Rethinking travel behavior modeling representations through embeddings

Francisco C. Pereira

REVIEW 3 major objections 5 minor 1 cited by

Rethinking travel behavior modeling representations through embeddings

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Re-representing categorical travel variables as learned low-dimensional embeddings improves out-of-sample mode choice models.

desk verdict Genuinely novel application of embeddings to categorical variables in discrete choice, but the headline out-of-sample gain probably reflects respondent-level train/test leakage. read the letter →

arxiv 1909.00154 v1 pith:I2P7AFGG submitted 2019-08-31 econ.EM cs.CLcs.LG

Francisco C. Pereira This is my paper · ORCID

classification econ.EMcs.CLcs.LG

keywords travelbehaviorembeddingscategoricalvariablesmodechoicemultinomiallogitlatentrepresentationword2vecSwissmetrolearning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Travel behavior embeddings re-represent the discrete variables used in mode choice models—trip purpose, age, income, ticket type, who pays, and origin–destination pair—as points in a low-dimensional latent space learned from data, rather than as dummy variables or PCA components. The paper applies this to the Swissmetro dataset and reports out-of-sample gains of up to 20% in log-likelihood over the corresponding dummy-variable model (and up to 60% over an initial baseline model), with test pseudo-$R^2$ of 0.326 versus 0.307–0.308 for the alternatives. Because the embedding space is shared, estimates for rare categories borrow strength from the whole dataset: the model recovers statistically significant coefficients for 164 of 178 origin–destination pairs, where a full dummy specification yields none. The practical stakes are that cheaper, coarser travel surveys could support rich choice models by reusing embeddings learned from larger, lighter datasets.

What carries the argument

The Travel Embeddings layer is a softmax-output neural network that takes a one-hot input for each categorical variable, multiplies by an embedding matrix $W$ of size $K \times D$ ($D$ categories in, $K$ embedding coordinates out), and feeds the resulting vector, together with other variables, into the final choice softmax. A second softmax regularizer branch tries to reconstruct the original one-hot vector, penalizing embeddings that throw away too much category identity. All embedding matrices are trained simultaneously on a train split, with the model chosen by development-set likelihood; after estimation the embeddings are projected back to dummy space to recover interpretable category coefficients and $p$-values. MDS plots of the resulting vectors let modelers read closeness between categories as similarity of effects on mode choice.

What would settle it

Using synthetic mode-choice data with known OD effects that are deliberately high-rank (e.g., 178 independent draws with no shared structure), fit the $K=3$ embedding model and a full dummy model; if the embedding still reports most OD coefficients as statistically significant, those significance claims are an artifact of forcing data through a rank-3 linear bottleneck rather than evidence of true structure.

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Extended reading notes

Core claim

The central claim is that a categorical variable's effect in a random-utility mode choice model can be carried by a small vector in an embedding space, estimated jointly with the choice model by a neural network with a softmax output, and then projected back to the original dummy-variable coefficient space without losing interpretability. In the Swissmetro experiment, the best embedding model estimates 39 parameters instead of the 232 of the full dummy specification, reaches test pseudo-$R^2$ 0.326, and yields 164 statistically significant OD-pair coefficients; the full dummy model collapses on the test set (pseudo-$R^2$ -0.789), the reduced dummy model reaches 0.307, and PCA reaches 0.308. The paper reads these results as evidence that sharing a latent space lets every observation contribute to every category's estimate, and that supervised, task-specific encodings carry information an unsupervised PCA projection does not.

Load-bearing premise

The load-bearing premise is that the effect of every category—especially each of the 178 origin–destination pairs—can be captured by a point in a three-dimensional Euclidean space, so that Euclidean distance between points faithfully mirrors similarity of the categories' effects on mode choice.

