Logic-Logit: A Logic-Based Approach to Choice Modeling

Shuhan Zhang; Wendi Ren; Shuang Li

cs.LGOct 4, 2026

Logic-Logit: A Logic-Based Approach to Choice Modeling

Authors: Shuhan Zhang, Wendi Ren, Shuang Li

Organizations: CUHK-Shenzhen

Abstract

In this study, we propose a novel rule-based interpretable choice model, Logic-Logit, designed to effectively learn and explain human choices. Choice models have been widely applied across various domains---such as commercial demand forecasting, recommendation systems, and consumer behavior analysis---typically categorized as parametric, nonparametric, or deep network-based. While recent innovations have favored neural network approaches for their computational power, these flexible models often involve large parameter sets and lack interpretability, limiting their effectiveness in contexts where transparency is essential. Previous empirical evidence shows that individuals usually use heuristic decision rules to form their consideration sets, from which they then choose. These rules are often represented as disjunctions of conjunctions (i.e., OR-of-ANDs). These rules-driven, consider-then-choose decision processes enable people to quickly screen numerous alternatives while reducing cognitive and search costs. Motivated by this insight, our approach leverages logic rules to elucidate human choices, providing a fresh perspective on preference modeling. We introduce a unique combination of column generation techniques and the Frank-Wolfe algorithm to facilitate efficient rule extraction for preference modeling---a process recognized as NP-hard. Our empirical evaluation, conducted on both synthetic datasets and real-world data from commercial and healthcare domains, demonstrates that Logic-Logit significantly outperforms baseline models in terms of interpretability and accuracy.

Figures & tables

Figure 1: The framework of our Algorithm.

Figure 2: DFS Visualization In the figure, each node corresponds to a predicate. When the search rule conjunction length increases from $n$ to $n+1$ , the depth-first search (DFS) algorithm initiates from the previously detected $n$ -conjunction rules and exhaustively searches through all extensions with other predicates in order to discover a potential augmentation of the existing $n$ -conjunction.

Figure 3: Rule Comparison . The figure shows the Jaccard index between the ground truth (GT) rules (Y-axis) and the rules learned by our risk seeking model (X-axis), denoted by the color intensity.

Ground Truth Type	Ground Truth Rules	Learned Rules	Jaccard Index
Type 1	$p_{1}^{c}$	/	0
	$p_{2}^{c}\wedge p_{3}^{c}$	$p_{2}^{c}\wedge p_{3}^{c}$	1
	$p_{4}^{c}\wedge p_{5}^{c}\wedge p_{6}^{c}$	$p_{4}^{c}\wedge p_{5}^{c}\wedge p_{6}^{c}$	1
Type 2	$p_{7}^{c}$	$p_{7}^{c}$	1
	$p_{8}^{c}\wedge p_{9}^{c}\wedge p_{10}^{c}$	$p_{8}^{c}\wedge p_{9}^{c}\wedge p_{10}^{c}$	1
	$p_{11}^{c}\wedge p_{1}^{o}$	$p_{11}^{c}\wedge p_{1}^{o}$	1

Table 1: Ground truth rules and closest learned rules on the synthetic dataset.

Figure 5: Preference Type Analysis of Expedia Hotel Dataset

Drug Name	Detected Rules
Norepinephrine	$PT>12.6\wedge ABPd\leq 59.0$ $PTT>31.6\wedge age\leq 76.0\wedge ABPd<=54.0$
Vasopressin	$PCO2(Arterial)>41.0$ $INR>1.1\wedge anchor_{a}ge\leq 66.0$
Packed Red Blood Cells	$ABPd\leq 57.0\wedge ABPm\leq 56.0$ $PT>12.6\wedge INR>1.4\wedge RR\leq 32.0$ $PlateletCount\leq 95.0\wedge PTT>31.6$

Table 2: MIMIC Drug Preference Rules Examples .

Category	Method	Train loss	Test loss	Train accu (Top1)	Test accu (Top1)
DeepNN	NN	2.5118 ( $\pm 0.137$ )	2.5215 ( $\pm 0.033$ )	0.1261 ( $\pm 0.043$ )	0.0727 ( $\pm 0.031$ )
	TasteNet	2.4223 ( $\pm 0.000$ )	2.4323 ( $\pm 0.000$ )	0.1079 ( $\pm 0.008$ )	0.0727 ( $\pm 0.064$ )
	DeepMNL	2.3696 ( $\pm 0.000$ )	2.4331 ( $\pm 0.000$ )	0.1102 ( $\pm 0.008$ )	0.0818 ( $\pm 0.065)$
	mixDeepMNL	2.3394 ( $\pm 0.000$ )	2.4672 ( $\pm 0.000$ )	0.1060 ( $\pm 0.008$ )	0.0848 ( $\pm 0.065$ )
	RUMNet	2.3530 ( $\pm 0.000$ )	2.4426 ( $\pm 0.000$ )	0.1008 ( $\pm 0.002$ )	0.1000 ( $\pm 0.064$ )
Ours*	Ours-NM-50	$2.098(\pm 0.0165)$	$2.2047(\pm 0.020)$	$0.2961(\pm 0.010)$	$0.264(\pm 0.029)$

