Friday, August 8, 2025

Spitballing: Scenic Route Mapping Problem

1. Objective: Mapping scenic routes over standard A to B rather than focusing on the straightest or fastest path
    a. Types of user search:
        a1: A to B: using better roads and not just the fastest route
        a2: A to A:Scenic route in a perimeter - Show me the best roads in a 10 km vicinity

2. Underlying assumption: Maps is a collection of images with information available through different layers - processing at different levels will help us determine what is a "good" road vs what isn't
Using 200m scale to determine twistiness
Using a higher scale to determine if we are actually getting from A to B

That's a ground up logic case scenario. For proof of concept stage, it is wiser to start with google maps  or OSM as a base, get a few alternatives for the same route and then assign a custom score to choose one. 

Correlation: For a journey chosen, there should be a set of parameters evaluated for feedback on what was suggested vs what actually happened.
1.  Time predicted vs actual - broken down into sectors and sub-segments, especially in portions that were already predicted to take a lot of time. (NOTE: THIS NEEDS TO BE INCORPORATED INTO the  original API call and data is pulled from google maps or OSM. Call needs to be taken whether it is to be a dynamic sector allocation or static based on distance or time.
 

3. Factors determining a good road (assigning a score to evaluate A vs B):
    a. Road based : how many bends, nature of bend, elevation change,
    b. Traffic based:  Level of traffic, safety of road, does it have hard lane separation,

4. Logic:
    a. Baseline starting point: Google maps/ OSM to determine different routes connecting A to B
    b. For the radius outlined, identify all the "good" roads
    c. Join them to determine the different options
    d. Using traffic overlay to determine traffic
    e. How to map hard lane separation and road safety?
    f.
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Wednesday, June 11, 2025

Interesting Reads

I hope I actually read through and retain something from these very interesting reads:

Complete tutorial on Python for Data Analysis: https://github.com/cuttlefishh/python-for-data-analysis/blob/master/lessons/lesson03.md

IBM THINK: https://www.ibm.com/think

What do LLMs understand: https://towardsdatascience.com/what-do-large-language-models-understand-befdb4411b77/

Gradient Descent: https://cs231n.github.io/optimization-1/

Basics of Nearest Neighbours: https://cs231n.github.io/classification/

What is a p-norm: https://planetmath.org/vectorpnorm

FLANN - Fast library for approximate nearest neighbours: https://github.com/flann-lib/flann

t-SNE: https://lvdmaaten.github.io/tsne/ - t-Distributed Stochastic Neighbor Embedding (t-SNE) is a technique for dimensionality reduction that is particularly well suited for the visualization of high-dimensional datasets. The technique can be implemented via Barnes-Hut approximations, allowing it to be applied on large real-world datasets. 

Few useful things to know about ML (2012 article): https://homes.cs.washington.edu/~pedrod/papers/cacm12.pdf




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Tuesday, June 10, 2025

Stop getting complacent

What's next:
1. Atlassian, SAP, 
2. FMCG: Mondelez, Pidilite
3. FAANG
4. Data Consulting

Need to learn/brush up:
1. Tableau, PowerBI, Visual Studio
2. Kaggle projects
3. Python
4. ML Models
5. PPT skills - need to communicate better
6. Get that Data degree you keep procrastinating on
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Thursday, June 5, 2025

How to think of weightages and thresholds

Interesting take on weights while reading about Perceptron Model:
It is not a new insight or anything groundbreaking but just a reminder to look at weights and thresholds differently.

I never really thought of thresholds as something deliberate. I assumed (incorrectly) that it was just a combination of different factors that determine a value and hence it would be situational. I never thought how weights can lead to a choice of thresholds.
How? (source: Neuralnetworksandeeplearning.com)

Imagine you have three criteria for selection of whether you will go attend an event that you have been wanting to visit for a long time:
a. Is the weather good on that day?
b. Does anybody want to accompany you?
c. Has the guest speaker that you wanted to hear confirmed their presence?

Now, we can have preferences on one over the other. In the above example, the person is said to really loathe bad weather as it will ruin the experience of an outdoor festival. Hence the weight given to weather can be 6 and the other two factors - 2 each.

