Reviewer 4 (chair) Expertise Passing Knowledge The Meta-Review The reviewers found the within-session budget idea novel and exciting -- good material for a short paper. Please note the extensive comments in preparing your revisions, especially enhancing the algorithm description. Final Recommendation after Meta-Review Probably accept: I would argue for accepting this paper. Reviewer 1 (PC) Review Rating Probably accept: I would argue for accepting this paper. Expertise Outsider's Perspective Contribution The authors outline a budget-aware model for predicting purchases on an e-commerce platform which combines notions of global and local (within-session / context) budget using learned purchase profiles that typify user behaviour. Relevance to RecSys This relates to the “User modelling” topic of interest as it seeks to model a user’s within-session budget by grouping their browsing patterns into various interpretable purchase profiles and exploiting the tendency of users to remain within certain patterns of behaviour in order to increase purchase predictability. Your Review ---Positives The model appears to be easy to understand and interpretable, as the authors state. All combinations of model components proposed here and reported on outperformed the usual BPR-MF model as well as the production model for this data and application. ---Negatives The sigmoid function is not mentioned in the explanation of equation 1 in section 3. The construction of the vectors rho_i is unclear and I don’t think that the assertion that “a vector in which the first element is activated indicates that c_i is cheaper than all previously viewed items, whereas a vector with the last element activated indicates that c_i is more expensive than all previously viewed items.” would be true if P = 2. The notions of "module" and what constitutes “top ranked” in section 4.1 are unclear. I would imagine that top ranked would be tied to the beta_i term but I think this should be stated. In equation 5, the linear combination has weights for the global and local budget components, but not for the user preference component, it is unclear whether another weighting term here would be unnecessary or if this was a modelling choice by the authors. The work relates to private data which the authors acknowledge is “unique”, and no potential open datasets that this may be applicable to are suggested. ---Suggested revisions Error bars in figure 1 extend into the negative, which is nonsensical for a budget. The use of something like non-parametric bootstrapping to draw up confidence intervals might make more sense. If possible, summarise the interpretation of equation 4 after defining its components to help with intuition. Something like, ‘the summation across purchase profiles of the components of the pattern’s price distribution vector pertaining to the item weighted by the user’s propensity to behave according to the purchase profile’. ---Missing related work The authors say that the system was “implemented in Tensorflow using the Adagrad Optimiser” and a reference for this is missing. I’m not familiar enough with the area to suggest further literature that might have been included. ---Typos The subscript order and form are inconsistent for the psi term in the equations in section 3.3 In equation 6 in section 4.2, the summation is over pairs (i,j) in E(u), but E(u) is a set of triples x_uij The word “only” is reused unnecessarily towards the end of section 4.3 Reviewer 2 (PC) Review Rating Probably accept: I would argue for accepting this paper. Expertise Knowledgeable Contribution The paper presents a session-based model for budge-aware recommendation. Different from the previous works that learns the global budge categories for each user, the proposed approach consider users' within-session budget, which is claimed to be highly predictive of users' willing-to-pay prices. Relevance to RecSys An important application of recommendation system, so it is relevant to the conference. Your Review Positive points: 1. The paper proposes a novel model that consider users' micro-behavior as an important prediction factor. The idea is intuitive and well-formulated into the model. Results demonstrate that it is improving the performance. 2. The model is interpretable. The authors did analysis in the experiment section to demonstrate why the model works better than baselines. They show the change of users' behavior in different purchase groups and price buckets identified from the models, and these differences are actually conforming to intuitions. Negative points: 1. The authors should be more clear about the fundamental difference between the proposed approach and the cited previous works, for example [23], which also focuses on users' micro-behavior. 2. It would great if the authors could describe examples or provide numeric analysis to backup their point of "session-based budget is predictive" in the Introduction section. 3. All ROC comparisons should be provided with statistical significance. Overall, the paper is well-written; it describes a valuable application of recommendation system, and provides a novel and effective solution to the problem. I would recommend accepting this paper as a short paper. Reviewer 3 (PC) Review Rating Probably accept: I would argue for accepting this paper. Expertise Knowledgeable Contribution * This paper proposes a first recommendation method modeling the within-session budget of users. This contribution is important because a user's browsing behavior for a given session is highly-determined by this user's target budget. * The novelty w.r.t. literature is clearly mentioned in Section 2. Relevance to RecSys * Within-session recommendation is a highly-relevant topic for RecSys. * Budget modeling in this recommendation scenario is a subject that required further investigation. Your Review Positives: * First method to exploit within-session bugdet. * Experimental results show usefulness of incorporating global and local budget information in the model. * Interesting analysis of purchase profiles learned by the model. Negatives: * The proposed model is a bit heuristic and would benefit from a stronger justification (e.g., global bugdet term in Eq (3), triplet sampling technique, etc.). However, this is less problematic for a short paper. * Use of private dataset, which makes this study difficult to repeat. * Comparison is a bit unfair, since other methods do not model budget. Other comments: * The global budget preference term is not clear to me. Is budget variable b_u session independent ? Is b_u learned from past data ? Shouldn't x^(2)_ui be asymetrical (i.e., treat b_u > c_i differently than the opposite case) ? * The model in Eq. (5) is highly non-convex. How sensitive are the results to optimization ? * Table 2: the difference between cheap and expensive items is smaller than I expected. Please explain.