond symptoms to find the fundamental underlying cause of the problem.

• (Time: 75s) A "funnel analysis" is typically used to:
a) Segment customers into different value tiers.
b) Understand and optimize a multi-step user journey, identifying where users drop off.
c) Forecast future sales.
d) Perform A/B tests on a website homepage.

• (Time: 75s) Tracking the engagement metrics of users grouped by their sign-up month is an example of:
a) Funnel Analysis
b) Regression Analysis
c) Cohort Analysis
d) Time-Series Forecasting

• (Time: 90s) A retail company wants to increase customer lifetime value (CLV). A data-driven first step would be to:
a) Redesign the company logo.
b) Increase the price of all products.
c) Perform customer segmentation (e.g., using RFM analysis) to understand the behavior of different customer groups and tailor strategies accordingly.
d) Switch to a new database provider.

#DataAnalysis #Certification #Exam #Advanced #SQL #Pandas #Statistics #MachineLearning

━━━━━━━━━━━━━━━
By: @DataScienceM ✨

📌 Why Nonparametric Models Deserve a Second Look

🗂 Category: MACHINE LEARNING

🕒 Date: 2025-11-05 | ⏱️ Read time: 7 min read

Nonparametric models offer a powerful, unified framework for regression, classification, and synthetic data generation. By leveraging nonparametric conditional distributions, these methods provide significant flexibility because they don't require pre-defining a specific functional form for the data. This adaptability makes them highly effective for capturing complex patterns and relationships that might be missed by traditional models. It's time for data professionals to reconsider the unique advantages of these assumption-free techniques for modern machine learning challenges.

#NonparametricModels #MachineLearning #DataScience #Statistics

📌 Power Analysis in Marketing: A Hands-On Introduction

🗂 Category: STATISTICS

🕒 Date: 2025-11-08 | ⏱️ Read time: 18 min read

Dive into the fundamentals of power analysis for marketing. This hands-on introduction demystifies statistical power, explaining what it is and demonstrating how to compute it. Understand why power is crucial for reliable A/B testing and campaign analysis, and learn to strengthen your experimental design. This is the first part of a practical series for data-driven professionals.

#PowerAnalysis #MarketingAnalytics #DataScience #Statistics

📌 The Machine Learning “Advent Calendar” Day 3: GNB, LDA and QDA in Excel

🗂 Category: MACHINE LEARNING

🕒 Date: 2025-12-03 | ⏱️ Read time: 10 min read

Day 3 of the Machine Learning "Advent Calendar" series explores Gaussian Naive Bayes (GNB), Linear Discriminant Analysis (LDA), and Quadratic Discriminant Analysis (QDA). This guide uniquely demonstrates how to implement these powerful classification algorithms directly within Excel, offering a practical, code-free approach. Learn the core concepts behind these models, transitioning from simple local distance metrics to a more robust global probability framework, making advanced statistical methods accessible to a wider audience.

#MachineLearning #Excel #DataScience #LDA #Statistics