The threshold for this decision is to be kept at 5. Why is the number significant? Because the other two factors can only add up to 4 and hence it makes weather the more important factor, regardless of the other two working in our favour.

Can this be taken further? What if the weight on weather was 4 and the rest were 2 and the threshold was 5. This would imply one other thing other than the weather needs to work in our favour for the decision to be in support of going to the festival.

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Monday, June 2, 2025

Detailed ML Learning Journey

6-Month Maths-Focused Machine Learning Program with Enhanced Resources

This program spreads the material from an intensive plan over 6 months, aiming for roughly 1-2 hours of focused study/coding per day on weekdays, with optional longer sessions on weekends for deeper dives or project work.

Month 1: Linear Algebra & Foundational Math

Goal: Build a solid understanding of vectors, matrices, and basic linear algebra operations crucial for ML.

  • Week 1: Introduction to Vectors

  • Week 2: Matrices - The Basics

  • Week 3: Systems of Linear Equations & Inverses

    • Day 15: Systems of Linear Equations (Matrix Form)
    • Day 16: Determinants (2x2, 3x3)
    • Day 17: Inverse Matrices (Conceptual & Calculation)
    • Day 18: Solving Systems with Inverses
      • MMLL: Chapter 2.3 (Using Matrix Inverse to Solve Systems)
      • SIA: Chapter 2.2 (Solving with A−1)
      • Assignment: Use np.linalg.solve to solve a system of linear equations in Python. Practice calculating inverses with np.linalg.inv.
    • Day 19: Hands-on Determinants & Inverses
      • Assignment: Write Python functions to calculate the determinant of a 2x2 matrix and the inverse of a 2x2 matrix from scratch (without np.linalg). Compare with NumPy.
    • Day 20: Review & Practice
      • Review notes. Ensure you understand when an inverse exists (non-zero determinant).
      • Assignment: MIT OpenCourseware (MIT 18.06SC Linear Algebra) Problem Set 3, Problem 1 (or similar problems related to inverses).
    • Day 21: Rest/Catch-up

  • Week 4: Eigenvalues, Eigenvectors & Review

    • Day 22: Eigenvalues & Eigenvectors - Intuition
    • Day 23: Calculating Eigenvalues & Eigenvectors (2x2)
      • MMLL: Chapter 2.4 (Calculation examples)
      • SIA: Chapter 6.1 (Finding Eigenvalues and Eigenvectors)
      • KA: Eigenvalues and eigenvectors
      • Assignment: KA - Find eigenvalues and eigenvectors of a 2x2 matrix
    • Day 24: Hands-on Eigen Decomposition
      • Assignment: Use np.linalg.eig to find eigenvalues and eigenvectors of a matrix. Verify Av=lambdav.
    • Day 25: Orthogonality (Conceptual)
      • MMLL: Chapter 2.1.2 (Orthogonal Vectors)
      • SIA: Chapter 4.1 (Orthogonal Vectors and Subspaces)
      • KA: Orthogonal vectors
      • YouTube: Orthogonal vectors (Khan Academy)
      • Assignment: Identify orthogonal vectors.
    • Day 26: Linear Algebra Review & Mini-Project Prep
      • Review: All concepts from Month 1. Revisit problem areas.
      • Project Prep: Understand the high-level goal of Principal Component Analysis (PCA) as a dimensionality reduction technique (you'll implement a basic version in Month 5). Focus on how it uses eigenvectors.
    • Day 27: REST/Catch-up
    • Day 28: Monthly Review & Catch-up

Month 2: Calculus, Probability & First ML Algorithm

Goal: Grasp essential calculus concepts for optimization, fundamental probability/statistics, and apply them to your first ML model.