Table 3: Treatment choice prediction on MIMIC-IV dataset. We report Negative log likelihood (NLL) loss and Top-1 choice prediction accuracy of the training and testing set. NM refers to the normal mode of our model, while RS indicates the risk-seeking mode. We extract 50 rules for both types. Our Logit-Logit model performs much better than all the baselines.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Utility Value	# Parameters	Grounds for Interpretability
Logic-Logit (Ours)	Rule-Based	$\mathcal{O}(Nn)$	Rules Content $\And$ Weights
MNL	Linear	$\mathcal{O}(d)$	Feature Weights
Mix-MNL	Linear	$\mathcal{O}(Nd)$	Feature Weights
Vanilla NN	NN-Based	$\mathcal{O}(dd_{v}+Ld_{v}^{2})$	/
TasteNet
Deep-MNL

Appendix

Table 4: Model Comparison , In the # parameter column,

N

represents the consumer type number,

n

denotes the maximum rule number, and

d

indicates the dimensionality of the product feature vector. For NN-based models,

d_{v}

are dimensions of latent features and

L

is the number of layers. As the inherent complexity of NN-based models, their interpretability is often considered negligible.

Category	Method	Train loss	Test loss	Train accu (Top1)	Test accu (Top1)
Classic	MNL	$2.7503(\pm 0.003)$	$2.7751(\pm 0.005)$	$0.16(\pm 0.002)$	$0.1312(\pm 0.007)$
Classic	Mix-MNL (Frank-Wolfe)	$2.7472(\pm 0.003)$	$2.7679(\pm 0.004)$	$0.1631(\pm 0.002)$	$0.1382(\pm 0.011)$
DeepNN	NN	$2.9671(\pm 0.016)$	$3.0075(\pm 0.007)$	$0.0739(\pm 0.008)$	$0.0553(\pm 0.014)$
	TasteNet	$2.7178(\pm 0.022)$	$2.7511(\pm 0.054)$	$0.1759(\pm 0.012)$	$0.1620(\pm 0.027)$
	DeepMNL	$2.4603(\pm 0.024)$	$2.6001(\pm 0.040)$	$0.2564(\pm 0.004)$	$0.2099(\pm 0.006)$
	mixDeepMNL	$2.4538(\pm 0.021)$	$2.5798(\pm 0.057)$	$0.2404(\pm 0.004)$	$0.2253(\pm 0.019)$

Appendix

Table 5: Choice prediction results on the synthetic dataset. We report Negative log likelihood (NLL) loss and Top-1 choice prediction accuracy of the training and testing set. NM refers to the normal mode of our model, while RS indicates the risk-seeking mode. We extract 5 / 20 rules for both types.

Category	Method	Train loss	Test loss	Train accu (Top1)	Test accu (Top1)
Classic	MNL	$3.1482(\pm 0.029)$	$3.1423(\pm 0.032)$	$0.177(\pm 0.020)$	$0.1595(\pm 0.005)$
Classic	Mix-MNL (Frank-Wolfe)	$2.9654(\pm 0.023)$	$2.9576(\pm 0.025)$	$0.1807(\pm 0.008)$	$0.1657(\pm 0.006)$
DeepNN	NN	$3.0991$ ( $\pm 0.028$ )	$3.1669$ ( $\pm 0.023$ )	$0.2168$ ( $\pm 0.001$ )	$0.2120$ ( $\pm 0.011$ )
	TasteNet	$3.0909$ ( $\pm 0.017$ )	$3.0863$ ( $\pm 0.015$ )	$0.1503$ ( $\pm 0.007$ )	$0.1431$ ( $\pm 0.013$ )
	DeepMNL	$3.0494$ ( $\pm 0.011$ )	$3.0696$ ( $\pm 0.022$ )	$0.1566$ ( $\pm 0.002$ )	$0.1586$ ( $\pm 0.007$ )
	mixDeepMNL	$3.0283$ ( $\pm 0.020$ )	$3.0755$ ( $\pm 0.025$ )	$0.1620$ ( $\pm 0.010$ )	$0.1507$ ( $\pm 0.010$ )

Appendix

Table 6: Choice prediction on the Expedia Hotel dataset. We report Negative log likelihood (NLL) loss and Top-1 choice prediction accuracy of the training and testing set. Our Logit-Logit model performs best. NM refers to the normal mode of our model, while RS indicates the risk-seeking mode. We extract 30 rules for both types.

Feature Type	Feature Name	Variable Type	Description
Hotel Feature	PageRank	Discrete	The recommendation position of the hotel
	Star Rating	Continuous	The historical star rating
	Location Score	Continuous	The desirability of a hotel’s location
	Historical Price	Continuous	Mean price of the hotel over the last period
	Branded	Binary	If the hotel is part of a major hotel chain
	Promotion	Binary	If the hotel had a sale price promotion

Appendix

Table 7: Descrption of feature description on the Expedia Hotel dataset.

