Pretty standard setup question but I fumbled the formal objective a bit.
Start by stating the objective function that K-means minimizes: the sum of squared distances between each point and its assigned cluster centroid. Then explain the alternating optimization procedure: first assign each point to the nearest centroid, then update each centroid to the mean of its assigned points, and repeat until convergence. Emphasize that this is a coordinate descent algorithm that monotonically decreases the objective and converges to a local minimum.
Pro tip: Mention that K-means assumes spherical clusters of similar size and is sensitive to initialization, so in practice you'd use K-means++ or multiple restarts; this shows awareness of practical limitations beyond the basic algorithm.
State that K-means minimizes the within-cluster sum of squares (WCSS), i.e., the sum over all clusters of the squared Euclidean distances between points and their cluster centroid.
Explain that given current centroids, each data point is assigned to the cluster whose centroid is closest (typically Euclidean distance), which minimizes the objective with respect to assignments.
Explain that given current assignments, each centroid is recomputed as the mean of all points assigned to it, which minimizes the objective with respect to centroids.
Highlight that these two steps are repeated alternately until assignments no longer change or a maximum number of iterations is reached; each step decreases or maintains the objective, guaranteeing convergence to a local minimum.
Mention that the algorithm is sensitive to initialization and may converge to different local minima; techniques like K-means++ or multiple restarts help mitigate this.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Got through it but my empty cluster handling was hand-wavy.
Start by clarifying the problem and assumptions, then outline the algorithm's steps: initialization, assignment, update, and convergence check. Write clean, modular code with clear variable names and discuss time complexity and potential pitfalls.
Pro tip: Mention that K-means is sensitive to initialization and suggest K-means++ as a robust alternative, showing awareness of practical improvements. Also, discuss how to handle empty clusters and choose k, demonstrating real-world experience.
Ask about input format, distance metric (usually Euclidean), stopping criteria (e.g., max iterations, tolerance), and whether to implement K-means++ or random initialization.
Randomly select k data points as initial centroids, or implement K-means++ for better initialization. Explain the chosen method and its impact.
For each data point, compute distance to each centroid and assign it to the nearest one. Efficiently vectorize if using NumPy.
Recompute each centroid as the mean of all points assigned to it. Handle empty clusters by reassigning or reinitializing.
Repeat assignment and update until centroids change less than a tolerance or a maximum number of iterations is reached. Return final centroids and labels.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
K-means++ was clearly what they wanted and I knew it.
Start by explaining the limitations of random initialization (e.g., poor convergence, empty clusters) and then introduce k-means++ as a superior strategy. Describe the algorithm step-by-step, emphasizing the probabilistic selection of centroids based on distance. Finally, implement it in code (e.g., Python) and discuss trade-offs like computational overhead and improved clustering quality.
Pro tip: Mention that k-means++ is the default in scikit-learn and is widely used in industry, but also note that for very large datasets, approximate variants or sampling can be used to reduce overhead. This shows awareness of practical constraints.
Discuss how random initialization can lead to suboptimal clustering, slow convergence, and empty clusters. Highlight that it's sensitive to initial seed.
Describe k-means++: it selects initial centroids sequentially, each with probability proportional to its squared distance from the nearest existing centroid. This spreads centroids out.
Walk through: 1) Choose first centroid uniformly at random. 2) For each subsequent centroid, compute D(x)^2 for each point (distance to nearest centroid) and select with probability proportional to D(x)^2. 3) Repeat until k centroids chosen. 4) Proceed with standard k-means.
Provide a concise Python implementation using NumPy, showing the selection loop and distance calculations. Optionally, mention using scikit-learn's KMeans with init='k-means++'.
Compare k-means++ to random: better quality but O(k) extra passes over data. Mention other strategies like k-means|| (parallel) or hierarchical initialization for large-scale data.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where the interview shifted gears completely.
