Start by clarifying the requirements: which statistics, what accuracy, and the data's characteristics (e.g., stationary vs. non-stationary). Then discuss efficient algorithms for each statistic, such as Welford's method for mean/variance and reservoir sampling or t-digest for percentiles, and explain how to handle memory and update time constraints.
Pro tip: Mention that for non-stationary streams, you might need to use a sliding window or exponential decay to weight recent data more heavily, and always consider the trade-off between accuracy and resource usage.
Ask about the specific statistics needed, the acceptable error margin, and whether the data distribution is stationary. Also, determine memory and latency constraints.
For mean and variance, use Welford's online algorithm. For percentiles, consider exact methods (if memory allows) or approximate ones like t-digest, GK sketch, or reservoir sampling.
If the stream is non-stationary, discuss sliding windows or exponential weighting. For stationary streams, simple online updates suffice.
Compare time and space complexity, accuracy, and implementation complexity of each approach. Highlight that exact percentiles require storing all data, which is often infeasible.
Outline how to implement the chosen algorithms, including handling edge cases like empty streams or numerical stability. Mention potential optimizations like parallel processing if applicable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.