Density-based User Representation using Gaussian Process Regression for Multi-interest Personalized Retrieval
Authors: Haolun Wu
Ofer Meshi
Masrour Zoghi
Fernando Diaz
Xue Liu
Craig Boutilier
MARYAM KARIMZADEHGAN
Venue: NeurIPS 2024 poster (2024)
Keywords: User Representation
Recommendation
Retrieval
Gaussian Process Regression
Primary area: machine_learning_for_other_sciences_and_fields

Abstract: Accurate modeling of the diverse and dynamic interests of users remains a significant challenge in the design of personalized recommender systems. Existing user modeling methods, like single-point and multi-point representations, have limitations w.r.t.\ accuracy, diversity, and adaptability. To overcome these deficiencies, we introduce density-based user representations (DURs), a novel method that leverages Gaussian process regression (GPR) for effective multi-interest recommendation and retrieval. Our approach, GPR4DUR, exploits DURs to capture user interest variability without manual tuning, incorporates uncertainty-awareness, and scales well to large numbers of users. Experiments using real-world offline datasets confirm the adaptability and efficiency of GPR4DUR, while online experiments with simulated users demonstrate its ability to address the exploration-exploitation trade-off by effectively utilizing model uncertainty.

Density-based User Representation using Gaussian Process Regression for Multi-interest Personalized Retrieval
Haolun Wu 1.2
Ofer Meshi
Masrour Zoghi"
Fernando Diaz*
Xue Liu 2
Craig Boutilier
Maryam Karimzadehgan'
McGill University
Mila Quebec Al Institute
Google Research
haolun. wwwmail mogialli.mmgil.l. ca, xueliu@cs sueliu@cs.mogill. ca, diazf@acm org
cbouti iier, maryamk
| @google. com
Abstract
Accurate modeling of the diverse and dynamic interests of users remains sig- nificant challenge in the design of personalized recommender systems. Existing user modeling methods, like single-point and multi-poin representations, have limitations w.r.t. accuracy, diversity, and adaptability. To overcome these deficien- cies, introduce density-bused user representations (DURs), novel method that leverages Gaussian process regression (GPR) for effective multi-interest recom- mendation and retrieval. Our approach, GPR4DUR, exploits DURs capture user interest variability without manual tuning. incorporates scales well large numbers of users. Experiments using real-world offline datasets confirm the adaptability and efficiency of GPR4DUR, while online experiments with simulated users demonstrate its ability to address the exploration-exploitttio trade-off off by effectively utilizing model uncertainty.
eeeertaintt-wwarenee and
Introduction
With the proliferation of online platforms, users have ready access content, products and services drawn from a vast corpus of candidates. Personalized recommender systems (RSs) play a vital role in reducing information overload and helping users navigate this space. It is widely recognized that users rarely have a single intent or interest when interacting with an RS [ 2 3. To enhance personalization, recent work focuses on discovering a user's multiple interests and recommending items that attempt to span their interests 3 5. However, this is challenging for two reasons. First, user interests are diverse and dynamic: diversity makes it hard to detect all interests, while their dynamic nature renders determining which user interest is active at any given time quite difficult. Second, is hard to retrieve items related to niche interests due to the popularity bias ().
User representation is fundamental design choice in any RS. The most widely used strategy for user modeling is the single-poin user representation (SUR), which uses a single point in an item embedding space to represent the user. The user's affinity for an item is obtained using some distance measure (e.g., inner product, cosine similarity) with the point representing the item. However, SUR can limit the accuracy and diversity of item retrieval 77); hence, most RSs generally use high-dimensional embedding vectors (with high computation cost).
To address the limitations of SUR, MaxMF [I adopts a multi-point user representation (MUR), where each user is represented using K points the embedding space, each reflecting a different "interest" MaxMF uses a constant, uniform K across all users (e.g., K = 4), which is somewhat ad hoc and
Work done while doing internship Google.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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restrictive. Subsequent research uses other heuristics 8 4 1O 11 or clustering algorithms [5 2 to determine the number of interests per user. However, these all require the manual choice of K or a specific clustering threshold, limiting the adaptability of MUR methods, since interests generally have high variability across users. Moreover, uncertainty regarding user's interests is not well-modeled by these methods, diminishing their ability to perform effective online exploration.
