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A Non-Parametric Choice Model That Learns How Users Choose Between Recommended Options

Thorsten Krause, Harrie Oosterhuis

arXiv:2507.20035v1cs.IR

TL;DR

Traditional recommendation methods often treat item interactions independently, while choice-model accuracy depends on assumptions about user behavior that may be wrong. LCM4Rec uses kernel density estimation to learn user preferences and the choice model together; experiments report recovery of the underlying model and robust performance across tested choice models.

  • Problem

    Choice models can bias choice probabilities when their assumed behavior mismatches users, while benchmarking among infinitely many possible models is impractical.

    Source: §1 · pp. 1–2

  • Method

    LCM4Rec uses a non-parametric kernel density estimator to infer the error distribution and user preferences without assuming a particular choice model.

    Source: §1 · pp. 1–2

  • Results

    Across tested choice models, LCM4Rec recovers the underlying choice model and has consistent competitive predictive performance and robustness to exposure bias from competition.

    Source: §6 · p. 9

  • Takeaways & Limitations

    The results support learning rather than assuming users' choice models as a robust way to infer preferences and model choice behavior.

    Source: §6 · p. 9

    LCM4Rec assumes IID errors, and the experiments were limited to synthetic data.

    Source: §6 · p. 9

Abstract

from arXiv · show

Choice models predict which items users choose from presented options. In recommendation settings, they can infer user preferences while countering exposure bias. In contrast with traditional univariate recommendation models, choice models consider which competitors appeared with the chosen item. This ability allows them to distinguish whether a user chose an item due to preference, i.e., they liked it; or competition, i.e., it was the best available option. Each choice model assumes specific user behavior, e.g., the multinomial logit model. However, it is currently unclear how accurately these assumptions capture actual user behavior, how wrong assumptions impact inference, and whether better models exist. In this work, we propose the learned choice model for recommendation (LCM4Rec), a non-parametric method for estimating the choice model. By applying kernel density estimation, LCM4Rec infers the most likely error distribution that describes the effect of inter-item cannibalization and thereby characterizes the users' choice model. Thus, it simultaneously infers what users prefer and how they make choices. Our experimental results indicate that our method (i) can accurately recover the choice model underlying a dataset; (ii) provides robust user preference inference, in contrast with existing choice models that are only effective when their assumptions match user behavior; and (iii) is more resistant against exposure bias than existing choice models. Thereby, we show that learning choice models, instead of assuming them, can produce more robust predictions. We believe this work provides an important step towards better understanding users' choice behavior.

1 Introduction

Recommendation choice models account for competition among presented items, but their usefulness depends on matching the true choice behavior. LCM4Rec learns both user preferences and the choice model, and experiments report robust preference inference and exposure-bias resistance across tested models.

1 Introduction

  • Unlike traditional implicit recommenders that treat item choices independently, choice models account for competition among options shown together.Choice models represent competitive effects through a probabilistic noise distribution; MNL uses Gumbel noise.Source: §1 · p. 1
  • Identifying the right choice model by benchmarking is impractical because infinitely many models exist and some lack closed-form solutions.Using a mismatched model can bias estimated choice probabilities.Source: §1 · p. 1
  • LCM4Rec uses kernel density estimation to infer the error distribution and user preferences without assuming a particular choice model, subject to IID error terms.Its estimator is described as applicable to any choice model whose error terms are IID.Source: §1 · pp. 1–2
  • LCM4Rec provides consistent competitive predictive performance and exposure-bias robustness across tested choice models, while existing models work accurately only when their assumptions match user behavior.The experiments also report that LCM4Rec recovers the underlying choice model and that inaccurate models skew choice probabilities and increase exposure-bias vulnerability.Source: §1 · p. 2
  • The paper presents LCM4Rec as the first method to learn both user preferences and how users choose between recommended options.The authors frame this as a contribution to modeling user behavior without assuming a choice model.Source: §1 · p. 2

2 Related work and Background

Discrete choice models estimate choices from displayed alternatives, while non-parametric approaches seek to learn rather than assume the error distribution. Prior work describes how choice-model assumptions shape cannibalization and exposure-bias behavior.