Category	Method	Train loss	Test loss	Train accu (Top1)	Test accu (Top1)
Classic	MNL	$2.9525(\pm 0.134)$	$2.9578(\pm 0.131)$	$0.1633(\pm 0.042)$	$0.1607(\pm 0.042)$
Classic	Mix-MNL (Frank-Wolfe)	$2.8267(\pm 0.029)$	$2.8341(\pm 0.028)$	$0.1883(\pm 0.014)$	$0.1875(\pm 0.013)$
DeepNN	NN	$3.1317(\pm 0.015)$	$3.2699(\pm 0.011)$	$0.1138(\pm 0.003)$	$0.0863(\pm 0.003)$
	TasteNet	$2.8278(\pm 0.032)$	$2.8384(\pm 0.025)$	$0.1877(\pm 0.007)$	$0.1885(\pm 0.009)$
	DeepMNL	$2.7722(\pm 0.022)$	$2.7833(\pm 0.030)$	$0.1999(\pm 0.006)$	$0.2020(\pm 0.007)$
	mixDeepMNL	$2.7453(\pm 0.025)$	$2.7717(\pm 0.015)$	$0.2036(\pm 0.004)$	$0.2035(\pm 0.008)$

Appendix

Table 8: Choice prediction on larger scale Expedia Hotel dataset. We report Negative log likelihood (NLL) loss and Top-1 choice prediction accuracy of the training and testing set. We extract 50/100 rules for both types.

Figure 6: Max Rule Number

Figure 7: Max Rule Length

Figure 8: Rule Prune Threshold

Category	Treatment
Vasoconstrictor	Epinephrine
	Phenylephrine
	Norepinephrine
	Dobutamine
	Dopamine
	Vasopressin

Appendix

Table 9: Description of the treatment extracted from MIMIC-IV dataset.

Item id	Abbreviation	Description	Normal Range
220546	WBC	White blood count	$4,000-10,000cells/mm^{3}$
225690	Total Bilirubin	Total Bilirubin	0.1 - 1.2 mg/dL
220235	PCO2 (Arterial)	Partial pressure of carbon dioxide (Arterial)	35 - 45 mmHg
226063	PO2 (Venous)	Partial pressure of oxygen (Venous)	30 - 40 mmHg
229761	Creatinine (whole blood)	Creatinine (whole blood)	0.5 - 1.2 mg/dL
226253	SpO2 Desat Limit	Oxygen saturation (SpO2)	95% - 100%

Appendix

Table 10: Description of the vital signs extracted from MIMIC-IV dataset. Item id is the ID extracted from MIMIC-IV tables.

Drug Name	Detected Rules
Norepinephrine	$PT>12.6\wedge ABPd\leq 59.0$ $PTT>31.6\wedge age\leq 76.0\wedge ABPd<=54.0$
Vasopressin	$PCO2(Arterial)>41.0$ $INR>1.1\wedge anchor_{a}ge\leq 66.0$
Epinephrine	$RR>20.0\wedge WBC<=6.8\wedge INR<=3.4$ $ABPs\leq 77.0$
Furosemide (Lasix)	$ABPs>93.0\wedge WBC\leq 14.55$ $ABPs>107.0$
Dobutamine	$INR<=1.4\wedge PCO2(Arterial)\leq 36.0$ $PCO2(Arterial)<=51.0\wedge ABPs<=89.0$
Dopamine	$PTT>65$ $PlateletCount<=287.0\wedge PTT>48.8$

Appendix

Table 11: MIMIC Drug Preference Rules Examples

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Discrete Choice Models Preference Learning Model Selection Choice Preference Alignment Learning

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Discrete choice modeling is a common tool used for preference elicitation during policy-making, but this is typically done through parametric models. Machine learning can push the boundaries of discrete choice modeling for policy-based preference elicitation by adopting a data-driven approach or learning individual preferences. However, there is limited knowledge of how well machine learning methods can estimate individual discrete choice rules under individual heterogeneity, especially in the context of challenges often experienced during preference elicitation. This study evaluates four machine learning models (multinomial logistic regression, generalized additive model, twinned neural network, and Gaussian process) with respect to their capacity to learn and predict five choice rules that are important in the behavioral and social sciences (linear strong utility, monotonic strong utility, ideal point, lexicographic semiorder, and multiattribute linear ballistic accumulator). Monte Carlo experiments were performed to assess model performance when increasing a) the number of attributes in the choice alternatives, b) the number of training choice sets, and c) the choice rule's determinism. The simulation results demonstrated that semi-parametric and non-parametric models generally outperform parametric models across all choice rules and experimental contexts. Model performance also generally improves by 6% to 96% and 0% to 55%, respectively, with an increase in training choice sets and choice rule determinism. A case study using real energy policy preference data was also conducted, where TNN performed best with a BIC of 13.351. This work demonstrated the viability and limitations of semi-parametric and non-parametric models in the context of policy-centric discrete choice modeling and showed how the choice task context should drive model selection.

Abstract

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