To address limitations of SUR and MUR point- based representations, we propose a user repre- sentation that emphasizes (i) adaptability, adapt- ing to different interest patterns; (ii) uncertainty- awareness, modeling uncertainty in assessing user interests; and (iii efficiency, avoiding high- dimensional emheddings. Specifically, we use a density-hased representation, where the user's preferences are encoded using a function over the item embedding space. Under this rep- resentation, the relevance score for user-item pairs should be higher in regions of embedding space where a user demonstrated more interest in the corresponding items, and lower in regions where users have shown limited interest. We propose the crrnsity-based user representation (DUR), a novel user modeling method which exploits Gaussian process regression (GPR)
SUR
MUR
Mean
GPR Std (uncortainty)
143
L23
Figure 1: The t-SNE visualization of the predic- tion score between a picked user to all items in the MovieLens dataset. The score is computed as the inner-product between the user embedding and item embedding. The triangles (A) indicate the latest 20 items interacted by the user. We use Ma- trix Factorization (MF) to obtain embeddings in this toy example. As depicted, only density- -based method (bottom row) can well capture user inter- ests with uncertainty.
13, a well-studied Bayesian approach to non-parametric regression using Gaussian pro- cesses (GPs) to extrapolate from training to test data. GPR has been applied across wide range of domains, though it has been under-exploree in user modeling. Given a sequence of user in- teractions, GPR predicts the level of a user's interest in any item using its posterior estimates. GP regressor for each user, effectively capturing their evolving preferences and assessing uncer- tainty. Top-N item retrieval performed using bandit algorithms, such as UCB 14 or Thompson sampling 15 based on GPR posterior estimates.
This allows us maintain a unique personalized
To illustrate, consider Fig. D which shows the prediction score (i.e., the inner-product between user and item embeddings) between a user and all movies from the MovieLens IM dataset [16] (reduced 2D for visualization purposes). We examine 20 movies from the recent history of particular user, shown as triangles ). We see that these movies lie in several different regions of the embedding space. However, when we fit either SUR or MUR (K 4) models, they fail to capture the user's multiple interests and instead assign high scores only to movies from a single region (Fig. [ top row). By contrast, we see in Fig. D (bottom left) that GPR fits the data well, assigning high values to all regions associated with the user's 's recent watches (interests). Fig. (bottom right) shows that our approach can also capture uncertainty in our estimates of user's interests, assigning high uncertainty to regions in embedding space with fewer samples.
Our approach has various desirable properties. First, it adapts different interest patterns, since the number of interests for any given user is not set manually, but determined by GPR, benefiting from the non-parametric nature of GPs. Second, the Bayesian nature of GPs measures uncertainty with the posterior standard deviation of each item. This supports the incorporation of bandit algorithms in the recommendation and training loop to address the intorratioo-expliitaaion trade-off in online settings. Finally, our method can effectively retrieve items spanning multiple user interests, including "niche" interests, while using a lower-dimensional embedding relative to SUR and MUR.
To summarize, our work makes the following contributions:
We develop GPR4DUR, a density-based user representation method, for personalized multi- interest retrieval. It the first use of GPR for user modeling this setting.
We propose new evaluation protocols and metrics for multi-interen retrieval that measure the extent to which a model captures user's multiple interests.

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We conduct comprehensive experiments on real-world offline datasets showing the adapt- ability and efficiency of GPR4DUR. Online experiments with simulated users show the value of GPR4DUR's uncertainty representation in balancing exploration and exploitation.
2
Related Work
Learning high-quality user representations is central good RS performance. The single-point user representation (SUR) is the dominant approach, where a user is captured by a single point in
some embedding space [17 [8), for example, as employed by classical 19 20 21 and neural [22] collaborative filtering methods. While effective and widely used, SUR cannot reliably capture user's s multiple interests. To address this limitation, the multi-point user representation (MUR) ( has been proposed, where a user is represented by multiple points in embedding space, each corresponding to a different "primary" interest. Selecting suitable number of points K' critical in MUR. Existing algorithms largely use heuristic methods, e.g., choosing global constant K for all users [I 8 3 2 TO [... Other methods personalize K by setting it to the logarithm of the number of items with which user has interacted [5]. More recently, Ward clustering of user's 's past items has been proposed, with a user's determined by the number of such clusters This too requires manual tuning of clustering thresholds.
At inference time MUR is similar to SUR, computing the inner- inner-product of the user embedding(s) and item embedding. Some methods compute K inner products, one per interest, and use the maximum as the recommendation (and the predicted score for that item) [ Others first retrieve the top-N items for each interest (N x K items), then recommend the top-N items globally 3 2) None of these methods capture model uncertainty w.r.t. a user's interests, hence they lack the ability to balance exploration and exploitation in online recommendation in a principled way (23].
Our density-based user representation, and our proposed GPR4DUR, differs from prior work w.r.t. both problem formulation and methodology. Most prior MUR methods focus on next-ilem prediction II. implicitly assuming single-stage stage RS, where the trained model is the main recommendation engine. However, many practical RSs consist of two stages: candidate selection (or retrieval) followed by ranking (24 25 This naturally raises the question: are the selected candidates diverse enough to cover user's 's interests or intents? This is especially relevant when a user's dominant interest the time of recommendation is difficult to discern with high probability; hence, it is important that the ranker have access to a diverse set of candidates that cover the user's range of potential currently active interests. In this paper, we focus on this retrieval task. As for methodology, almost all prior work uses SUR or MUR point-based representations. 02 5 - fail to satisfy all the desiderata outlined in Sec. [] criteria, and, to the best of our knowledge, the first to adopt GPR for user modeling in multi-interest recommendation//etiivall We frame our solution as a candidate generator to be used in the retrieval phase of an RS. Other candidate generators with different objectives can be used in parallel to ours.
