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Better Capturing Interactions Between Products in~Retail: Revisited Negative Sampling for~Basket Choice Modeling

Jules Désir, Vincent Auriau, Martin Možina, Emmanuel Malherbe

arXiv:2610.17963v1cs.LGcs.AI

TL;DR

Retailers need to choose assortments and promotions while accounting for product complementarity and cannibalization. This paper models basket choices with learned product interactions and assortment-aware negative sampling; experiments report better interaction capture on synthetic data and promising performance and scalability in a large retailer evaluation.

  • Problem

    Retail assortment and promotion decisions require understanding product preferences and interactions, including complementarity and cannibalization.

    Source: §1 · p. 1

  • Method

    The model learns item, shop, and basket representations for choice modeling and uses soft negative sampling that accounts for the available assortment.

    Source: §1 · p. 2, §3.3 · p. 4

  • Results

    Assortment-aware negative sampling better captures product interactions on synthetic data, while the large-scale retailer evaluation reports competitive predictive performance and computing scalability.

    Source: §5.1.2 · pp. 8–9, §5.2 · p. 10, §6 · p. 11

  • Takeaways & Limitations

    The model has potential to support category managers' assortment optimization and promotion planning through enriched retail interfaces.

    Source: §6 · p. 12

    The model targets settings with few or no item, shop, or customer features; its main signals are co-purchase patterns.

    Source: §3.1 · p. 3

Abstract

from arXiv · show

Brick-and-mortar retailers face many different challenges that involve understanding thoroughly its products catalog and customer preferences. In particular, assortment optimization - proposing the ideal mix of products - and promotion planning hold a pivotal role in their strategy. By leveraging sales data, retailers can make informed decisions on which products to sell and how to manage inventory, based on customer preferences as well as regional and seasonal trends. It is especially crucial to capture interactions between products, in order to minimize the number of items that cannibalize each other's sales and to ensure that complementary products, which are often purchased together, are conjointly available and sold across all stores. In this paper, we propose a model of shopping basket that learns embeddings to represent interactions between products, prices and stores. Our model is built to uncover sales patterns from very large transaction datasets. In particular, the optimization loss is computed with random negative samples in order to overcome the computational bottlenecks that arise with large number of items. Our experiments on synthetic data show the efficiency of drawing such negative samples based on the actual assortment of available products, with better results than approaches from the literature. We also validate our approach by training and evaluating our model on a dataset composed of millions of transactions from Fortenova Group, one of the leading retail company in Southeast Europe. Our model showcases promising applications in the sector of retail, with enriched interfaces to efficiently support category managers.

1 Introduction

Retail assortment and promotion decisions depend on understanding product preferences and interactions, including complementarity and cannibalization. The paper proposes a neural-network choice model and assortment-aware negative sampling for learning such interactions from large purchase datasets.

1 Introduction

  • Retailers must select products and promotions from large catalogs, using sales insights to guide assortment decisions.Source: §1 · p. 1
  • Complementary products may need to be offered together, while similar products can cannibalize each other's sales.Source: §1 · p. 1
  • Co-purchased baskets reveal patterns that can inform category managers' assortment decisions, while assortments remain relatively stable for logistical reasons.Source: §1 · p. 2
  • Choice models use purchase data to estimate preferences, but large product catalogs make modeling their exponentially many interactions difficult.Source: §1 · p. 2
  • The proposed neural-network choice model learns item, shop, and basket representations to capture product interactions from purchase receipts.Source: §1 · p. 2
  • The paper proposes assortment-aware soft negative sampling and evaluates the model on synthetic data and a retailer dataset against existing models.Source: §1 · p. 2

2 Related Work

Related work spans discrete choice modeling and representation learning. Prior work addresses option availability and categorical embeddings, but has limitations in modeling interactions across purchased bundles at retail scale.

2 Related Work

  • The paper situates its approach across discrete choice modeling and representation learning, with similarities to word embeddings.Source: §2 · p. 2

2.1 Discrete Choice Models

  • Discrete choice models estimate latent utility from observed choices; classical conditional logit uses linear utility, while later work also uses nonlinear neural-network and tree-based models.Source: §2.1 · p. 2
  • Retail choice models handle changing assortments, but bundle interactions are difficult to estimate because possible bundles grow exponentially with the number of items.Source: §2.1 · p. 2

2.2 Representation learning

  • Embeddings represent categorical data with learned continuous vectors, and word-embedding training commonly uses negative sampling on large-scale natural data.Source: §2.2 · p. 3
  • Prior choice-model embeddings may omit interactions, focus on single choices, or require costly Bayesian inference and subset generation rather than leveraging purchased bundles.Source: §2.2 · p. 3

3 Model

The model targets retail settings with limited item features, using baskets, assortments, stores, and prices to estimate item utilities and interactions. Conditional choice probabilities are derived from these utilities under a random-utility assumption.