  • Week 5: Calculus - Derivatives

    • Day 29: Functions, Limits, Continuity
    • Day 30: Derivatives - Intuition & Power Rule
    • Day 31: Product, Quotient, Chain Rule
    • Day 32: Critical Points & Local Min/Max
    • Day 33: Hands-on Symbolic Differentiation (Optional)
      • Assignment: Experiment with SymPy in Python to symbolically differentiate simple functions. (e.g., import sympy; x = sympy.symbols('x'); f = x**2 + 3*x; sympy.diff(f, x))
    • Day 34: Review & Practice
      • Assignment: Search for "univariate calculus differentiation problems," solve 5-10.
    • Day 35: Rest/Catch-up

  • Week 6: Calculus - Gradients & Optimization Intro

    • Day 36: Functions of Multiple Variables & Partial Derivatives
    • Day 37: Gradient Vector
    • Day 38: Hessian Matrix (Conceptual)
      • MMLL: Chapter 3.1.4 (Hessian) - Understand it represents curvature.
      • KA: The Hessian matrix
      • YouTube: Hessian Matrix (mathematicalmonk)
      • Assignment: No explicit problem, focus on conceptual understanding of second partial derivatives and the Hessian's purpose.
    • Day 39: Introduction to Optimization
    • Day 40: Hands-on Gradient Calculation
      • Assignment: Write a Python function that calculates the gradient of a simple multivariate function (e.g., ).
    • Day 41: Review & Practice
      • Assignment: Review partial derivatives and gradients. MIT OpenCourseware (MIT 18.02 Multivariable Calculus) Problem Set 1, Problem 1 (or similar).
    • Day 42: Rest/Catch-up

  • Week 7: Probability Fundamentals

  • Week 8: Probability Distributions & Linear Regression (Math)

    • Day 50: Common Discrete Distributions (Bernoulli, Binomial)
      • MMLL: Chapter 5.2.5 (Bernoulli, Binomial)
      • KA: Bernoulli
      • YouTube: The Binomial Distribution (StatQuest with Josh Starmer)
      • Assignment: KA - Bernoulli, Binomial distribution problems
    • Day 51: Normal (Gaussian) Distribution
    • Day 52: Expectation & Variance
    • Day 53: Simple Linear Regression - Mathematical Formulation
    • Day 54: Least Squares Method - Conceptual
      • MMLL: Chapter 6.1.3 (Least Squares Estimation) - Focus on the intuition of finding the "best fit" line.
      • YouTube: Least Squares Regression (Khan Academy)
      • Assignment: No coding, just understanding the conceptual goal of Least Squares.
    • Day 55: Monthly Review & Catch-up
      • Assignment: Review all concepts from Month 2. Focus on the intuition of derivatives, gradients, and how probability distributions describe data.
    • Day 56: Rest/Catch-up

Month 3: Regression & Core ML Concepts

Goal: Deepen understanding of regression, explore optimization for ML, and grasp bias-variance.

  • Week 9: Linear Regression Implementation

    • Day 57: Derivation of Coefficients (Calculus)
      • MMLL: Chapter 6.1.3 (Least Squares Estimation) - Understand the partial derivatives of the SSE.
      • YouTube: Deriving the Normal Equation for Linear Regression (StatQuest with Josh Starmer)
      • Assignment: Walk through the derivation of the coefficients for simple linear regression (or watch a video explaining it).
    • Day 58: Multiple Linear Regression & Normal Equation (Matrix Form)
      • MMLL: Chapter 6.1.4 (Multiple Linear Regression), 6.1.5 (Normal Equation).
      • YouTube: The Normal Equation (Andrew Ng's ML Course)
      • Assignment: Understand y=Xbeta and the Normal Equation beta=(XTX)−1XTy.
    • Day 59: Hands-on Simple Linear Regression from Scratch
      • Assignment: Implement simple linear regression from scratch using NumPy. Plot the regression line on a small dataset.
    • Day 60: Hands-on Multiple Linear Regression (Normal Equation)
      • Assignment: Implement multiple linear regression using the Normal Equation with NumPy. Test on a synthetic dataset.
    • Day 61: Assumptions of Linear Regression
      • MMLL: Chapter 6.1.6 (Assumptions)
      • YouTube: Assumptions of Linear Regression (StatQuest with Josh Starmer)
      • Assignment: List and understand the key assumptions (linearity, independence, homoscedasticity, normality of errors).
    • Day 62: Review & Practice
      • Assignment: Review linear regression. Search for "linear regression normal equation problems" and solve one.
    • Day 63: Rest/Catch-up

