Implicit and Explicit Feedback

Definition

Implicit and Explicit Feedback

The two kinds of preference signal a Recommender System learns from.

• Explicit feedback is a deliberate, stated judgement of preference: a 1–5 star rating, a thumbs up/down, a review score. The value is (roughly) on an interpretable preference scale, and a missing entry means “not rated”, i.e. genuinely unknown.
• Implicit feedback is an indirect behavioural signal interpreted as preference: a click, play, watch-duration, purchase, skip, add-to-playlist. It is observed as a by-product of using the system. The signal is (usually) positive-only — we see what the user did, never an explicit “I dislike this”.

Both are recorded in the user–item Interaction Matrix $R$ with users $U=\{u_1,\dots ,u_n\}$ and items $I=\{i_1,\dots ,i_m\}$, but the semantics of an observed value and of a missing value differ, which changes how we model and evaluate.

Intuition

What does a missing cell mean?

The crux of the distinction is the meaning of an unobserved entry $r_{ui}$.

• With explicit ratings, an unrated cell is missing data: the user simply has not told us. We should not treat it as a negative. Models are fit on the observed entries only.
• With implicit feedback, there is no “negative” channel. A user who never clicked an item might (a) dislike it, or (b) never have seen it. Treating all non-interactions as negatives is wrong (most are unseen), but ignoring them entirely leaves only positive examples and the model collapses to predicting “everything is good”.

Practical reality (RS-L01 case studies): explicit ratings are scarce, expensive, and biased (few users rate; those who do are not a random sample). Implicit signals are abundant and cheap — every play, skip, and purchase is logged — which is why production systems (Spotify Daily Mix, bol.com deals, YouTube feed) run almost entirely on implicit feedback. The price is noise and ambiguity: a play could be a mis-click, a purchase could be a gift.

Mathematical Formulation

The same architecture can be trained on either signal; the loss function is what differs. RS-L01 frames Neural Collaborative Filtering as binary classification with label $y_{ui}$ and prediction ${\hat{y}}_{ui}$, and gives two losses:

Explicit feedback — (weighted) squared loss

${\mathcal{L}}_{\text{exp}}={\sum }_{(u,i)\in \mathcal{O}}{w}_{ui}(r_{ui}-{\hat{r}}_{ui}{)}^2$ where:

• $\mathcal{O}$ — set of observed (rated) user–item pairs; the sum runs over these only
• $r_{ui}$ — the actual rating (e.g. on a 1–5 scale)
• ${\hat{r}}_{ui}$ — predicted rating (e.g. dot product ${\bar{u}}_u\cdot {\bar{v}}_i$ in Matrix Factorization, or NCF output)
• $w_{ui}$ — optional per-entry weight (set $w_{ui}=1$ for plain squared error)

Implicit feedback — binary cross-entropy with negative sampling

${\mathcal{L}}_{\text{imp}}=-{\sum }_{(u,i)\in {\mathcal{O}}^{+}}\log {\hat{y}}_{ui}-{\sum }_{(u,j)\in {\mathcal{O}}^{-}}\log (1-{\hat{y}}_{uj})$ where:

• ${\mathcal{O}}^{+}$ — observed interactions, treated as positives ($y_{ui}=1$)
• ${\mathcal{O}}^{-}$ — sampled unobserved pairs treated as negatives ($y_{uj}=0$); drawn by Negative Sampling to avoid summing over the huge set of all non-interactions
• ${\hat{y}}_{ui}\in (0,1)$ — predicted probability that item $i$ is relevant to $u$ (sigmoid output)

An alternative for implicit data is to rank a positive above a sampled negative rather than classify each. This is Bayesian Personalized Ranking (BPR) (Rendle et al., 2012), the canonical implicit-feedback objective:

BPR — pairwise ranking from implicit feedback

${\mathcal{L}}_{\text{BPR}}=-{\sum }_{(u,i,j)\in D_S}\log \sigma ({\hat{r}}_{ui}-{\hat{r}}_{uj})$ where:

