LinkedIn interview questions

Join each impression to the profile as of that timestamp, label clicks positive and skips negative, then split by time: train on the past, validate on the next window, and keep anything fitted, like vocabularies or normalizers, to the training slice.

Model: a two-tower text encoder for member and item, trained contrastively with in-batch negatives plus skips as hard negatives. Evaluate recall at k against a popularity baseline.

For reproducibility, pin seeds, model versions and a data-snapshot hash in one config, ship preprocessing with the model, and test that inference reproduces the training embeddings.

import numpy as np

def sigmoid(z):
    out = np.empty_like(z, dtype=float)
    pos = z >= 0
    out[pos] = 1 / (1 + np.exp(-z[pos]))
    ez = np.exp(z[~pos])
    out[~pos] = ez / (1 + ez)
    return out

def train(X, y, lr=0.1, steps=1000):
    # X (N, D), y (N,) of 0/1
    w, b = np.zeros(X.shape[1]), 0.0
    for _ in range(steps):
        p = sigmoid(X @ w + b)
        err = p - y          # dLoss/dz for log loss
        w -= lr * X.T @ err / len(y)
        b -= lr * err.mean()
    return w, b

The usual bugs: a sigmoid that overflows for large negative inputs; a derivative written as s(1 minus z) instead of s(1 minus s); and multiplying by that derivative again, when log loss already gives a logit gradient of exactly p minus y. Also check the sign of the update, dividing by N, and a y of shape (N, 1) silently broadcasting to (N, N). Confirm with a finite-difference gradient check.

Sigmoid and tanh saturate, so gradients vanish; ReLU is cheap but units can die; GELU and SiLU are smooth and standard in transformers.

The loss follows the output distribution: MSE for Gaussian-ish regression, Huber against outliers, sigmoid plus binary cross-entropy, softmax plus cross-entropy.

m = b1 * m + (1 - b1) * g
v = b2 * v + (1 - b2) * g * g
m_hat = m / (1 - b1 ** t)
v_hat = v / (1 - b2 ** t)
w -= lr * m_hat / (np.sqrt(v_hat) + eps)

Adam keeps momentum and a per-parameter scale, bias-corrected. Defaults: beta1 0.9, beta2 0.999, eps 1e-8; tune the learning rate first.

Deep trees have low bias but high variance, so averaging many helps. For B trees, each with variance σ² and pairwise correlation ρ, the average has variance ρσ² + (1 − ρ)σ²/B. More trees shrink only the second term; ρσ² is a floor.

So forests attack correlation: bootstrap samples, plus a random subset of features at each split, so one dominant feature doesn't make every tree alike. Fewer features per split lowers ρ but weakens each tree.

No single label works: raw watch time favours long videos, completion favours short ones. So predict several labels with a multi-task ranker: watch time normalized by duration, completion, like, share, follow, and hides or fast skips as negatives, then combine them with weights tuned against long-term retention in A/B tests.

The pipeline: two-tower retrieval over video embeddings, the ranker, then re-ranking for diversity and freshness. Model position bias separately so the ranker learns preference.