  • Week 10: Gradient Descent in Depth

    • Day 64: Gradient Descent for Linear Regression
      • MMLL: Chapter 6.1.7 (Gradient Descent)
      • YouTube: Gradient Descent, Step-by-Step (StatQuest with Josh Starmer)
      • Assignment: Understand the update rule beta_new=beta_old−alphanablaJ(beta).
    • Day 65: Learning Rate & Convergence
      • MMLL: Chapter 4.3 (Gradient Descent) - Focus on learning rate.
      • YouTube: How to choose a learning rate for gradient descent (sentdex)
      • Assignment: Experiment with different learning rates in your GD implementation from Day 60. Observe divergence/slow convergence.
    • Day 66: Stochastic Gradient Descent (SGD) - Intuition
    • Day 67: Mini-batch Gradient Descent
      • MMLL: Chapter 4.3.3 (Mini-batch Gradient Descent)
      • YouTube: Mini-Batch Gradient Descent (DeepLearning.AI)
      • Assignment: Understand the trade-off between GD and SGD.
    • Day 68: Hands-on SGD for Linear Regression
      • Assignment: Implement SGD for linear regression in NumPy. Compare its performance to batch GD on a slightly larger dataset.
    • Day 69: Review & Practice
      • Assignment: Review Gradient Descent variants. MIT 6.036 (Introduction to Machine Learning) problem set on Gradient Descent (search for recent versions).
    • Day 70: Rest/Catch-up

  • Week 11: Regularization

    • Day 71: Overfitting & Underfitting
      • MMLL: Chapter 6.3 (Regularization) - Intro.
      • YouTube: Overfitting vs. Underfitting (StatQuest with Josh Starmer)
      • Assignment: Understand the concepts of overfitting and underfitting. Identify them visually.
    • Day 72: Ridge Regression (L2 Regularization) - Math
    • Day 73: Lasso Regression (L1 Regularization) - Math
    • Day 74: Hands-on Regularization (Scikit-learn)
      • Assignment: Use sklearn.linear_model.Ridge and sklearn.linear_model.Lasso. Experiment with the alpha parameter on a dataset prone to overfitting.
    • Day 75: Choosing Lambda (Regularization Strength)
      • Assignment: Research cross-validation as a method for selecting hyperparameters like lambda. (No implementation yet, just conceptual).
    • Day 76: Review & Practice
      • Assignment: Search for "Ridge vs Lasso explained" or "regularization in linear regression problems."
    • Day 77: Rest/Catch-up

  • Week 12: Polynomial Regression & Bias-Variance

    • Day 78: Polynomial Regression
      • MMLL: Chapter 6.2 (Polynomial Regression)
      • YouTube: Polynomial Regression Explained (StatQuest with Josh Starmer)
      • Assignment: Understand how polynomial features are created. Implement polynomial regression using sklearn.preprocessing.PolynomialFeatures and LinearRegression.
    • Day 79: Bias-Variance Trade-off - Intuition
      • MMLL: Chapter 6.4 (Bias-Variance Decomposition) - Focus on 6.4.1 (Introduction).
      • Medium: Bias Variance Tradeoff (MLU-Explain - interactive)
      • YouTube: Bias and Variance (StatQuest with Josh Starmer)
      • Assignment: Conceptualize bias (model's simplifying assumptions) and variance (model's sensitivity to training data).
    • Day 80: Mathematical Breakdown of Bias-Variance
      • MMLL: Chapter 6.4.2 (Derivation) - Go through the derivation of the MSE decomposition (if comfortable, otherwise understand the terms).
      • Assignment: Understand how MSE = Bias² + Variance + Noise.
    • Day 81: Visualizing Bias-Variance
      • Assignment: Search for online visualizations of the bias-variance trade-off (e.g., using target practice analogy).
    • Day 82: Hands-on Bias-Variance Example
      • Assignment: Create a synthetic dataset. Fit a low-degree polynomial (high bias) and a high-degree polynomial (high variance) to it. Plot and observe the fit and generalization.
    • Day 83: Monthly Review & Project Prep
      • Review: All concepts from Month 3. Focus on regression, optimization, regularization, and bias-variance.
      • Project Prep: Brainstorm simple regression datasets you could use for a mini-project (e.g., house price prediction, car mileage).
    • Day 84: Rest/Catch-up

Month 4: Classification Algorithms

Goal: Understand the mathematical underpinnings of key classification models.