Editorial extensions

If this is right

High-cardinality categorical variables like OD pairs can enter choice models without the dimensionality explosion that makes dummy-variable estimation fail; the Swissmetro result of 164 significant OD coefficients is the direct evidence.
Survey design can be split into a cheap light part (mode plus OD plus ticket) and a small detailed part; embeddings learned from the light part keep the choice model competitive at detailed-sample percentages as low as 10%.
Because embeddings are task-specific, the same variable will receive different encodings for different choice problems, unlike PCA or dummy schemes, which are fixed representations.
Coefficients remain interpretable: by projecting back to the dummy-variable space, the model yields category-level coefficients and significance tests, so the method is not a black box.
The advantage shrinks as datasets grow; with large, well-balanced samples the paper expects dummy variables to be sufficient.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A testable extension of the paper's logic is that one categorical variable should receive different embeddings for different targets (mode choice versus departure time versus destination choice), and the distances between categories should reshuffle accordingly; this follows from the supervised design but is not demonstrated in the paper.
The strong OD result suggests a geometric prediction: if OD effects are truly low-rank in $K=3$, the dominant axes should align with major transport corridors or city-pair volumes, a check that the paper's MDS plots only hint at.
The transferability claim predicts that embeddings trained on one city's or country's travel survey should improve out-of-sample fit in another survey precisely when travel behavior is consistent between them; running that cross-dataset test would settle the community-database vision.
Because the embedding is a linear projection, it could be inserted into nested or mixed logit specifications as continuous covariates in taste parameters, preserving the projection-to-dummy interpretation; this is a natural next step the paper mentions only as future work.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new thing here is the application of word2vec-style embeddings to categorical variables inside a multinomial logit mode choice model, with a regularizer that reconstructs the one-hot input and a projection back to dummy space for interpretability. On the practical side, the author has done the right things: open data, released PyTre, repeated runs, an explicit train/dev/test split, and a candid limitations section that admits the stochasticity problem. The MDS visualizations and the idea of shared latent spaces for small categoricals are a real contribution to travel behavior modeling.

But the central empirical claim is not established. The stress-test note about the panel structure is correct and important. Swissmetro is 10,469 responses from 1,188 individuals, and the split is described as 60/20/20 of vectors, not of respondents. Nothing in the text says all choices from a given person were kept in the same fold. A row-level split puts repeated choices from the same respondent in train and test. For a stated-preference panel, that is leakage: the model can memorize person-level response patterns through OD, ticket, age, and income combinations. The test log-likelihood then no longer measures generalization to new travelers, and the comparison with PCA and dummies is unfair. This is not a minor quibble; it undermines the abstract's 'up to 20% out-of-sample' claim.

Even taking the numbers at face value, the typical run is only slightly better than PCA: mean test LL -1415.7 vs PCA -1427.0, with SD 11.3. The headline uses the best of 300 runs, which is a selected maximum. The paper honestly reports the range but does not correct for selection. Also, K values and regularization hyperparameters come from an unspecified grid search on the development set, and the projection-back p-values treat embeddings as known rather than estimated, so the 164 'significant' OD coefficients should be read as illustrative, not inferential.

Who gets value? Travel demand modelers curious about representation learning will find the idea and the package worth their time. The paper is clearly written and the method is reproducible. But as it stands, the empirical section needs major work: redo the split at the respondent level, report mean/median and a proper selection rule, and either fix the p-value procedure or drop the significance claims. I would send this to peer review, not desk reject, because the core method is novel and the author has provided the tools to verify it. A serious referee should run the leakage check first.

Referee Report

3 major / 5 minor

Summary. The paper proposes 'travel behavior embeddings,' a method that re-represents categorical variables from travel surveys (e.g., origin-destination, ticket type, who pays, age, income) as low-dimensional continuous vectors learned by a neural network, in the spirit of word2vec. The embeddings are trained simultaneously with a regularizer layer, then fed as regressors into a multinomial logit mode-choice model for the Swissmetro dataset. The authors compare out-of-sample performance against dummy-variable encodings (with and without origin-destination effects) and PCA encodings, reporting that their best embeddings model achieves the highest test pseudo-R2 and can estimate statistically significant coefficients for 164 of 178 OD pairs. They also present scenario analyses for efficient survey design and release a Python package, PyTre, with replication code and data.

Significance. If the empirical claims hold, the paper makes a useful methodological contribution by adapting embedding techniques to discrete-choice travel behavior modeling, with the practical benefits of dimensionality reduction and shared latent structure. The open-source package and reproducible notebook are clear strengths, as is the repeated-run design with a development set (300 runs) and the explicit reporting of mean and standard deviation. The projection back into dummy-variable space for interpretability is also a valuable feature. However, the headline result depends on several load-bearing assumptions about the experimental design and the stability of the reported gains; the stated 'up to 20% out-of-sample improvement' is not robustly established by the evidence in the current version.

major comments (3)

