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The Deconfounded Recommender: A Causal Inference Approach to Recommendation

Yixin Wang, Dawen Liang, Laurent Charlin, David M. Blei

arXiv:1808.06581v2cs.IRcs.LGstat.ML

TL;DR

Recommendation aims to predict how users would rate items they were made to watch, but nonrandom exposure can confound observational ratings. The deconfounded recommender estimates substitute confounders from exposure patterns and uses them in a ratings model; it improves recommendation and rating prediction while showing greater robustness to unobserved confounding.

  • Problem

    Users’ nonrandom movie choices can create unobserved confounders that affect both which movies they watch and how they rate them, complicating causal prediction from observed ratings.

    Source: §1 · p. 1

  • Method

    The deconfounded recommender models movie exposure to estimate substitute confounders, then incorporates them into a ratings model.

    Source: §1 · p. 2

  • Results

    The deconfounded recommender improves recommendation and rating prediction and is more robust to unobserved confounding than existing approaches.

    Source: §1 · p. 2, §4 · p. 8

  • Takeaways & Limitations

    Classical recommendation models can be augmented for causal predictions about how users would rate recommended movies.

    Source: §4 · p. 8

    The approach requires strong ignorability, meaning all confounders must be measured; this assumption is untestable.

    Source: §2 · p. 4

Abstract

from arXiv · show

The goal of recommendation is to show users items that they will like. Though usually framed as a prediction, the spirit of recommendation is to answer an interventional question---for each user and movie, what would the rating be if we "forced" the user to watch the movie? To this end, we develop a causal approach to recommendation, one where watching a movie is a "treatment" and a user's rating is an "outcome." The problem is there may be unobserved confounders, variables that affect both which movies the users watch and how they rate them; unobserved confounders impede causal predictions with observational data. To solve this problem, we develop the deconfounded recommender, a way to use classical recommendation models for causal recommendation. Following Wang & Blei [23], the deconfounded recommender involves two probabilistic models. The first models which movies the users watch; it provides a substitute for the unobserved confounders. The second one models how each user rates each movie; it employs the substitute to help account for confounders. This two-stage approach removes bias due to confounding. It improves recommendation and enjoys stable performance against interventions on test sets.

1 Introduction

Recommendation asks how a user would rate an item if they were made to watch it, but observational ratings can be confounded by users’ nonrandom movie choices. The deconfounded recommender models exposure and ratings separately, using exposure patterns to estimate substitute confounders and adjust a ratings model.

1 Introduction

  • Recommendation is an interventional question: how would a user rate a movie if they were forced to watch it?Predictions under intervention differ from ordinary out-of-sample predictions.Source: §1 · p. 1
  • Traditional rating models support valid causal inferences only if users watched and rated movies at random.The paper compares this condition to a randomized clinical trial in which the movie is the treatment and rating is the response.Source: §1 · p. 1
  • Because users choose which movies to watch, unobserved factors can affect both exposure and ratings, biasing causal inferences from observed ratings.For example, users may choose films by directors they like and then rate those films highly.Source: §1 · pp. 1–2
  • The deconfounded recommender uses exposure data to estimate substitute confounders, then adjusts a ratings model such as matrix factorization to account for them.Correlations among the movies users consider provide indirect evidence about confounders, following Wang & Blei (2018).Source: §1 · p. 2
  • Its performance is more robust to unobserved confounding, predicts ratings better, and consistently improves recommendation compared with existing approaches.The studies use simulated data with controlled confounding and real shopping and movie data.Source: §1 · p. 2
  • Unlike related missingness and inverse-propensity approaches, this work takes an explicitly causal view and relies on observed ratings rather than randomized exposure or external covariates.Earlier work includes missingness models (Liang et al., 2016; Ling et al., 2012) and inverse propensity weighting (Schnabel et al., 2016).Source: §1 · pp. 2–3

2 The deconfounded recommender

The section frames movie recommendation as estimating ratings under an intervention and develops a two-model approach to address unobserved confounding. It models exposures to construct a substitute confounder, then conditions the ratings model on that substitute to predict ratings for unseen movies.

Matrix factorization as potential outcomes

  • A movie rating is treated as a potential outcome: yui(1) is the rating if watched, and yui(0) is the rating if not watched.Only the rating for a watched movie is observed; unrated entries are often represented as zeros.Source: §2 · p. 3

Classical causal inference and adjusting for confounders in recommendation

  • Estimating ratings under intervention requires ignorability; conventional adjustment instead requires measuring all confounders, an assumption the paper calls strong ignorability.The paper notes that this requirement is untestable.Source: §2 · pp. 3–4

The deconfounded recommender

  • The deconfounded recommender models exposures to construct substitute confounders, then conditions its ratings model on them.It reconstructs exposures from a Poisson factorization fit and uses them as substitutes for unobserved confounders.Source: §2 · p. 4
  • Poisson factorization models exposure data, with user factors capturing movie-choice preferences and item vectors capturing attributes.The paper describes it as a scalable variant of nonnegative factorization suited to binary data.Source: §2 · p. 4
  • The fitted outcome model uses observed ratings to estimate user, item, and substitute-confounder coefficients, then ranks predicted ratings for unseen movies.The substitute-confounder coefficient is fit using all movies, while user and item coefficients are fit using observed ratings.Source: §2 · p. 4

4. Estimate potential ratings ˆyui(1) with the fitted outcome model (Eq. 11)

The substitute confounder need not match the true confounder or the exposure model’s latent variable. The approach can also pair its exposure model with outcome models beyond probabilistic matrix factorization.