2.1 Discrete choice models for recommendation

  • Discrete choice models estimate choice probabilities from displayed alternatives using relative utility; their random error term represents unobserved utility and allows choices to vary under identical circumstances.The section notes that choice-set data are increasingly available for recommendation.Source: §2.1 · p. 2

2.2 Non-parametric discrete choice models

  • Non-parametric methods learn the error distribution, but prior estimators are limited by binary-choice scope, nondifferentiability, or computational demands for large choice sets.The reviewed approaches include methods that cannot infer choice probabilities or are not directly applicable to recommender systems.Source: §2.2 · pp. 2–3

2.3 Competitive effects and cannibalization

  • Cannibalization is the reduction in an item's choice probability when a substitute is present, and MNL and exponomial models predict different reductions despite agreeing on the most-probable ordering.MNL reduces all choice probabilities by the same proportion, whereas exponomial assigns larger losses to low-utility alternatives.Source: §2.3 · p. 3, Table 1 · p. 3

2.4 Exposure bias in recommender systems

  • Exposure bias can arise from overexposure or competition among co-present items, and choice models can reduce both; prior unbiasedness proof assumes the model matches ground truth.Exposure bias can also reinforce popularity and contribute to feedback loops and subgroup harms.Source: §2.4 · p. 3

3 Method: The Learned Choice Model for Recommendation (LCM4Rec)

LCM4Rec replaces a prespecified choice-model error distribution with a learned, differentiable kernel-density estimate, jointly modeling user utilities and choice behavior. Its optimization fits observed choices, while its approximation guarantee is limited to choice models with IID error terms.

3 Method: The Learned Choice Model for Recommendation (LCM4Rec)

  • LCM4Rec uses a smooth kernel density estimator to learn an error distribution and user preferences, avoiding the non-parametric methods’ barriers to recommender-system use.The prior methods discussed are non-differentiable, restricted to binary choices, or computationally complex for large choice sets.Source: §3 · p. 3

3.1 Learned choice model architecture

  • A weighted average of sigmoid functions estimates the error CDF and density; learned user and item embeddings plus item constants define utilities.The error terms are IID, a restriction that excludes models such as nested logit. The function family can approximate any choice model with IID error terms.Source: §3.1 · pp. 3–4

3.2 Optimizing for the most likely choice model

  • LCM4Rec fits the error distribution and utility parameters by minimizing an approximated negative log-likelihood with gradient descent.Because the likelihood integrals lack a closed form, the gradient is approximated using Monte Carlo integration; a third-order Taylor expansion corrects logarithm-induced bias.Source: §3.2 · pp. 4–5

3.3 Computational complexity

  • The straightforward loss computation has O(K^2NS|C|) complexity, but the authors report no practical problem because K remains small.They observe no benefit above K=10 and note that uniform-support Monte Carlo sampling can instead achieve linear scaling in K.Source: §3.3 · p. 5

3.4 Identification and regularization

  • To prevent overfitting, LCM4Rec rescales item-specific constants c_j to [0, 1] after each gradient update, keeping utilities and width on a comparable scale.The authors say ordinary L2 regularization is ineffective because other parameters can compensate for shrinking embeddings, causing the estimated error distribution to collapse.Source: §3.4 · p. 5

4 Experimental Setup

The experiments test probability accuracy, recovery of the underlying choice model, and robustness to exposure bias using synthetic data and comparisons with parametric models. The setup also identifies boundaries on how well these findings may transfer to real-world data.

