Неявная обратная связь и метод наименьших квадратов

Explicit-feedback systems use ratings or direct preference judgments. Implicit-feedback systems instead observe behavior such as clicks, watch time, purchases or saves. These events provide evidence of interest but are noisy and incomplete: a click may be accidental, and no click may mean the item was never exposed. Treating every missing user-item pair as an explicit dislike can distort learning. A common latent-factor approach assigns each user and item a vector and predicts preference from their inner product. Implicit ALS defines a binary preference p_ui indicating whether an interaction occurred, and a confidence c_ui that is larger for stronger evidence. One formulation sets c_ui = 1 + alpha*r_ui for observed strength r_ui and a baseline confidence for unobserved pairs. It minimizes a confidence-weighted squared error plus regularization. The exact encoding and strength transform are modeling choices. The objective couples user and item vectors, so directly optimizing all factors jointly is difficult. ALS alternates: fix item vectors and solve for each user's regularized least-squares vector, then fix user vectors and solve item updates. Each subproblem has a closed-form solution under the common objective. Iterations continue until improvement or another stopping rule. Sparse interaction matrices make this approach practical because unobserved pairs share a baseline and observed events adjust confidence. Interaction data carry exposure and popularity bias. A user cannot interact with an item they never encounter, and raw frequency can overvalue already popular content. Evaluation should use time-aware splits and ranking metrics, while tracking catalog coverage, novelty and user outcomes. ALS produces latent representations and candidate scores; it does not inherently provide explanations or causal evidence that a recommendation will satisfy a user. Incorporate eligibility, safety and freshness constraints separately, and monitor changes in item availability and behavior patterns.