4. Estimate potential ratings ˆyui(1) with the fitted outcome model (Eq. 11)

  • The true confounding mechanism need not coincide with Poisson factorization, and the real confounder need not be the latent variable πu.The method instead uses a substitute confounder that is sufficient to debias confounding.Source: §4 · p. 5
  • A substitute confounder produced by Poisson factorization can be sufficient to debias confounding without being the real confounder.Source: §4 · p. 5
  • With Poisson factorization as the exposure model, the approach can use Poisson matrix factorization or weighted matrix factorization as its outcome model.Source: §4 · p. 5

3 Empirical Studies

The empirical studies evaluate causal recommendation under simulated confounding and on real datasets. The deconfounded recommender is reported as more robust to unobserved confounding and as improving prediction and recommendation across the reported evaluations.

3 Empirical Studies

  • Across simulated and real datasets, the deconfounded recommender is more robust to unobserved confounding and improves prediction and recommendation.The studies compare it with existing recommendation algorithms.Source: §3 · p. 5

3.1 Evaluation of causal recommendation models

  • Causal evaluation targets performance across potential outcomes, but ordinary random data splits bias causal-error estimates toward popular items and active users.Randomized test sets can estimate average loss across all items; when these are unavailable, average per-item accuracy treats popular and unpopular items equally.Source: §3.1 · pp. 5–6

3.2 Simulation studies

  • As simulated confounding increases, the deconfounded recommender is more robust and has smaller rating MSEs and higher NDCGs than classical and IPW matrix-factorization counterparts.The comparison covers probabilistic, Poisson, and weighted matrix factorization variants.Source: §3.2 · p. 6, Figure 1 · p. 7

3.3 Case studies I: The deconfounded recommender on random test sets

  • On Yahoo! R3 and coat-shopping random test sets, the deconfounded recommender outperforms classical and IPW matrix factorization for weak and strong generalization across NDCG, recall, and MSE.The random test sets support evaluation of predicted potential outcomes.Source: §3.3 · pp. 6–7, Table 1 · p. 8, Table 2 · p. 8

3.4 Case studies II: The deconfounded recommender on regular test sets

  • Across two datasets, the deconfounded recommender achieves lower average per-item MSEs and MAEs on predictions over all items than classical approaches and IPW MF.The average per-item predictive accuracy equally treats popular and unpopular items.Source: §3.4 · pp. 7–8

4 Discussion

The deconfounded recommender uses classical recommendation models for causal predictions by inferring confounders from exposure data and incorporating them into ratings models. It improves recommendation and rating predictions, including per-item accuracy across all items.

  • The deconfounded recommender uses Poisson factorization to infer confounders in exposures, then augments common recommendation models to correct confounding bias.Source: §4 · p. 8
  • It targets causal predictions about how a user would rate a recommended movie and is more robust to unobserved confounding in user exposures.Source: §4 · p. 8
  • The deconfounded recommender achieves lower per-item MSEs and MAEs over all items than classical approaches and IPW MF.Table 3 reports average per-item predictive accuracy on heldout ratings; lower is better.Source: §4 · p. 8, Table 3 · p. 9

Supplementary Material

The theoretical justification gives conditions under which the deconfounded recommender yields unbiased causal inference. The supplementary method also extends the approach beyond probabilistic matrix factorization to general outcome models.

A Theoretical justification of the deconfounded recommender

  • With no confounders affecting exposure to only one item and as the number of items tends to infinity, the deconfounded recommender forms unbiased causal inferences.The justification invokes Wang & Blei (2018) for substitute-confounder ignorability and causal identification; the outcome here concerns exposure to one item.Source: A Theoretical justification of the… · p. 11

B Beyond probabilistic matrix factorization

  • Keeping Poisson factorization as the exposure model, the method extends the deconfounded recommender to general outcome models.Source: B Beyond probabilistic matrix… · p. 11
  • The augmented outcome model includes the estimated substitute confounder as a covariate, with a user-specific coefficient for its contribution to ratings.The model predicts potential ratings for existing users and can fit exposure and rating vectors for a new user with only a few ratings.Source: B Beyond probabilistic matrix… · p. 12

C Detailed simulation results

Simulations vary confounding associated with either exposures or rating outcomes. Across both settings, the deconfounded recommender is more robust than classical matrix-factorization counterparts and IPW MF.

  • One simulation examines an unobserved confounder highly correlated with exposures and its effects on rating predictions and ranking quality.Source: C Detailed simulation results · p. 12
  • The other simulation examines an unobserved confounder highly correlated with rating outcomes and its effects on rating predictions and ranking quality.Source: C Detailed simulation results · p. 12
  • In both simulations, the deconfounded recommender has smaller rating-prediction MSEs and higher recommendation NDCGs than classical counterparts and IPW MF.Source: C Detailed simulation results · p. 12

D Performance measures

The section defines ranking and rating-prediction measures and presents robustness figures for confounding variations. The experimental details also specify selected model and propensity-weighting settings.

D Performance measures

  • NDCG measures ranking quality, Recall@k measures relevant-item selection, and MSE measures rating-prediction error.Items rated at least 3 count as relevant for NDCG.Source: D Performance measures · pp. 12–13
  • Figure 2 varies exposure-confounder correlation γθ from 0.0 to 1.0 with γy = 3.0, comparing ranking robustness across three recommenders.The deconfounded recommender is reported as more robust; results average 10 runs.Source: Figure 2 · p. 13

E Experimental Details

  • The weighted-MF setup uses c_ui = 1 + αy_ui with α = 40, while IPW MF uses propensities estimated from ratings.Source: E Experimental Details · p. 13
  • Figure 4 varies confounding strength γy from 0.0 to 5.0 with γθ = 0.6 and compares ranking quality across the three recommenders.The deconfounded recommender is reported as more robust; results average 10 runs.Source: Figure 4 · p. 14

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