  • Week 13: Logistic Regression

    • Day 85: Logistic Regression - Concept & Sigmoid
      • MMLL: Chapter 7.1 (Logistic Regression) - Focus on 7.1.1 (Binary Classification) and 7.1.2 (Sigmoid function).
      • YouTube: Logistic Regression, Clearly Explained!!! (StatQuest with Josh Starmer)
      • Assignment: Understand how the sigmoid function maps linear output to a probability between 0 and 1. Plot the sigmoid.
    • Day 86: Cross-Entropy Loss Function
    • Day 87: Gradient Descent for Logistic Regression
      • MMLL: Chapter 7.1.4 (Gradient Descent) - Understand the update rule (similar to linear regression, but with different derivatives).
      • YouTube: Logistic Regression Details: Calculating the Gradient (Andrew Ng's ML Course)
      • Assignment: Walk through the derivation of the gradients (or watch a detailed explanation).
    • Day 88: Hands-on Logistic Regression from Scratch
      • Assignment: Implement binary logistic regression from scratch using NumPy (forward pass, loss, and gradient descent update). Test on a simple synthetic dataset.
    • Day 89: Hands-on Logistic Regression (Scikit-learn)
      • Assignment: Use sklearn.linear_model.LogisticRegression. Compare results with your custom implementation. Understand predict_proba.
    • Day 90: Review & Practice
      • Assignment: Review logistic regression. Search for "logistic regression explained math" and re-read.
    • Day 91: Rest/Catch-up

  • Week 14: Softmax & SVMs

    • Day 92: Softmax Regression (Multinomial Logistic Regression)
      • MMLL: Chapter 7.2 (Softmax Regression)
      • YouTube: Softmax Regression (Andrew Ng's ML Course)
      • Assignment: Understand the softmax function and its use for multi-class classification.
    • Day 93: Categorical Cross-Entropy Loss
      • MMLL: Chapter 7.2 (Loss function).
      • YouTube: Categorical Cross Entropy Explained (StatQuest with Josh Starmer - same as binary, just extended)
      • Assignment: Understand the extension of cross-entropy to multiple classes.
    • Day 94: Support Vector Machines (SVMs) - Hyperplane & Margin
    • Day 95: Kernel Trick (Conceptual)
      • MMLL: Chapter 8.2 (Non-linear SVM) - Focus on the idea of mapping data to higher dimensions implicitly.
      • Medium: Kernel Trick in Support Vector Classification (GeeksforGeeks)
      • YouTube: SVMs and the Kernel Trick (StatQuest with Josh Starmer)
      • Assignment: No explicit math problem, focus on understanding the concept of making linearly inseparable data separable.
    • Day 96: Hands-on SVM (Scikit-learn)
      • Assignment: Use sklearn.svm.SVC. Experiment with different kernels (linear, rbf, poly) on a dataset like Iris or circles/moons.
    • Day 97: Review & Practice
      • Assignment: Review Softmax and SVMs. Search for "SVM kernel trick explained" if needed.
    • Day 98: Rest/Catch-up

  • Week 15: Decision Trees & Ensembles Intro

    • Day 99: Decision Trees - Basics & Splitting
      • MMLL: Chapter 10.1 (Decision Trees)
      • YouTube: Decision Trees, Clearly Explained!!! (StatQuest with Josh Starmer)
      • Assignment: Understand how decision trees make predictions by splitting data.
    • Day 100: Gini Impurity & Entropy (Mathematical Definitions)
    • Day 101: Information Gain
      • MMLL: Chapter 10.1.2 (Information Gain)
      • YouTube: Information Gain in Decision Tree (Machine Learning with Phil)
      • Assignment: Understand how information gain is used to choose the best split.
    • Day 102: Introduction to Ensemble Methods (Bagging)
    • Day 103: Boosting (Conceptual)
    • Day 104: Hands-on Decision Tree & Random Forest (Scikit-learn)
      • Assignment: Use sklearn.tree.DecisionTreeClassifier and sklearn.ensemble.RandomForestClassifier. Compare their performance.
    • Day 105: Rest/Catch-up

