Math for AI

The Must-Know Mathematics & Statistics Behind AI

Probability

• probability and conditional probability

probability of an event occuring = # outcomes / total # outcomes

probability of event A happening given B = probability of both events A and B happening / probability of event B happening

Bayes Rule

Naive Bayes

Determine probability of a hypothesis based on prior knowledge and new evidence

probability of A happening given B = (probability of B happening given A * Probability of A happening) / probability of event B happening

Business application

• spam email detection - calculate probability that an email is spam, given certain words in the subject/body
• medical diagnosis
• fraud detection

P(COVID

Test = yes) can be read as:

What is the probability that patient has covid given that test came out to be positive.

Types of Statistics

• Inferential Stats - use a sample to infer about a larger population
  • Confidence Intervals - size of transistor on a chip lies in 95% confidence interval [4.95, 5.5] nm.
  • Hypothesis Testing - Does the conversion rate of a marketing campaign vary with the font style of infographics?
    • Another example, LLM model evaluations comparison to detect the right configuration that works best for a GenAI application.
    • A/B testing done on websites on where to place the ads where customer is most likely to click on it
• Descriptive Stats
  • Central Tendency
    • mean = avg. value in a distribution = sum of data points / total number of data points.
      • is not reflective of center of data when extreme values are present.
      • this is where median comes in - it identifies the center of the data by sorting the values.
      • mean gets skewed towards extreme value
      • sensitive to extreme values
    • median = mid point in sorted values in a distribution.
      • odd number of data points = actual middle number
      • even numbers of data points = avg of two middle numbers
      • symmetrical data (See graph below) hence mean = median = mode
      • bell curve
      • most resilient
    • mode = most frequently occurring value in a distribution
      • center of data when data is non-numerical
      • highest occurring value
      • multiple highest occurring values present = multiple modes
      • mode gets skewed towards highest value
  • Dispersion
    • Variance
    • Range
    • Standard Deviation - how disperse data is in relation to the mean
      • low = data clustered around mean value
      • high = data is more spread out
      • np.std() = numpy has a function for this

Matrices

• each row = record
• each column = attribute Example:
• image pixels converted to matrix
  • 0 = black
  • 255 = white
  • grey scale is used to convert each pixel in image to a number based on greyness of the pixel
  • for a colored image, scale could be RGB

Dimensionality Reduction

• increasing interpretability of data while preserving the max amount of information
• helps reduce storage space consumed by data
• reduces complexity