Instead, we propose DUR, a novel method satisfying these
related non parammaeetiic recommendation approach with similar preferences are identified (e.g., in user embedding space), and their ratings generate recommendations (see, e.g., (26). Our approach differs by not using user embeddings, but fitting a GPR model directly to item embeddings (see Sec. 4.4) allowing for uncertainty in the user model.
neighbos (kNN), where users
3 Formulation and Preliminaries
In this section, we outline our notation and multi- retrieval problem formulation, and provide some background on GPR, which lies at the core of our DUR method.
Notation.
We consider scenario where each item is associated with category information (e.g., genre for movies). Denote the set of all users, items, and categories by 4. V. and C, respectively. For each U, whose interaction history has length l,,, partition the sequence of items V,, in u's history into two disjoint lists based on the interaction timestamp (which are monotonic increasing):
(i) the history set !! = [[uu, Uu,2 ..., Vw, serves as the model input; and (ii) the holdout set y [Fu.k_ +1: Vn,l, +2; ..., v, is used for evaluation. We define u's interests C(V,) to be the set of categories associated with all items in u' history. Our notation is summarized in Appendix A.I
3

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Pre-fraiming
GPR4DUR
Retrieval
Predicted scores
Observed points
high uncerberity
uncaybarnty
UC,
Recommesdbiion Rcclbonn
Thompson Sampling
Observed 2
Emboddiing:
All points
GPR
Top-N Items
GPR Parameter Tuning
Figure 2: The architecture of GPR4DUR: an example movie recommendation for single user.
Problem Formulation. We formulate the multi-inten inntr-sitterest retrieval problem follows: given Va aim to retrieve the top N items R,, (i.e., [R... = N) w.r.t. some matching metric connecting R. and Vu that measures personalized retrieval performance. We expect R, contain relevant items, and given focus multi-interest retrieval, R., should ideally cover all categories in C(VW).
Our problem is related to sequential recommendation,, where the input is sequence of interacted items sorted by the timestamp per user, and the goal is to predict the next item with which the user will interact. However, here we focus on retrieving a set of items that cover a user's diverse interests. We defer the task of generating precise recommendation list to downstream ranking model.
GPR.
The core of our model is Gaussian process regression (GPR). A Gaussian Process (GP) is con-paraettric model for regression and classification. GPR models a distribution over over functions, providing not only function value estimates for any input, but also uncertainty quantification via predictive variance, enhancing robust decision-making and optimization [27
The key components of the GP are the mean function and the covariance (kernel) function, which capture the prior assumptions about the function's 's behavior and the relationships between input points, respectively [13]. Let X = [x1,..... x,) E R." nxd be set of input points and y = ... Vn. E TR." be the corresponding output values. A GP is defined as: ~ GP (p, k), where μ(x) the mean and k(x, x') is the covariance function. The joint distribution of the observation and the output at a new point is derived using Gaussian distribution, illustrated in Appendix A.
4 Methodology
We outline density-based user representation using GPR and its application to multi-interest retrieval.
4.1 GPR for Density-based User Representation
We use GPR to construct novel density- -ased user representation (DUR) for in RSs. Our key insight involves using GPR learn DUR, using user's interaction history, that naturally embodies their diverse interest patterns. For any user u. let V.. [V,,1, Va,2. ..., Vu,t, I xd be the embeddings of items in their history. This derived from their interaction list V. and an item embedding matrix V (we describe how to obtain V in Sec. (.4). Let o, [o,,vlv E
modeling
v.J R be the vector of u's observed interactions with items in V., We employ a GP to model u's interests given the input points V, and corresponding observations o In. (pur k.), where, Ju. H4, and k, are u's personalized GP regressor, mean, and kernel function, respectively. The joint distribution of observation o,, and the predicted observation of novel item V4 is:
[ [v((v.)
1 - M. (V.)