[Section 5.1 (experimental split)] Section 5.1 states that the Swissmetro data consist of 10,469 responses from 1,188 individuals, and then describes the split only as '60% of the dataset (6373 vectors)', '20% (2003 vectors)', and '20% (2003 vectors)'. Because this is a stated-preference panel with repeated choices per person, a row-level random split likely places the same respondents in both the training and test sets. The test-set log-likelihoods in Table 12, which are the basis of the paper's central out-of-sample claims, would then reflect within-person leakage rather than prediction for new travelers, and the pseudo-R2 differences would not measure true out-of-sample generalization. The paper needs either an individual-level split, a clustered evaluation that accounts for repeated observations, or an explicit and defensible justification for treating each choice as independent.
[Section 5.3 and Table 12 (model selection and reported gains)] The test-set comparison in Table 12 uses the single best embeddings model out of 300 runs, selected by development-set log-likelihood. The reported mean test log-likelihood is -1415.7 with standard deviation 11.3, versus -1427.0 for PCA and -1429.3 for reduced dummies; the 'best' value is -1389.9. The mean improvement over PCA is only about 0.8% and is well within one standard deviation of the run-to-run variation. The headline 'up to 20%' improvement is therefore an extreme-statistic artifact unless the full distribution of test performances and the selection procedure justify it. The authors should report the distribution, compare mean embedding performance against PCA, and, if claiming superiority, provide a statistical test that accounts for the multiple comparisons across the 300 runs.
[Section 5.2 (Table 3) and Section 5.3 (projected OD coefficients)] The embedding dimensions K in Table 3 are chosen through an 'incremental grid search' whose exact range, criterion, and number of configurations are not specified; this makes it unclear how much model selection is being performed and whether the reported results capitalize on chance. Additionally, the 164 'statistically significant' projected OD coefficients in Table 6 treat the learned embeddings as fixed when applying normal-distribution linear-combination rules, ignoring the sampling variability of the embedding estimates themselves. The p-values are thus conditional on a stochastic, data-driven representation and are likely anticonservative. The authors should either provide a bootstrap procedure that re-estimates embeddings, or clearly state and justify the conditional interpretation.

minor comments (5)

[Abstract and Section 1] The abstract contains the typo 'model choice model' instead of 'mode choice model,' and Section 1 has 'efects' for 'effects.' These should be corrected.
[Table 12] The row labeled 'Embeddings (mean)' reports the same training log-likelihood (-4,397.0) as the 'Embeddings (best)' row despite the standard deviation of 10.7; this is either a typo or requires clarification of what the mean was computed over.
[Section 5.2] The choice of K using the '90% variance explained' PCA rule is mentioned only parenthetically, and the reader is told the results were 'generally worse' but not shown. Since this is a natural data-driven baseline for setting K, a brief summary of those results would improve transparency.
[Section 5.6] The 'Big Data + detailed survey' simulation (Figure 10, right) is described at a high level, but the exact procedure for splitting the Swissmetro data into 'big data' and 'detailed' portions, and the number of repetitions used, are not specified; error bars or confidence intervals would help interpret the comparisons.
[References] Reference [1] is given as 'Tech. rep.' without a number or year; the standard Swissmetro report (Bierlaire, Axhausen, and Abay, 2001) should be cited in a complete form.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the embeddings are supervised, but the claimed improvements are measured on a held-out test set against independent baselines.

full rationale

The paper's central claim is empirical: embedding encodings of categorical variables improve out-of-sample mode-choice log-likelihood relative to dummy and PCA encodings. This claim is not equivalent to an input by construction. The embeddings and the final MNL are both estimated on the training set, but the reported headline numbers (Table 12: test log-likelihood -1,389.9 for embeddings vs -1,429.3 for reduced dummies and -1,427.0 for PCA) are evaluated on a 20% test split (Section 5.1) that is not used for estimating the embeddings or the choice-model coefficients. The K values come from a grid search on the development set (Section 5.2), and the best of 300 stochastic embedding runs is selected by development-set log-likelihood (Section 5.3); this is ordinary model selection, not a fitted parameter renamed as a prediction, because the test set remains out-of-sample for the reported comparisons. The projection of 164 statistically significant OD coefficients is a linear reparameterization of the low-dimensional embedding coefficients, with significance propagated by the stated normal-rule in Section 3; it is an interpretation of the fitted model, not a separate prediction. The only self-citation ([11], Rodrigues, Markou, and Pereira) is motivational and is not load-bearing for the Swissmetro experiment, which uses open data and external baselines (Swissmetro, PyLogit). No uniqueness theorem is invoked, and no equation is assumed as its own conclusion. A separate validity concern exists: the row-level random split may leak repeated choices from the same 1,188 respondents between folds (Section 5.1 reports only percentages of vectors, not respondent-level separation), and the paper's limitation discussion acknowledges stochasticity but not panel structure. That is an empirical correction issue relevant to the strength of the comparison, but it is not a circularity of definition.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central comparison rests on several fitted or hand-chosen quantities: embedding dimensions K per variable, regularization strengths that are not reported, and the number of training epochs. In addition, the method assumes low-dimensional Euclidean structure in category semantics and a valid supervised feature-learning protocol.

