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DeepHalo: A Neural Choice Model with Controllable Context Effects

Shuhan Zhang, Zhi Wang, Rui Gao, Shuang Li

TL;DR

DeepHalo introduces a neural framework for context-dependent choice modeling that explicitly controls the order of interaction effects among alternatives while incorporating features. It decomposes utility as $u_j(S) =\sum_{p=0}^{|S|-1} \sum_{T \subset S\setminus\{j\}, |T|=p} v_j(X_{T\cup\{j\}})$, enabling permutation equivariance and interpretable identification of context effects by order. Its architecture uses a layered, residual design with a nonlinear base embedding $\\chi$ and head-specific modulators to realize first- and higher-order interactions up to order $L$, with a specialization to the featureless setting yielding a universal approximator of context-dependent choice. Empirically, DeepHalo achieves strong predictive performance on synthetic and real datasets and provides interpretable diagnostics (e.g., relative halo effects $\\alpha_{jk}(T)$) that illuminate the drivers of context-dependent choice.

Abstract

Modeling human decision-making is central to applications such as recommendation, preference learning, and human-AI alignment. While many classic models assume context-independent choice behavior, a large body of behavioral research shows that preferences are often influenced by the composition of the choice set itself -- a phenomenon known as the context effect or Halo effect. These effects can manifest as pairwise (first-order) or even higher-order interactions among the available alternatives. Recent models that attempt to capture such effects either focus on the featureless setting or, in the feature-based setting, rely on restrictive interaction structures or entangle interactions across all orders, which limits interpretability. In this work, we propose DeepHalo, a neural modeling framework that incorporates features while enabling explicit control over interaction order and principled interpretation of context effects. Our model enables systematic identification of interaction effects by order and serves as a universal approximator of context-dependent choice functions when specialized to a featureless setting. Experiments on synthetic and real-world datasets demonstrate strong predictive performance while providing greater transparency into the drivers of choice.

DeepHalo: A Neural Choice Model with Controllable Context Effects

TL;DR

DeepHalo introduces a neural framework for context-dependent choice modeling that explicitly controls the order of interaction effects among alternatives while incorporating features. It decomposes utility as , enabling permutation equivariance and interpretable identification of context effects by order. Its architecture uses a layered, residual design with a nonlinear base embedding and head-specific modulators to realize first- and higher-order interactions up to order , with a specialization to the featureless setting yielding a universal approximator of context-dependent choice. Empirically, DeepHalo achieves strong predictive performance on synthetic and real datasets and provides interpretable diagnostics (e.g., relative halo effects ) that illuminate the drivers of context-dependent choice.

Abstract

Modeling human decision-making is central to applications such as recommendation, preference learning, and human-AI alignment. While many classic models assume context-independent choice behavior, a large body of behavioral research shows that preferences are often influenced by the composition of the choice set itself -- a phenomenon known as the context effect or Halo effect. These effects can manifest as pairwise (first-order) or even higher-order interactions among the available alternatives. Recent models that attempt to capture such effects either focus on the featureless setting or, in the feature-based setting, rely on restrictive interaction structures or entangle interactions across all orders, which limits interpretability. In this work, we propose DeepHalo, a neural modeling framework that incorporates features while enabling explicit control over interaction order and principled interpretation of context effects. Our model enables systematic identification of interaction effects by order and serves as a universal approximator of context-dependent choice functions when specialized to a featureless setting. Experiments on synthetic and real-world datasets demonstrate strong predictive performance while providing greater transparency into the drivers of choice.
Paper Structure (58 sections, 1 theorem, 45 equations, 2 figures, 11 tables)

This paper contains 58 sections, 1 theorem, 45 equations, 2 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Preliminaries
  4. Choice Model
  5. Context Effects
  6. Modeling the Context Effects in the Presence of Features
  7. Utility Decomposition and Permutation Equivariance
  8. Neural Net Parameterization
  9. Pairwise Interactions
  10. Higher-order Interactions
  11. Discussions
  12. Residual Connection for Large Choice Sets
  13. Specialization to the Featureless Setting
  14. Estimating the Context Effects
  15. Empirical Study
  16. ...and 43 more sections

Key Result

Proposition 1

Every utility function $u: \mathbb{R}^{d_x \times J} \to \bar{\mathbb{R}}^J$ that is permutation equivariant can be decomposed as where $v_j$ is a function over subsets of feature vectors that includes $x_j$ and is itself permutation equivariant in its arguments.

Figures (2)

  • Figure 1: Market-share table (left) and relative Halo effect visualization (right)
  • Figure 2: Effect of model depth on approximation error.

Theorems & Definitions (2)

  • Proposition 1
  • proof