K(V., Vo k(v..V.)
k(V..v.) 1) t(v..v))to
(u((v)) [L
For simplicity, we assume ,4, and a commom kernel function and variance across all users. Assuming implicit feedback, we have o., i.c., shows "interest" in all interacted items. Thus,

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the posterior (prediction) (v) for any v E V is:
Iu [v) (Nw cov(gu)),
(2)
where the GP mean In and variance cov(gu) are:
fu =k(v, V.)[K(V.. V.) o I'1 ow. cov(g.) = =k(vv)++ -Kv..V.I k(V
(3)
(4)
4.2 Retrieval List Generation
After obtaining DUR Iu for E U using GPR, generate the retrieval list using the posterior gv(v) over all unobserved items. The top itemss with the highest values form our retrieval list. We consider methods for selection: (i) Thompson sampling (TS), probabilistic method that selects items based on posterior sampling [15] and (ii) Upper Confidence Bound (UCB), a deterministic method that selects items based on their estimated rewards and uncertainties [4] the retrieval list generation is shown in Appendix A.2
The details for
4.3 GPR Parameter Tuning
The free parameters in our model are the kemne function & and the standard deviation in Eq. [ treat these as byperparameters of GPR which are optimized using evaluation on separate holdout set. Specifically, to generate R., for user u, fit the GPR model not to the complete interaction history Vu. but to the reduced history yh using the item embeddings and observed ratings. We assess retrieval performance using specific metrics (see Sec. 5.3) on both R,, and the holdout set Va We tune GPR parameters using these criteria (we detail the adjustable parameters in Sec. 5.2)
We
4.4 Item Embedding Pre-training
we assume that item embeddings are fixed and precomputed: this ensures rapid computation and real-time updates at serving time. For item embedding pre-training, we use extreme multi-class classification [3 29 30) given a training sample (u, 12), we first compute the likelihood of ui interacting with Uj. i.e., p(u)lu;) = exp(u, ΣvEV exp(u,v'). where u; and Vj are embeddings of u, and v/y. Our objective is maximize the log- likelihoooo of user interacting with their items. Moreover, we want to ensure that item embeddings align with their categories since categories explicitly indicate user's interests. We capture teemccategory information by computing the likelihood that an item belongs to category in similar way: p(cx exp(v) c2 Ex log-likelihoods using scaling factor
Following [2]
exp(v)cc), The overall objective for pre-training combines the two negative
C= Σ 1ogp(1,lu))>> Σ logr(calu,). CLEC.
RYEV..
where V,, is the set of items that u, interacted with and Cr, is the set of categories that vy belongs to. The full item embedding matrix V is jointly learned and fixed after the pre-training phase. We do use user and category embeddings after pre-training; other schemes, such as using item co-occurrence information derive item embeddings without user or category embeddings, are possible. The full architecture for GPR4DUR is depicted in Figure 2
4.5
Computational Complexity
The complexity of GPR is (( where by the number of training samples, due to covariance matrix inversion (Eq 3 and Eq. 4). This inversion is required only once and is manageable with few thousand examples, If the history length is too large, we either select representative subset of interactions or focus on the most recent interactions (we adopt this latter approach in our experiments).
Inference costs for each test point are O for mean and O((e,) )²) for variance prediction, thus linear in the number of test points |V]. As shown in Appendix A.7 our method has reasonable computational costs, slightly higher than strong baselines with better performance on retrieval
and ranking, demonstrating its applicability in real-worl world scenarios. Our approach is best-suited
5

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Table I: Result comparison the retrieval task. For the same metric on each dataset, the best is bold and the second best is underlined. We use four different symbols to indicate the different categories of methods detailed in Sec. Sec.1..4 Cases where with s 0.01 according to the paired [-test, are marked with *
model significantly outperforms the best baseline,