4 Experimental Setup

  • The experiments ask whether LCM4Rec estimates accurate choice probabilities, recovers the true choice model, and resists exposure bias compared with parametric models.Comparisons include cases where parametric assumptions match or mismatch the data-generating error distribution.Source: §4 · p. 5

4.1 Experiment 1: Accuracy and robustness

  • Experiment 1 generates choices for 500 users and 500 items under Gumbel, signed-exponential, or Gaussian-mixture errors, then compares probability and prediction metrics.Users make up to 500 choices from uniformly random sets of four items; the Gaussian mixture lacks a corresponding parametric model. Evaluation uses KLD, nDCG, NLL, and accuracy, averaged over 100 repetitions.Source: §4.1 · pp. 5–6

4.2 Experiment 2: Correcting for exposure bias

  • Experiment 2 compares MNL, ENL, and LCM4Rec across exposure-frequency and competition shifts, measuring differences in predicted ranks for equivalent models.One setting raises exposure for 25 items to 1.9 times per item; another presents those items with either highly or lowly popular alternatives.Source: §4.2 · p. 6

4.3 Assumptions and possible extensions

  • The synthetic setting uses 500 choices per user and four options per choice, a scale the authors say is realistic only in some scenarios.They also flag sparse-data convergence, non-uniform choice sets and utilities, and partially unobserved choice sets as open real-world considerations.Source: §4.3 · p. 7

5 Results and Discussion

Across the synthetic settings, LCM4Rec predicts choice probabilities consistently across true error distributions and recovers their shapes. It is least affected by competition bias, while overexposure affects the compared models similarly.

5.1 Accuracy and robustness

  • Univariate BCE and gBCE consistently perform worst, while BL can excel under Gumbel; MNL and ENL perform best when correctly specified but lose KLD accuracy when misspecified.The authors caution that their uniform-random choice sets are idealized, so the observed compensation by MNL and ENL may not hold in less ideal settings.Source: §5.1 · p. 7, Table 2 · p. 7
  • LCM4Rec predicts choice probabilities across true error distributions without a performance trade-off, reaching competitive performance on all reported metrics.It has the best observed NLL, nDCG, and accuracy across distributions, and the best KLD for Gaussian mixtures; for signed exponential and Gumbel, its KLD is second-best, with limited differences from the best.Source: Table 2 · p. 7, §5.1 · pp. 7–8

5.2 Learning the choice model

  • Mean KLD is low for LCM4Rec and much lower than for MNL and ENL when their assumed error distribution is incorrect.The paper concludes that LCM4Rec recovers the true error-distribution shape and learns the user choice model.Source: Table 3 · p. 7, §5.2 · p. 8
  • LCM4Rec’s estimated CDFs track the true CDFs, and their derivatives recover the true PDF shapes, including skew and the Gaussian mixture’s two columns.Signed-exponential estimates oscillate, which the authors suggest may result from the kernel estimator’s resolution (K=5).Source: §5.2 · p. 8, Figure 1 · p. 8

5.3 Exposure bias resistance

  • Overexposure has limited effects across models, and confidence intervals do not show meaningful differences in their robustness to it.Figure 2 shows rank differences close to zero across true item ranks; although LCM4Rec is less affected, the authors conclude the models appear similarly robust to overexposure.Source: Table 4 · p. 8, §5.3 · pp. 8–9, Figure 2 · p. 9
  • Competition causes larger ranking differences: parametric-model effects depend on the true choice model, while LCM4Rec is least affected across distributions.The most-preferred items are affected most; conservative ENL ranks them lower, whereas non-conservative MNL ranks them higher.Source: Table 4 · p. 8, §5.3 · p. 9, Figure 2 · p. 9

6 Conclusion

Existing parametric choice models assume an error distribution and can misestimate choice probabilities and exposure-bias susceptibility when that assumption is wrong. LCM4Rec learns the error distribution and user preferences jointly, with consistent performance across tested models, but the experiments use synthetic data and assume IID errors.

  • Existing parametric choice models assume an error distribution, and mismatched assumptions yield inaccurate choice probabilities and susceptibility to exposure bias.Source: §6 · p. 9
  • LCM4Rec is a non-parametric multivariate recommendation model that simultaneously infers the most likely error distribution and user preferences.Source: §6 · p. 9
  • Across all tested choice models, only LCM4Rec combines consistent competitive predictive performance with exposure-bias robustness and recovers the correct choice model from interactions.Source: §6 · p. 9
  • The experiments are limited to synthetic data, and LCM4Rec assumes IID errors; extending it to non-IID errors is future work.Source: §6 · p. 9

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