• $D_S$ — triples $(u,i,j)$ with $i$ an observed (positive) item for $u$ and $j$ a sampled unobserved item
• ${\hat{r}}_{ui},{\hat{r}}_{uj}$ — model scores for the positive and negative item
• $\sigma (\cdot )$ — sigmoid; the loss pushes the positive’s score above the negative’s, encoding "$i{\succ }_{u}j$" rather than fitting an absolute value

Key Properties / Variants

• Missing-data semantics (the central exam point):
  • Explicit → missing = unknown; fit on observed entries only; a regression/rating-prediction task evaluated with error metrics (the implicit assumption being “missing at random”, which is itself questionable).
  • Implicit → missing = unlabeled (mostly unseen, some disliked); a ranking / one-class task; you must synthesise negatives (Negative Sampling) because there is no negative channel.
• Task framing. Explicit feedback naturally suits rating prediction (${\hat{r}}_{ui}$, evaluated by RMSE/MAE). Implicit feedback naturally suits Top-K Recommendation / Next-Item Prediction, evaluated by ranking metrics — Recall/HR@K, MRR, NDCG (RS-L01/RS-L02). The modern course default is implicit + ranking.
• Confidence weighting. Implicit signals carry strength: watching a film twice or purchasing is stronger evidence than a single click. A common trick is to weight the positive term by an interaction-derived confidence $c_{ui}$ (e.g. $c_{ui}=1+\alpha {\text{count}}_{ui}$), the implicit analogue of $w_{ui}$ above.
• Bias. Implicit logs are not an unbiased sample of preference: they are filtered through what the system already exposed and through Position Bias (RS-L02 motivates simulation and debiasing precisely because logged implicit data is biased). Explicit ratings carry selection bias (users rate what they feel strongly about).
• Where each model sits:
  • Matrix Factorization / user-based rating prediction — classically explicit (squared loss on observed ratings).
  • Neural Collaborative Filtering — either, via the loss switch above.
  • Bayesian Personalized Ranking (BPR), GRU4Rec (BPR loss), SASRec (BCE + negatives), BERT4Rec (masked CE over the catalogue) — implicit / sequential, learned from interaction order.
  • Generative Recommendation (TIGER, OneRec) — implicit by construction: trained on the sequence of items the user actually interacted with, decoding the next item’s identifier.

Choosing the objective from the feedback type
─────────────────────────────────────────────
if feedback is EXPLICIT (ratings / scores):
    task   = rating prediction
    train  = squared loss over OBSERVED entries only      (do NOT impute 0)
    eval   = RMSE / MAE   (and/or rank the predicted ratings)
else feedback is IMPLICIT (clicks / plays / purchases):
    positives = observed interactions
    negatives = SAMPLE from unobserved pairs              (negative sampling)
    train  = BCE  (pointwise)   or   BPR  (pairwise ranking)
    weight positives by confidence c_ui if signal strength varies
    eval   = ranking metrics: Recall/HR@K, MRR, NDCG
    beware: logged implicit data is BIASED (exposure / position)

Connections

• Recorded in: Interaction Matrix / User-Item Interaction
• Trained via: Negative Sampling, Bayesian Personalized Ranking (BPR), Matrix Factorization, Neural Collaborative Filtering
• Drives task choice: Top-K Recommendation vs rating prediction; Next-Item Prediction in Sequential Recommendation
• Evaluated with: Recall, Hit Rate, MRR, NDCG (ranking) for implicit; error metrics for explicit
• Confounded by: Position Bias, Popularity Bias (implicit logs are not unbiased preference samples)
• Underlies: Collaborative Filtering, GRU4Rec, SASRec, BERT4Rec, Generative Recommendation

Appears In

• RS-L01 - Course Overview & Introduction
• RS-L02 - Evaluation Beyond Accuracy
• RS-L03a - Sequential Recommendation Models
• RS-L04 - Generative Recommendation