Interest Coverage (IC@))
Interest Relevance ()
Exp. Deviation (ED(E)
Tail Exp, Improv, (TEl@k)
Methods
The higher the better
The htgher the better
The lower the better
The higher the better
k=20
k=50
K=100
K=20
k=50
1=100
k=20
k=50
K=100
K=20
k=50
k=100
Random
0.690
0.888
0,961
0.251
0.428
0,558
0.515
0.483
0.472
-0.041
-0.04]
-0.041
MostPop
0.704
0.766
0.788
0.324
0.426
0.490
0.563
0.501
0.485
-0.045
-0.045
-0.045
YoutubeDNN
0.672
0.810
0.878
0.432
0.550
0.623
0.470
0.439
0.423
40.400
.0.041
-0.041
GRU4Rce
0.676
0.810
0.884
0.415
0.524
0.602
0.485
0.452
0.438
40.40
-0.040
-0.041
Amazon
BERTARec
0.683
0.815
0.892
0.416
0.534
0.613
0,512
0.479
0.472
00089
-0.092
gSASRee
0.672
0.418
0.618
0.506
0.472
0.469
-0.069
-0.069
MIND
0.650
0.787
0.861
0.390
0,503
0.575
0.509
0.477
0.461
-0.041
.0044
-0.041
ComiRec
0.656
0.785
0.861
0.399
0.510
0.595
0.492
0.453
0.432
40,400
-0.040
-0,040'
CAMI
0.640
0,710
0.833
0.373
0,483
0.521
0.522
0.493
0.473
-0,071
-0.88
+0.080
PIMI
0.705
0.821
0.897
0.415
0.535
0.622
0.497
0.462
0.441
-0.092
-0.091
-0,144
REMI
0.717
0.418
0.627
0.494
0.456
0.435
40.081
-0.082
-0.091
GPR4DUR
0.739
0.895
0,956
0.429
0.560
0.643
0,458
0.423
0,412
-0.041
-0,039
-0,039
Random
0.835
0.961
0.992
0.272
0.422
0.534
0.252
0,229
0.221
-0.185
-0.184
4..18
MostPop
0.914
0.973
0.986
0.498
0.655
0.727
0.261
0.223
0.217
-0.022
-0.013"
-0.08*
YoutabeDNNN
0.879
0,938
0.974
0.722
0.846
0.873
0,250
0.229
0.218
-0.012"
-0.031
...51
MovieLens Lnns
GRUARec
0.832
0.939
0.976
0.646
0.784
0.863
0.228
0.226
0.195
-0,070
00076
40.084
BERT-Rec
0.883
0,852
0.963
0.732
0.847
0.883"
0.271
0.258
0.256
-0,072
-0.087
-0. 103
ReASRee
0.885
0.857
0,964
0,730
0,843
0.879
0.276
0,261
0.260
-0.084
-0.092
40.114
MIND
0.869
0.951
0
0.653
0.786
0.863
0.245
0.223
0.212
-0.049
-0.05%
-0.073
ComiRec
0.844
0.946
0
0.635
0,776
0.859
0.227
0.203
0.192
00069
-0.074
-0.082
CAMI
0.853
0,933
0.954
0.625
0.742
0.830
0.272
0.263
0.253
-0.082
-0.094
-0,101
0.856
0,929
0.662
0.762
0.264
0.237
0.221
4.092
-0.105
REMI
0.861
0,930
0.947
0.718
0.792
0.368
0,270
0.252
0.230
-0.102
-0.113
10.156
GPR4DUR
0.929
0.974
0.973
0.825
0.862
0.891
0.252
0.222
0.201
4..11
-0,007
40.016
Random
0.302
0.563
0.873
0.232
0,416
0.493
0.425
-0.049
-0.051
MostPop
0.342
0.583
0.863
0.362
0.439
0.643
0.512
0.437
0.343
-0.076
-0.050
-0.03
YoutubeDNN
0.305
0.523
0.822
0.471
0.529
0,713
0.498
0.443
0.356
-0.054
0.0444
-0.030
GRU4Rcc
0,295
0,503
0.810
0.492
0,533
0,724
0.469
0.413
0,300
-0.053
-0.041
-0.030
Tamban
BERTTRec
0.301
0.508
0.814
0.494
0.535
0.721
0.482
0.433
0.376
-0.062
-0.053
-0.040
gSASRee
0.302
0.506
0.817
0.502
0.552
0.730
0.502
0.447
0.396
-0.082
-0.077
-0.064
MIND
0.295
0.517
0.813
0.502
0,552
0,733
0,463
0.411
0.294
-0,522
-0.041
-0.029
ComiRec
0.284
0.501
0.807
0.509
0.561
0.731
0,433
0.380
0.291
-0,051
-0.042
-0.030
CAMI
0.296
0.522
0.518'
0.573
0.734
0.424
0.363
0.281
-0.039
-0.027'
PIMI
0.343
0.579
0.860
0.516
0,566
0.729
0.498
0.447
0.328
-0.089
-0.052
-0.035
REMI
0.339
0.576
0.855
0.511
0.540
0.698
0.477
0.408
0.377
-0.077
-0.048
-0.030
GPR4DUR
0.363
0.601
0.891
0.609
0.624
0,781
0.453
0.367
0.273
-0,050
-0.040
-0.023
to scenarios with millions or tens of millions of items, when retrieving hundreds for ranking, as is common in real-world RSs (e.g., see (1I) Similarly, in music recommendation, it would be especially useful for defining user interests over artists (a few millions at most per geographical region/language) vs. individual songs. Previous work improves GPR efficiency using Toeplitz and Kronecker structures, achieving ((f,) training and O(1) prediction complexity [32]. Other sublinear
approximations partition the item space find candidates adaptively [33 34). While not our focus, it would be straightforward to apply these well-studied methods to our setting.
Finally note that we do not expect users' interest collections to be highly dynamic; hence, they will not require real-time updates. Our method is best-suited to use as a candidate generator, with the model updated periodically to create a pool of potentially interesting items for users.
5
Offline Experiments
We next evaluate our GPR4DUR on three real-world datasets, and compare our DUR technique with other state-of-the-art methods for multi-interest personalized retrieval.
