Optiver·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Interviewed for a Data Scientist role at Optiver and got hit with a pretty deep sequence inference problem that was more of an algorithms design question than anything I expected. The whole thing felt like a quant-flavored coding challenge dressed up as a data science interview.

Questions Asked (1)

Given an integer sequence of up to 50 terms that may follow arithmetic, geometric, alternating, polynomial, digit-level, or interleaved patterns, describe a systematic approach to infer the governing rule and predict the next several terms. Cover the heuristics you'd apply in order, how you'd handle ambiguous or noisy sequences, and how you'd implement this as a scored, ranked program with time complexity analysis.

Algorithms & Data StructuresTechnical Trade-offsAdaptability & Ambiguity

Author's notes

This one took me a while to even parse.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by describing a systematic pipeline: first compute simple differences and ratios to detect basic patterns, then apply more advanced detectors for alternating, polynomial, digit-level, and interleaved sequences. Emphasize that you would score each hypothesis using a combination of fit quality and complexity penalty, rank them, and predict the next terms from the top-scoring rule while handling ambiguity via confidence thresholds and fallback strategies.

Pro tip: In trading interviews, interviewers care more about how you handle ambiguity and edge cases than about finding a single perfect rule. Explicitly discuss how you'd detect and reject spurious patterns (e.g., using cross-validation on the sequence) and how you'd quantify uncertainty in your predictions.

1. Preprocess and compute basic statistics

Clean the sequence (handle missing/noisy values), compute first and second differences, ratios, and check for constant, alternating, or periodic behavior. This quickly identifies arithmetic, geometric, and simple alternating patterns.

2. Apply specialized detectors for complex patterns

For polynomial patterns, fit polynomials of increasing degree and check for zero higher-order differences. For digit-level patterns, analyze individual digits or digit sums. For interleaved patterns, split the sequence into subsequences (e.g., odd/even indices) and recursively apply detectors.

3. Score and rank hypotheses

For each candidate rule, compute a fit score (e.g., mean squared error on known terms) and penalize complexity (e.g., number of parameters, degree). Use a scoring function like AIC/BIC or a custom weighted score to rank rules.

4. Handle ambiguity and noise

If multiple rules fit equally well, use cross-validation (e.g., leave-one-out on the sequence) to assess predictive power. If noise is present, consider robust fitting or smoothing. Set a confidence threshold; if no rule is confident, fall back to a simple model (e.g., last value or linear extrapolation) and flag uncertainty.

5. Predict and analyze complexity

Use the top-ranked rule to predict the next several terms. Analyze time complexity: most detectors are O(n) or O(n^2) for n up to 50, which is negligible. The overall approach is polynomial in n and the number of hypotheses, making it efficient for real-time or batch processing.

Key Points to Mention

Difference and ratio analysis for arithmetic and geometric sequences.
Polynomial fitting and finite differences for polynomial patterns.
Digit-level analysis (e.g., digit sums, individual digits) for patterns like 1, 11, 21, 1211.
Interleaved sequences: split into odd/even or modulo-k subsequences.
Scoring with complexity penalty (e.g., AIC/BIC) to avoid overfitting.
Handling ambiguity via cross-validation and confidence thresholds, with fallback to simple extrapolation.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.