  • Week 16: KNN & Naive Bayes, Classification Project

    • Day 106: K-Nearest Neighbors (KNN)
    • Day 107: Naive Bayes - Intuition
      • MMLL: Chapter 5.1.3 (Bayes' Theorem application - conceptually)
      • YouTube: Naive Bayes, Clearly Explained!!! (StatQuest with Josh Starmer)
      • Assignment: Understand the "naive" assumption of conditional independence.
    • Day 108: Different Naive Bayes Variants (Conceptual)
      • Assignment: Research Gaussian, Multinomial, and Bernoulli Naive Bayes and when to use them.
    • Day 109: Hands-on Naive Bayes (Scikit-learn)
      • Assignment: Use sklearn.naive_bayes.GaussianNB or MultinomialNB.
    • Day 110: Monthly Review & Project Prep
      • Review: All classification algorithms.
      • Project Prep: Prepare for a classification project.
    • Day 111: Classification Project
      • Assignment: Choose a classification dataset (e.g., Pima Indians Diabetes, Titanic). Apply at least 3 different classification algorithms learned (e.g., Logistic Regression, SVM, Random Forest). Evaluate performance using appropriate metrics (accuracy, precision, recall, F1-score).
    • Day 112: Rest/Catch-up

Month 5: Unsupervised Learning & Optimization Deep Dive

Goal: Explore methods for finding patterns in unlabeled data and delve deeper into optimization techniques.

  • Week 17: Clustering

    • Day 113: K-Means Clustering - Objective Function
    • Day 114: Lloyd's Algorithm
      • MMLL: Chapter 9.1.1 (Algorithm).
      • Assignment: Walk through the steps of Lloyd's algorithm.
    • Day 115: Hands-on K-Means from Scratch
      • Assignment: Implement K-Means from scratch using NumPy. Test on a simple 2D dataset and visualize clusters.
    • Day 116: Hierarchical Clustering (Conceptual)
    • Day 117: Hands-on Hierarchical Clustering (SciPy)
      • Assignment: Use scipy.cluster.hierarchy to perform hierarchical clustering and plot a dendrogram.
    • Day 118: Review & Practice
      • Assignment: Review clustering algorithms. Search for "K-Means problems."
    • Day 119: Rest/Catch-up

  • Week 18: Dimensionality Reduction (PCA)

    • Day 120: PCA - Recap & Covariance Matrix
    • Day 121: PCA - Eigenvalues & Eigenvectors for Reduction
      • MMLL: Chapter 11.1.1 (PCA Algorithm)
      • YouTube: PCA Algorithm (Mathematicalmonk)
      • Assignment: Understand how eigenvectors correspond to principal components and eigenvalues to explained variance.
    • Day 122: Singular Value Decomposition (SVD) for PCA
      • MMLL: Chapter 11.1.2 (SVD for PCA)
      • SIA: Chapter 7.2 (Singular Value Decomposition)
      • YouTube: Singular Value Decomposition (SVD) and PCA (StatQuest with Josh Starmer)
      • Assignment: Understand that SVD provides a robust way to compute PCA.
    • Day 123: Hands-on PCA from Scratch (using SVD)
      • Assignment: Implement PCA from scratch using NumPy's np.linalg.svd. Apply it to a high-dimensional dataset (e.g., MNIST digits) and visualize the first 2 components.
    • Day 124: Hands-on PCA (Scikit-learn)
      • Assignment: Use sklearn.decomposition.PCA and compare results with your custom implementation. Understand explained_variance_ratio_.
    • Day 125: Review & Practice
      • Assignment: Review PCA. Search for "PCA explained visually."
    • Day 126: Rest/Catch-up