free parameters (7)

Embedding size K for OD = 3
Selected by incremental grid search on the development set; controls the capacity of the OD latent space (§5.2, Table 3).
Embedding size K for TICKET = 5
Selected by the same grid search for a 10-category ticket variable (§5.2, Table 3).
Embedding size K for WHO = 1
Selected by grid search for a four-category payer variable (§5.2, Table 3).
Embedding size K for AGE = 3
Selected by grid search for a six-category age variable (§5.2, Table 3).
Embedding size K for INCOME = 3
Selected by grid search for a four-category income variable (§5.2, Table 3).
Regularization penalty hyperparameters = not reported
The loss includes regularization terms for embeddings and regularizer layers, but their values are not given, so the results depend on unreported tuning (§4.2, §5.3).
Training epochs and optimizer settings = 80 epochs; optimizer not specified
The paper reports 80 epochs per run but not learning rate, batch size, or optimizer, which affect the learned embeddings (§5.3).

assumptions (6)

domain assumption Random utility maximization and multinomial logit are appropriate for mode choice analysis.
All models in the paper are MNL estimated with PyLogit; if IIA or linear utility is violated, the comparison may not reflect real behavior, though all baselines share the same limitation.
ad hoc to paper Categories with similar effects on mode choice are close in a low-dimensional Euclidean embedding space.
This is the core modeling assumption of the method, not derived from RUM or data; it is introduced in Section 4.1.
ad hoc to paper A 3-dimensional linear space is sufficient for the mode-choice-relevant variation of 178 OD pairs.
K=3 for OD is chosen by grid search; if OD effects have higher intrinsic dimensionality, the projected OD coefficients and their significance are artifacts.
domain assumption Using the same choice outcome to learn embeddings and to estimate the final choice model, on the same training set, yields a fair comparison.
The paper does not discuss this double use of labels; it relies on the train/dev/test split to ensure generalization.
domain assumption The 10469 Swissmetro responses from 1188 individuals can be treated as independent observations.
No clustering or panel correction is applied, so standard errors and p-values are likely optimistic.
ad hoc to paper Projected dummy-space coefficients and p-values can be obtained by treating learned embeddings as fixed and applying normal linear-combination rules.
The covariance of the estimated embeddings is not accounted for; the distributional claim in Table 6 is not established.

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Cite this review

Pith. "Pith review of Rethinking travel behavior modeling representations through embeddings." pith.science (2026). https://pith.science/paper/I2P7AFGG

@misc{pith2026190900154,
  author       = {Pith},
  title        = {Pith review of: Rethinking travel behavior modeling representations through embeddings},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I2P7AFGG}},
  note         = {Machine review of arXiv:1909.00154}
}

read the original abstract

This paper introduces the concept of travel behavior embeddings, a method for re-representing discrete variables that are typically used in travel demand modeling, such as mode, trip purpose, education level, family type or occupation. This re-representation process essentially maps those variables into a latent space called the \emph{embedding space}. The benefit of this is that such spaces allow for richer nuances than the typical transformations used in categorical variables (e.g. dummy encoding, contrasted encoding, principal components analysis). While the usage of latent variable representations is not new per se in travel demand modeling, the idea presented here brings several innovations: it is an entirely data driven algorithm; it is informative and consistent, since the latent space can be visualized and interpreted based on distances between different categories; it preserves interpretability of coefficients, despite being based on Neural Network principles; and it is transferrable, in that embeddings learned from one dataset can be reused for other ones, as long as travel behavior keeps consistent between the datasets. The idea is strongly inspired on natural language processing techniques, namely the word2vec algorithm. Such algorithm is behind recent developments such as in automatic translation or next word prediction. Our method is demonstrated using a model choice model, and shows improvements of up to 60\% with respect to initial likelihood, and up to 20% with respect to likelihood of the corresponding traditional model (i.e. using dummy variables) in out-of-sample evaluation. We provide a new Python package, called PyTre (PYthon TRavel Embeddings), that others can straightforwardly use to replicate our results or improve their own models. Our experiments are themselves based on an open dataset (swissmetro).

