Classify Variable-Length, Unordered Point Sequences with Missing Features

You are in a live coding round with a plain Python environment in which PyTorch is available. Within about 35 minutes of working time you must end up with a model that trains and runs inference end to end. The problem is revealed in stages, and each stage removes an assumption the previous one relied on. The data is a collection of labeled examples. Each example is a sequence of points, each point has 6 numeric features, and each whole sequence carries a binary label (0 or 1). The goal is to predict the label of a whole sequence. ### Clarifying Questions - Roughly how many labeled sequences are there, and how balanced are the two classes? - Are the 6 features continuous and on comparable scales, or do some need normalization? - Which libraries may be used besides PyTorch (for example numpy or scikit-learn), and does "build the model" mean writing the training loop yourself? - How is the result judged at the end: a held-out metric such as accuracy or ROC AUC, or only that training and inference run? ### Part 1 — Fixed-length time series Every sequence has exactly 16 points with 6 features each, and the points are in time order (the interviewer confirms this is a time series). Build a binary classifier for the whole sequence, train it, and run inference with it. ```hint Size the model to the input A single example is only 16 × 6 numbers. Before choosing an architecture, ask what the smallest model is that can use all of them and have a training loop running within minutes. ``` #### What This Part Should Cover - A concrete input tensor shape and a model that maps it to one logit per sequence. - A complete training loop and an inference function that actually run. - A justified choice between a simple baseline and a sequence architecture, given the time budget. ### Part 2 — Variable sequence length Sequences now contain anywhere from 16 to 100 points. You may not resample or augment the data (no upsampling or downsampling to a fixed length); the interviewer wants the variable length handled inside the model. ```hint Fixed size out of variable size in Think about which operations turn any number of per-point vectors into one vector of fixed size, and how padded positions must be kept from influencing them. ``` #### Clarifying Questions for this Part - Could the length of a sequence itself be predictive of the label? #### What This Part Should Cover - A batching scheme for unequal lengths (padding with a mask, or packing). - A length-independent reduction and why it stays correct in the presence of padding. - Why resampling is ruled out and what the model-based alternative preserves. ### Part 3 — Point order is not fixed The points inside a sequence no longer arrive in a meaningful order. The interviewer asks whether a linear model could handle this. Adapt your approach, then train and run inference with the adapted model before time runs out. ```hint Test with a shuffle If shuffling the points of an example must never change its prediction, go through each component of your current model and ask which ones would produce a different output after a shuffle. ``` #### Clarifying Questions for this Part - Does "order not fixed" mean the order carries no information at all, or that time information is available in some other form? #### What This Part Should Cover - Recognizing that each example is now a set, and which earlier choices (positional encodings, recurrent or convolutional layers over time) no longer fit. - A permutation-invariant representation and a direct answer to the linear-model question. - A simple, fast-to-train model on that representation, with its training and inference path. ### Part 4 — Missing feature values Some feature values are missing (NaN). How does your model handle them? ```hint Compare the options Work out what filling with the mean, filling with zero, and leaving the value missing each do to your specific model, and whether the fact that a value is missing could itself be informative. ``` #### What This Part Should Cover - How missing values flow through feature construction and the model without crashing or silently producing a NaN loss. - The effect of mean filling versus zero filling versus native missing-value handling for the chosen model family. - Preserving missingness as a signal, and avoiding leakage when computing fill statistics. ### What a Strong Answer Covers - Starting from the simplest model that respects the structure of the data instead of defaulting to a heavy architecture. - Explicit reasoning about invariances: to length in Part 2 and to order in Part 3. - A model that trains and predicts end to end within the time box, updated at every stage. - Missing-value handling matched to the model family, and a sound evaluation plan. ### Follow-up Questions - How would you choose between hand-built summary statistics with a tree and a learned per-point encoder with pooling, and what evidence would make you switch? - If the label depended on relationships between pairs of points, how would a permutation-invariant model capture that? - If a single decision tree underfits, how would you move to an ensemble of trees, and what changes in how missing values are handled? - If the labeled dataset is small, how would you detect and control overfitting in these models?