  • Week 19: Advanced Optimization

    • Day 127: Limitations of Basic Gradient Descent
      • Assignment: Understand local minima, saddle points, and issues with learning rate (e.g., slow convergence, oscillations).
    • Day 128: Momentum
    • Day 129: Adagrad & RMSprop (Conceptual)
    • Day 130: Adam Optimizer (Conceptual)
      • MMLL: Chapter 4.3.7 (Adam)
      • YouTube: Adam Optimizer, Clearly Explained!!! (StatQuest with Josh Starmer)
      • Assignment: Understand Adam as a combination of Momentum and RMSprop ideas.
    • Day 131: Hands-on Optimizers (TensorFlow/PyTorch)
      • Assignment: Build a simple linear regression model using TensorFlow or PyTorch. Experiment with SGD, Adam, and RMSprop optimizers, observing their convergence behavior.
    • Day 132: Review & Practice
      • Assignment: Search for "deep learning optimizers explained" videos/articles. Focus on their mathematical update rules.
    • Day 133: Rest/Catch-up

  • Week 20: Convex Optimization (Conceptual) & Unsupervised Project

    • Day 134: Convex Sets & Functions (Conceptual)
    • Day 135: Why Convexity Matters in ML
      • Assignment: Understand that many traditional ML models (linear regression, logistic regression with cross-entropy) have convex loss functions, guaranteeing convergence to global optima.
    • Day 136: Anomaly Detection (Brief Introduction)
      • MMLL: Chapter 9.3 (Anomaly Detection) - Basic overview.
      • YouTube: Anomaly Detection, Clearly Explained!!! (StatQuest with Josh Starmer)
      • Assignment: Understand the goal of anomaly detection. Explore simple statistical methods (e.g., Z-score).
    • Day 137: Monthly Review & Project Prep
      • Review: All concepts from Month 5.
      • Project Prep: Prepare for an unsupervised learning project.
    • Day 138: Unsupervised Learning Project
      • Assignment: Take a dataset (e.g., customers with features, or gene expression data). Perform K-Means clustering and PCA. Visualize the clusters in reduced dimensions. Interpret the results.
    • Day 139: Rest/Catch-up
    • Day 140: Monthly Review & Catch-up

Month 6: Deep Learning Fundamentals

Goal: Understand the core mathematical principles behind neural networks and popular architectures.

  • Week 21: Neural Network Basics & Forward Pass

    • Day 141: Perceptrons & Biological Analogy
      • MMLL: Chapter 12.1 (Feedforward Neural Networks) - Focus on the basic unit.
      • YouTube: The Perceptron (Andrew Ng's ML Course)
      • Assignment: Understand how a single perceptron works.
    • Day 142: Activation Functions (Sigmoid, Tanh, ReLU)
      • MMLL: Chapter 12.1.2 (Activation Functions)
      • YouTube: Activation Functions, Clearly Explained!!! (StatQuest with Josh Starmer)
      • Assignment: Understand the mathematical forms and properties of each activation function. Plot them.
    • Day 143: Feedforward Neural Networks (MLPs) - Architecture
    • Day 144: Forward Propagation - Matrix Math
      • MMLL: Chapter 12.1.3 (Feedforward Pass)
      • YouTube: Forward Propagation, Clearly Explained!!! (StatQuest with Josh Starmer)
      • Assignment: Understand how each layer's output is calculated using matrix multiplication and activation functions.
    • Day 145: Hands-on MLP Forward Pass (NumPy)
      • Assignment: Implement a simple 2-layer MLP (input, 1 hidden, output) forward pass using NumPy. Use random weights and biases.
    • Day 146: Review & Practice
      • Assignment: Review the forward pass. Search for "neural network forward propagation example" and trace the calculations.
    • Day 147: Rest/Catch-up