Figures

Figures reproduced from arXiv: 1909.00154 by the authors.

**Figure 1.** The skip gram architecture [7] yn are one-hot (dummy) encodings of categorical variables4 . The dimensionality of xn is D × 1, with D being the number of different categories in xn, while the dimensionality of yn is C × 1, with C being the number of categories (alternatives) in yn. The full expression for the embeddings model as described is: p(yn = c|xn) = e BcW xn+αc PC j=1 e BjW xn+αj where W is the embeddings m… view at source ↗

**Figure 2.** Visualization of a subset of words from FastText word embeddings database [8] [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Some classical examples of embeddings algebra [9] [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: The general idea From an experimental design and application perspective, the approach followed in this paper is the following: 1. Create list of categorical variables to encode (the encoding set) 2. Split dataset into train, development and test sets 3. For each vari…

**Figure 5.** Figure 5: Travel embeddings model The dataset sizes in transportation behavior modeling are substantially smaller than typical word embeddings ones, and the risk of overfitting is therefore higher. To mitigate this problem, besides adding regularization penalties in the objecti…

**Figure 6.** Figure 6: Travel embeddings model with regularization (left); Complete model, combining [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: Embeddings model training performance Since the dimensionality of embeddings is higher than 2, it becomes humanly impossible to directly visualize them. A common technique to use is called Multi-dimensional scaling (MDS), which is similar to the one presented in [PITH…

**Figure 8.** Figure 8: MDS visualizations of embeddings results [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

**Figure 9.** Figure 9: Switzerland’s cantons Notice that the number of parameters will be higher than the simpler model presented before. The original one has 14 variables, but it now grows up to 39. This is still quite small, if we consider the fully expanded dummy variables specification (…

**Figure 10.** Figure 10: R-square performance with percentage of “expensive" survey. Left: light+detailed [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Aligning LLM with human travel choices: a persona-based embedding learning approach
cs.AI 2025-05 conditional novelty 6.0 of 10

A persona-based embedding learning framework aligns LLM predictions with human travel mode choices, outperforming MNL and few-shot LLM baselines on the Swissmetro dataset.

Reference graph

Works this paper leans on

15 extracted references · 13 canonical work pages · cited by 1 Pith paper

[1]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Bierlaire, K

M. Bierlaire, K. Axhausen, G. Abay, The acceptance of modal innovation: The case of swissmetro, Tech. rep. (2001)

work page 2001

[2] [2]

M. E. Ben-Akiva, S. R. Lerman, S. R. Lerman, Discrete choice analysis: theory and application to travel demand, Vol. 9, MIT press, 1985

work page 1985

[3] [3]

N.Arora, G.M.Allenby, J.L.Ginter, Ahierarchicalbayesmodelofprimary and secondary demand, Marketing Science 17 (1) (1998) 29–44

work page 1998

[4] [4]

M. J. Davis, Contrast coding in multiple regression analysis: Strengths, weaknesses, and utility of popular coding structures, Journal of Data Sci- ence 8 (1) (2010) 61–73

work page 2010

[5] [5]

Guthrie, B

D. Guthrie, B. Allison, W. Liu, L. Guthrie, Y. Wilks, A closer look at skip-gram modelling., in: LREC, 2006, pp. 1222–1225

work page 2006

[6] [6]

Mikolov, K

T. Mikolov, K. Chen, G. Corrado, J. Dean, Eﬃcient estimation of word representations in vector space, arXiv preprint arXiv:1301.3781

arXiv

[7] [7]

Word2vec tutorial - the skip-gram model, http://mccormickml.com/ 2016/04/19/word2vec-tutorial-the-skip-gram-model/ , accessed: 2019-06-30

work page 2016

[8] [8]

Fasttext - embeddings for 157 languages,https://fasttext.cc, accessed: 2019-06-19

work page 2019