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Probability and Statistics Foundations

• Calculate mean, median, mode, range of a dataset

• Discuss variance measures (standard deviation, variance, covariance)

• Characteristics and importance of Gaussian distribution

• Calculate expected value of a random variable

• Differentiate between continuous and discrete variables

Data Analysis and Statistics for AI

• Select appropriate visual medium for datasets

• Describe diagrams (boxplots, histograms, scatterplots)

• Techniques for multivariate data (dependence methods, regression)

• Importance of data cleaning

• Factors affecting data quality (duplicates, low-quality sources)

• Application of data science algorithms (linear regression, decision trees)

Tools for Data and AI

• Write SQL queries

• Common packages/libraries (Pandas, NumPy, PyTorch)

• Use Python for data cleaning and wrangling

• Use R for data science

• Characteristics of relational databases

AI Basics

• Nature of generative AI

• Capabilities and limitations of generative AI

• Uses of generative AI (healthcare, research, digital art)

• AI subfields (computer vision, NLP, robotics)

• Define large language models (LLMs)

• Capabilities of large language models

Machine Learning

• Nature of machine learning

• Use of training, test, validation datasets

• Behavior of machine learning algorithms (neural networks, decision trees)

• Characterize unsupervised, supervised, reinforcement learning

• Select appropriate algorithm for reasoning problems

• Explain deep learning concept

Perception, Representation, and Reasoning

• Use of predicate logic in AI models

• Examples of predicate logic

• Differences between logic-based and probability-based reasoning

• Describe Bayesian networks (nodes, edges, Directed Acyclic Graphs)

• Knowledge representation and reasoning in AI

Privacy and Ethics

• Dilemmas from AI systems (self-driving vehicles, generative AI)

• AI bias (algorithmic bias)

• Security and privacy risks of LLMs

• Credibility concerns of LLMs (hallucinations, misinformation)

Data Literacy and Foundations

• Nature of data science

• Differences between structured and unstructured data

• Identify numeric and categorical data

• Convert between data representations (binary, hexadecimal, decimal)

• Types of data from various sources

• Importance of data wrangling and transformation

• Stages of the data science process

1. Probability and Statistics Foundations

• Measures of Central Tendency:

  • Mean: $\mu = \frac{\sum x_i}{n}$

  • Median: Middle value of a sorted dataset.

  • Mode: Most frequent value.

  • Range: $\text{Max} - \text{Min}$

• Variance Measures:

  • Variance ($\sigma^2$): Average squared deviation from the mean: $\sigma^2 = \frac{\sum (x_i - \mu)^2}{n}$

  • Standard Deviation ($\sigma$): $\sqrt{\sigma^2}$

  • Covariance: Measures how two variables change together.

• Gaussian (Normal) Distribution: Bell-shaped, symmetric; defined by mean ($\mu$) and standard deviation ($\sigma$). $68\%$ of data falls within $1\sigma$, $95\%$ within $2\sigma$.

• Expected Value ($E[X]$): For discrete variables, $E[X] = \sum x<em>i P(x</em>i)$.

• Variables: Discrete (countable, e.g., number of students) vs. Continuous (measurable, e.g., height).

2. Data Analysis and Statistics for AI

• Visual Media:

  • Boxplots: Show distribution through quartiles and detect outliers.

  • Histograms: Show frequency distribution of a single variable.

  • Scatterplots: Visualize relationships/correlations between two variables.

• Multivariate Techniques: Regression (predicting continuous outcomes) and dependence methods.

• Data Quality: Cleaning involves removing duplicates and handling low-quality sources to prevent "garbage in, garbage out."

3. Tools for Data and AI

• SQL: Language for querying and managing relational databases.

• Python Ecosystem:

  • Pandas: Data manipulation and analysis.

  • NumPy: Numerical computing and arrays.

  • PyTorch: Deep learning and neural networks.

• R: Primarily used for statistical computing and graphics.

• Relational Databases: Organised into tables with predefined schemas.

4. AI Basics and Machine Learning

• Generative AI: Focuses on creating new content (text, art, research) using Large Language Models (LLMs).

• Machine Learning Types:

  • Supervised: Training on labeled data (mapping inputs to known outputs).

  • Unsupervised: Finding hidden patterns in unlabeled data (e.g., clustering).

  • Reinforcement Learning: Learning through rewards and penalties.

• Deep Learning: A subset of ML based on multi-layered neural networks.

• Datasets: Training (learning), Validation (tuning), Test (final evaluation).

5. Representation and Reasoning

• Predicate Logic: Uses variables and quantifiers to express facts ($P(x)$).

• Bayesian Networks: Probabilistic graphical models representing variables and their conditional dependencies via Directed Acyclic Graphs (DAGs).

• Reasoning: Logic-based (deterministic rules) vs. Probability-based (dealing with uncertainty).

6. Ethics and Data Literacy

• Key Risks: Algorithmic bias, privacy leakage in LLMs, and hallucinations (outputting factually incorrect information).

• Data Types: Structured (tabular) vs. Unstructured (text, audio, video). Categorical (labels) vs. Numeric (counts/measurements).

• Data Conversion: Binary (Base 2), Hexadecimal (Base 16), Decimal (Base 10).

• Processes: Data wrangling (transforming raw data) is a critical stage in the data science process.