  • Week 22: Backpropagation - The Core of Learning

    • Day 148: Backpropagation - The Chain Rule in Action
    • Day 149: Deriving Gradients for Output Layer
      • MMLL: Chapter 12.2.2 (Output Layer Gradients)
      • YouTube: Backpropagation for a Neural Network (Andrew Ng's ML Course)
      • Assignment: Walk through the derivation of gradients for the output layer's weights and biases (e.g., for MSE loss).
    • Day 150: Deriving Gradients for Hidden Layers
      • MMLL: Chapter 12.2.3 (Hidden Layer Gradients)
      • Assignment: Understand how errors are "propagated backward" to update hidden layer weights.
    • Day 151: Hands-on Backpropagation (Simple MLP in NumPy)
      • Assignment: Extend your MLP from Day 145 to include a loss function (e.g., MSE) and implement the backpropagation algorithm to update weights and biases. This is a significant challenge, but highly rewarding.
    • Day 152: Loss Functions in Deep Learning (Recap)
      • MMLL: Chapter 12.1.4 (Loss Functions)
      • YouTube: Loss Functions for Machine Learning (StatQuest with Josh Starmer)
      • Assignment: Revisit MSE (for regression) and Cross-Entropy (for classification) in the context of NNs.
    • Day 153: Hands-on Basic NN with Framework (TensorFlow/PyTorch)
      • Assignment: Build a basic MLP using TensorFlow Keras or PyTorch. Train it on a simple dataset (e.g., MNIST digits). Focus on model.compile/model.fit or the training loop.
    • Day 154: Rest/Catch-up

  • Week 23: CNNs - Convolutions Explained

    • Day 155: Convolution Operation - Mathematical Definition
    • Day 156: Padding & Stride
      • YouTube: CNNs Part 2: Padding and Strides (DeepLearning.AI)
      • Assignment: Understand how padding (same, valid) and stride affect the output dimensions of a convolution.
    • Day 157: Pooling Layers (Max Pooling, Average Pooling)
      • YouTube: CNNs Part 3: Pooling Layers (DeepLearning.AI)
      • Assignment: Understand the purpose of pooling (downsampling, translation invariance).
    • Day 158: Hands-on Basic Convolution (NumPy)
      • Assignment: Implement a simple 2D convolution operation (without padding/stride) using NumPy. Test it on a small matrix and a simple filter.
    • Day 159: CNN Architecture Overview (Conceptual)
    • Day 160: Hands-on CNN (TensorFlow/PyTorch)
      • Assignment: Build a simple CNN for image classification (e.g., Fashion MNIST or CIFAR-10) using your chosen framework.
    • Day 161: Rest/Catch-up

  • Week 24: RNNs & Advanced Concepts (High-Level)

    • Day 162: Recurrent Neural Networks (RNNs) - Math of Recurrence
    • Day 163: Vanishing/Exploding Gradients in RNNs
    • Day 164: LSTMs & GRUs (Conceptual)
    • Day 165: Attention Mechanisms & Transformers (Very High-Level)
    • Day 166: Monthly Review & Capstone Project Prep
      • Review: All deep learning concepts, especially the role of math in NNs.
      • Project Prep: Brainstorm ideas for your final capstone project.
    • Day 167: Capstone Project Work Day 1
      • Assignment: Begin working on your chosen project. Focus on data loading, preprocessing, and setting up the basic model.
    • Day 168: Rest/Catch-up

  • Week 25 (Optional Extension/Buffer): Capstone Project & Future Learning

    • Day 169: Capstone Project Work Day 2
      • Assignment: Continue implementing and training your model.
    • Day 170: Capstone Project Work Day 3
      • Assignment: Evaluate your model, try different hyperparameters, and analyze results.
    • Day 171: Information Theory for ML (Entropy, KL Divergence)
    • Day 172: Causal Inference (Basic Concepts)
    • Day 173: Comprehensive Math Review
      • Assignment: Go back through your notes and MMLL. Revisit any challenging math concepts from Linear Algebra, Calculus, Probability, and Statistics.
    • Day 174: Capstone Project Finalization
      • Assignment: Prepare your project report/notebook. Clearly explain the problem, your approach, the models used, and the mathematical insights gained.
    • Day 175: Final Project Presentation & Future Learning Plan
      • Assignment: Present your project to yourself or a peer. Outline your next steps in ML and math.
    • Day 176-180: Buffer/Deep Dive/Review
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