Structure your answer around a multimodal trajectory prediction pipeline: encode scene elements (target, agents, map) with a graph or transformer, fuse them into a shared representation, and decode a distribution over future trajectories. Emphasize how each design choice (input representation, architecture, output parameterization, loss) addresses multimodality, social interaction, and map constraints.
Pro tip: Anchor your answer in Waymo's real-world constraints: latency, safety, and interpretability. Mention that you'd start with a strong baseline (e.g., constant velocity) and iterate, and that you'd evaluate with both minADE/minFDE and miss rate to capture multimodality.
Confirm the prediction horizon (2 positions, e.g., 1s and 2s ahead), coordinate frame (agent-centric vs. global), and available inputs (past trajectories, map, agent types). State that you'll assume a fixed time step and that the target's past is observed.
Represent each agent's past as a sequence of positions/velocities; encode map as polylines or raster; include agent attributes (type, size). Use a graph or set-based representation to handle variable numbers of agents and map elements.
Propose an encoder-decoder architecture: e.g., a transformer or graph neural network to encode agents and map, with attention-based fusion to model social interactions and map compliance. The decoder outputs a set of future trajectories with probabilities.
Output a multimodal distribution: K trajectory hypotheses, each with a probability and a sequence of 2 future positions (or parameters of a distribution per step). This captures uncertainty and multiple possible futures.
Use a multi-task loss: classification (probability of each mode) + regression (e.g., negative log-likelihood or Huber loss on positions). Evaluate with minADE/minFDE over K modes, miss rate, and probability-weighted metrics to assess calibration.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Explained it as learning multiple different 'relationship types' between agents simultaneously, so one head might capture following behavior, another lane-sharing dynamics, etc.
Start by defining multi-head attention as a mechanism that allows the model to jointly attend to information from different representation subspaces at different positions. Then explain how in multi-agent trajectory prediction, it enables each agent to selectively focus on relevant other agents and past timesteps, capturing complex social interactions. Conclude by highlighting why this is useful: it improves accuracy by modeling diverse interaction types and scales to many agents.
Pro tip: Emphasize that multi-head attention is not just about performance but also about interpretability—you can visualize attention heads to understand which agents influence each other, which is crucial for safety-critical systems like autonomous driving.
Explain that it runs multiple attention mechanisms in parallel, each with its own learned query, key, and value projections, allowing the model to capture different types of relationships.
Describe how each agent's future trajectory depends on its own history and the behavior of other agents; multi-head attention lets the model weigh these dependencies dynamically.
Discuss how multiple heads capture diverse interaction patterns (e.g., yielding, overtaking, following) and how attention handles variable numbers of agents without fixed adjacency matrices.
Mention computational complexity (quadratic in number of agents) and how techniques like sparse attention or clustering can mitigate it, balancing accuracy and efficiency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This was the hardest question in the whole interview.
Start by clearly defining the exposure bias problem in autoregressive models, then present a structured overview of mitigation strategies ranging from data augmentation to architectural changes. For each approach, discuss tradeoffs in terms of training complexity, inference cost, and performance gains, and conclude with a recommendation tailored to the constraints of the role (e.g., real-time systems at Waymo).
Pro tip: Emphasize that the best solution depends on the specific application: for safety-critical systems like autonomous driving, robustness to errors is paramount, so methods like scheduled sampling or reinforcement learning may be preferred despite their complexity. Also, mention that sometimes a simple fix like teacher forcing with dropout can be surprisingly effective.
Explain exposure bias: the discrepancy between training (ground-truth inputs) and inference (model's own predictions) in autoregressive models, and its consequences like error accumulation.
Group approaches into data-level (e.g., data augmentation, noise injection), training-level (e.g., scheduled sampling, professor forcing), and inference-level (e.g., beam search, re-ranking).
For each category, discuss tradeoffs: training stability, computational cost, ease of implementation, and impact on final performance. Highlight that some methods trade training complexity for inference robustness.
Choose a recommended approach based on the context (e.g., Waymo's need for safety and real-time inference) and justify why it balances the tradeoffs effectively.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.