5.1 Datasets
We use three widely studied datasets: Amazon [35). MovieLens [16, and Taobao [6). Following previous work (37 3 we filter out items with fewer than 10 appearances and users with fewer than
25 interactions to ensure sufficient history for indicating multiple interests. Each interest corresponds to category: for Amazon, we use the single principal category of each item; for Moviel.nn, we use 18 movie genres (each movie can belong to multiple genres); for Taobao, we cluster items into 20

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categories using Ward clustering on the pretrained item embeddings as in 22 The same categories are used during training and inference. Dataset statistics are shown in Table and an ablation analysis of various clustering algorithms and numbers of clusters is provided in Table 8 (See Appendix).
5.2 Experiment Setup
Most prior work on recommendation and retrieval evaluates model performance on generalization to new items per user. Instead, similar to recent work (39 3
we assess model performance on
the ability to generalize to new users. We split users into disjoint subsets: training users (L"""") validation users (1,")), and lest users (L1"t)) in ratio of 8:1:1. The last 20% of each user's interaction sequence is treated as a holdout set for evaluation, and the first 80% as a history set for fitting the GPR model. We cap history length to 60, 160, and 100 for the three datasets. aligning with their average user interactions. For item embedding pre-training we train the recommendation backbones using the history set of all training users and tune parameters based on the performance on the holdout set for validation users (details in Appendix A.3) Training is capped at 100,000 iterations with early stopping if validation performance does not improve for 50 successive iterations. We tune GPR hyperparameters by fitting the GP regressor to the history set of all training and validation users, then using the holdout set to fine-tune parameters (kernel and standard deviation). Metries are reported on the holdout set for all test users (see Appendix A.5 for hyperparameter sensitivity).
5.3 Metrics
Metrics used in prior work on sequential recommendation are not well-suited assess performance in our multi-interest retrieval task, for several reasons: (i) Conventional metrics, such as precision and recall, often employed in multi-interest research, do not adequately quantify whether an item list reflects the full range of a user's (multiple) interests. A model may primarily recommend items from narrow range of highly popular categories and still score high on these metries while potentially overlooking niche interests. (ii) Metrics like precision and recall are overly stringent, only recognizing items the recommendation list that appear in the holdout set. We argue that credit should also be given if similar, though not identical, item is recommended (e.g.. Iron Man instead of Iron Man 2). This requires soft version of these metrics. (iii) Multi-interest retrieval systems should expose users to niche content to address their diverse interests. However, conventional metrics may neglect the item perspective, potentially underserving users with specialized interests. Consequently, we propose the use of the following four metrics that encompass the aforementioned factors.
Interest wise Coverage (IC) This metric is similar to subtopic-recall [40], which directly measures whether the model can comprehensively retrieve all user interests reflected in the holdout set. The higher the value of this metric the better:
IC(V)) n c((R! 1:k Ic(v2))
IC@K
(6)
Interest-wise Relevance (IR) To further measure the relevance of retrieved items, we introduce "soft" recall metric, calculating the maximum cosine similarity between items in the retrieval list and the holdout set within the same category. The motivation for IR is that the success of retrieval or recommendation list often depends on how satisfying the most relevant item is:
Σ max S(U,, 1T))
CEC(VL) B.EDL.
IR@k= =
s.t. C(v,) C(U,) =c,
IC(V
where S(1, n2)) is the cosine similarity between item iú and uy. To obtain ground-truth similarities between items, and to mitigate the influence of the chosen pre-trained model, we pretrain the item embeddings using YoutubeDNN [41] with higher dimension size (d = 256) to compute uniform St,j for any backbone. A higher value of this metric is better.
Exposure Deviation (ED) In addition to measuring performance from the user side, we also measure from the item side to test whether exposure of different categories in the retrieval list close to that in the holdout set. We treat each occurrence of an item category as one unit of exposure,
7

---

1:k E Rlll for u's holdout set and retrieval list,
and compute the normalized exposure vectors Eus Cu respectively. Lower values of this metric are better.
Evers LEEC()) 1sk
EvERIA LeE((e) Every [c(v)] Cu. EnERYE Ic(x)]
EDOK-
1sk 11:. S.L., uue lk - Cu &
Σ
(8)
12
Tail Exposure Improvement (TEI) With respect category exposure, it is crucial to ensure that niche interests are not under-exposed. To evaluate this, we select a subset of the least popular categories and measure their exposure improvement in the retrieval list versus that in the holdout set. higher value indicates better performance, and a positive value indicates improvement:
THICK
Σ
Σ cEclail
1:k (Cu,e -c,,))
-x,,) 2t,
Here, Chall refers to the set of niche categories (i.e., the last 50% long-tail categories), denoting those niche interests. 1=i,,>0 indicates that we only compute the improvement for categories that appear in the user's holdout set, reflecting their true interests.
5.4 Methods Studied
We study the following 12 methods from four categories. (i) Heuristic + Random recom- mends random items, MostPop recommends
Table 2: Result comparison on the ranking task mea-
sured at top-50 across all methods on three datasets.