3.1 Context and Objectives

  • The model targets large retail datasets whose main signals are co-purchases, capturing complementarity and cannibalization despite few or no item features beyond price and promotion.Source: §3.1 · p. 3

3.2 Notations

  • Each observation includes a purchased basket, the available assortment, store, and item prices; baskets exclude duplicate items to focus on catalog-item interactions.Source: §3.2 · pp. 3–4

3.3 Conditional definition of the utility

  • Conditional utility adds an item's preference to its interaction with the existing basket; preference depends on item, price, and store, while basket context uses learned item representations.Source: §3.3 · p. 4

3.4 Purchase probability

  • Assuming rational utility maximization and independent zero-mean Gumbel noise, the model gives each not-yet-selected item a softmax probability over the remaining assortment.Source: §3.3 · p. 4, §3.4 · p. 4

4 Implementation for large-scale data

The model is trained by maximizing the probability of each purchased item given the rest of its basket, using random negative samples to make estimation practical at scale. Restricting those samples to the available assortment avoids penalizing unavailable items as potential alternatives.

4.1 Training Procedure

  • Training maximizes the conditional probability of each purchased item given the remaining basket, a self-supervised prediction objective.Source: §4.1 · p. 5
  • Because computing choice probabilities over a large item set is costly, the model approximates them using randomly drawn negative samples.The passage notes that this approach approximates softmax log probabilities and matters when there are thousands of products.Source: §4.1 · p. 5
  • The resulting binary-cross-entropy loss is minimized by stochastic gradient descent, with negative samples redrawn for each epoch.Source: §4.1 · p. 5

4.2 Negative Sampling

  • Negative samples exclude items already in the basket and come only from the available assortment, restricting comparisons to feasible options.Source: §4.2 · pp. 5–6
  • Restricting negatives to the assortment avoids reducing an unavailable item's utility and falsely treating it as cannibalizing a purchased item.Source: §4.2 · p. 6

5 Experiments

Experiments test assortment-aware negative sampling on controlled synthetic data and large-scale retail transactions. The reported findings support improved interaction recovery and scalability, with product-category patterns emerging in learned embeddings and examples of complementary-item rankings.

5 Experiments

  • The experiments include synthetic validation and evaluation on a large industrial dataset from Fortenova Group supermarkets.The synthetic tests use controlled interactions; the retail evaluation uses a temporal split.Source: §5 · p. 6, §5.3 · p. 10

5.1.1 Dataset

  • The synthetic catalog contains eight items grouped into cannibalizing, complementary, and neutral products, with training and test baskets generated from different assortments.The test includes an assortment not seen in training, as well as the full assortment.Source: §5.1.1 · pp. 6–7

5.1.2 Protocol

  • Assortment-aware negative sampling better captures product interactions than naive sampling, which tends to underestimate complementarity for items not always sold together.The authors report that this approach better learns the underlying distribution and generalizes to new assortments.Source: §5.1.2 · pp. 8–9, Table 1 · p. 9

5.2 Large scale experiments: Computation time and memory usage

  • Our approach and the Python Shopper implementation scale better with dataset size, while our approach is competitive in training speed with Shopper’s C++ implementation.Our approach is faster than the Shopper reimplementation because it does not consider basket permutations.Source: §5.2 · p. 10, Table 2 · p. 10

5.3 Experiments on real-world retail data

  • The Fortenova evaluation uses purchases from hundreds of supermarkets over 2017–2021, with more than 6,000 food products and a temporal train/test split.Training covers 2017–2020, and 2021 is held out for testing; the reported metrics again stress assortment-adapted negative sampling.Source: §5.3 · p. 10, Table 4 · p. 11
  • Learned item embeddings cluster by product category in a t-SNE projection, although the model receives no product information beyond price.The authors interpret this as learning a logical product hierarchy from basket information.Source: §5.3 · p. 10, Figure 5 · p. 11

5.4 Application: Highlighting complementary products

  • Complementarity rankings recover plausible combinations, including pasta, bread, and pizza dough for tomato sauce and cake ingredients for vanilla powder.The rankings also distinguish large and small soda bottle formats, including a single-portion to-go ice cream pairing for small bottles.Source: §5.4 · pp. 10–11

6 Conclusion

The model uses negative sampling to learn item embeddings for basket choice, with experiments indicating scalable, competitive performance and promising complementary-item rankings. The authors see potential for retail decision support and identify additional product and customer features as future directions.

6 Conclusion

  • More than one million transactions validated practical applicability, with promising top complementary items and competitive predictive performance and computing scalability versus literature.Table 5 ranks top-10 complementary products for four examples, with products anonymized by letter.Source: §6 · p. 11, Table 5 · p. 12
  • Synthetic experiments demonstrated the added value of the model and its negative-sampling method for capturing product interactions in retail.Source: §6 · p. 11
  • Future work proposes adding shelf proximity and personalized customer profiles to examine spatial and customer-segment variation in product interactions.Source: §6 · p. 12
  • The authors identify assortment optimization and promotion planning as potential applications, and suggest extending the approach to other large-scale consumer-choice domains.Source: §6 · p. 12

A Synthetic Data Generation

Synthetic baskets are generated iteratively from an assortment: a first item is selected, items are added from remaining nests, and random assortment items may introduce noise.

A Synthetic Data Generation

B Experiments on real-world retail data

The real-world experiments used latent dimensions of 12 for α and β and 128 for γ, with 24 negative samples, Adamax, batch size 256, and 20 epochs.

B Experiments on real-world retail data

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