Ainzzon
MovieLans
Taohon
Recall
Recall
aDCC
the most popular items. (ii) SUR Methods
Random
0.836
0.848
0.685
0.716
0.838
0.866
YoN [41 is successful deep learn- ing model for industrial recommendation plat-
MostPop
0.710
YoutubeDNNN
0,875
0.904
GRU4Ree
0.873
0
0,714
0,746
0.873
0.902
forms. GRU4Rec 330 is the first work to use
BERT-RRc
0.881
0
0.723
0.758
0.883
0.914
recurrent neural networks for recommenda-
gSASRec
0.880
0.894
0.725
0.760
0.884
0.915
tion. BERT4Rec [42 adopts the self-attention
MIND
0.842
0.885
0.713
0.745
0.872
0.901
Comiléee
0.887
0.900
0.731
0.757
0.886
0.915
mechanism. gSASRec 43] is improvement over SASRec that deploys an increased num-
CAMI
0.920
PIMI
0.891
0.899
0.724
0.757
0.886
0.911
REMI
0.916
ber of negative samples and novel loss func-
GPR4DUR
0.908
0.922
0.730
0.768
0.906
0.936
tion. (iii) MUR Methods + MIND [5] designs
a multi-interest extractor layer based on the capsule routing. ComiRec 3 captures multiple interests
from user behavior sequences with a controller for balancing diversity. CAMI [1]] uses category- aware multi-interest model to encode users as multiple preference embeddings. PIMI 44 models the user representation by considering both the periodicity and interactivity in the item sequence. REMI [45] consists of an interest-aware hard negative mining strategy and a routing regularization method. (iv) DUR Method (Ours) GPR4DUR uses GPR density-based user representation tool for capturing users' diverse interests with uncertainty
Overall Performance Our overall performance comparison addresses two central research ques- tions (RQs): whether our proposed method offers superior retrieval performance for users with multiple interests (RQI); and whether it induces appropriate item-sided exposure w.r.t. both popular and niche interests (RQ2).
Performance on the retrieval task. To assess RQI, we evaluate the effectiveness of the retrieval phase. As shown in Table GPR4DUR outperforms almost all baselines across datasets w.r.t Interest Coverage (CC@)) and Interest Relevance (IR @ k), demonstrating high degrees of retrieval coverage and relevance. Specifically, on the Amazon dataset, GPR4DUR achieves the highest performance in 4 out of 6 interest metrics, in Movielens leads in 5 out of 6 metrics, and in Taobao, it excels across all 6 interest metries. This shows that GPR4DUR covers wide range of user interests while simultancously maintaining high relevance. To assess the statistical significance of our model's s performance compared to the best baseline, we performed paired t-test, which evaluates whether the means of two paired samples differ significantly, ensuring that the observed improvements are not due to random variation.
'The implementation can be found httt:://gittub..oo/hatlluuwww

---

For RQ2, our objective is to ascertain whether item exposure suitably balanced. We mea- sure this using the Exposure Deviation (ED@k) k) and Tail Exposure Improvement (THI@k) @k) met- rics. Lower values of ED@k suggest more sat- istying category exposure, while higher values of TEI@K k are indicative of enhanced exposure in the long tail item categories. GPR4DUR is highly effective
100
Interest Relevanced220 (99920)
Tell Exp. iwtp://oooo.oo.... (TERR20)
0.0
Nexthpp
0.0
0.2
0.0
92
92
03
-0.3
gi
02
(a) Users grouped by mamber of fitteraction
Interest Relevanceeg20 (Ri220)
Improw 920 (T81920)
these metrics, consistently performing well across all datasets in most cases, and validating its ability to provide an optimal level of category exposure. Notably, GPR4DUR achieves the best results in 8 of 9 TEI @ k met- rics, indicating its superior ability to generate exposure to niche categories/interess.. We point out, however, that all TEI@K k values are nega- tive, which suggests that none of the methods we tested improve exposure for niche categories relative to the exposure in the user holdout sets. This is explained by the bias inherent in most recommendation methods, and suggests that further work is required on di- versification strategies to mitigate such effects.
0.5
0.0
0.0
-0.1
0.U3
-0.3
(b) Uhers grospuel by namber of Intereeds
Figure 3: Methods comparison across different user groups on MovieLens. Best viewed in color.
Inter and Donaraged (C3520)
Interaal Delooumaatg0 018820)
popularity
14.13
0.5
Menihng
12.5
0.72
0.70
0.50
Performance on the ranking task. While our primary emphasis is on the retrieval phase, we also present model comparisons for the rank- ing task. As illustrated in Table 2 GPR4DUR demonstrates competitive performance on the traditional relevance metrics relative to the baseline models. This further validates the strength of our proposed method.
0.51
223
16
mensinn Size
merccon Size
Figure 4: Robustness comparison across different
dimension sizes on Amazon. Best viewed in color.
Performance across User Groups (RQ3) We conduct fine-grained analysis of GPR4DUR performance on users grouped into quantiles, gl (lowest) through g5 (highest), based on the number of interaction or number of interests; results are provided in Fig. 3 Due to space constraints, we show results only for IR @220 and @EI@20 on MovieLens, and only plot the best SUR and MUR strategies; DUR denotes our GPR4DUR method. We see that GPR4DUR consistently outperforms the baselines w.r.t. relevance and exposure metrics. This improvement is more pronounced as the number of user interactions (resp., interests) increases. Interestingly, while model enhances overall exposure of niche interests (see Table GPR4DUR improves niche interest exposure considerably for users with large numbers of interactions (resp., interests); i.e., TEI @ 20 is positive for 94 and g5. These observations confirm the effectiveness of GPR4DUR in capturing a user's multiple interests-esspccialy for those with non-trivial histories-and its potential to maintain fair exposure w.r.t. items.
Robustness to Dimension Size (RQ4) We underscored the importance of efficiency for good user representation in Sec. [ To shed light on this, we examine the IC@ 20 and IR @ 20 performance of various methods on Amazon. As shown in Fig. 4 GPR4DUR is effective w.r.t. interest coverage even when operating with din-dimensional embeddings (i.e., d = 8 and = 4). By contrast, the performance of the SUR and MUR methods degrades the dimensionality decreases. GPR4DUR consistently outperforms other methods w.r.t. interest relevance across all dimensionalities examined. We note that lower dimensions facilitate higher interest relevance due to increased cosine similarity (Eq. 7. explaining the inverse correlation between IR @ 20 and dimension size in Figure (right).
6 Online Simulation
To demonstrate the efficacy of GPR4DUR in capturing uncertainty in user interests and support exploration, we conduct an online simulation in a synthetic setting, using specific model of stochastic user behavior to generate responses to recommendations.

---

Data Preparation. We assume |C] = 10 interest clusters, each represented by d-dim (d = 32) multivariate Gaussian. We randomly select a (user-specific) subset of these interests as the ground- truth interest set for each user. We set |4|| = 1000 and |v] 3000, with 300 items in each interest cluster. Each item belongs to single cluster and its embedding sampled from the corresponding interest distribution. Each user is modeled by multi-modal Gaussian, a weighted sum of the corresponding ground-truth interest distributions. To simulate a sequence of item interactions Vy (i.e., user history), we follow (46,, first running Markov Chain using predefined user interest transition matrix to obtain the user's 's interest interactions for S = 10 steps. We do not consider the cold-start problem in this experiment, so simply recommend one item from each generated cluster to form the user history (i.e., Vull = S). The observation O,, over items in V., is set to if the item belongs to ground truth cluster, and -1 otherwise.
GPR Fit and Prediction. After obtaining item embeddings V. user history Vu. and user observations Our we use GPR4DUR to learn a DUR for each user, using the methods described in Sec. 4
User History and Observation Update. Using a predetermined user browsing model, clicked and skipped items are generated and appended to the user interaction history (and the corresponding user observation is likewise updated, for clicked, for skipped). This process continues until maximum iteration of T = 10 is reached. In this online setting, we adopt the dependent click model (DCM) of user browsing behavior, widely used in web search and recommendation [47 48). In the DCM, users begin by inspecting the top-ranked item, progressing down the list, engaging with items of interest and deciding to continue or terminate after each viewed item.
Experiment Results. We compare different recommendation policies by assessing various metries at each it- eration; due to space limitations, we report results only for interest cover- age, see Table Specifically, we com- pute a "cumulative" version of interest coverage by reporting the interest cov- erage averaged across all users on all previously recommended items prior to the current iteration. Our goal is to test whether policies that use uncertainty models outperform those that do not, specifically, whether such policies can exploit the inherent uncertainty representation of user interests offered by GPR4DUR.
Table 3: Comparison between different policies in online set- ting. The reported values are the interest coverage averaged across all users on all cumulative recommended items up to each iteration. The highest value per column is bold.
Policy
(=1
1=4
1=5
1=6
[=7
(=8
(=9
1=10
Random Greedy
0.29
0.49
0.64
0.74
0.82
0.87
0.91
0.91
0.92
0.93
0.71
0.88
0.90
0.90
0.91
0.91
0.91
0.92
0.92
0.92
(3-1)
0.89
0.91
0.92
0.92
0.94
0.95
UCB (0=5)
0.72
0.88
0.90
0.90
0.91
0.91
0.92
0.92
0.93
0.94
Thompson
0.29
0.50
0.65
0.75
0.82
0.89
0.91
0.92
0.95
0.98
We assume each policy recommends the top-10 10 items to each user at each iteration. Table 3 shows that methods using uncertainty (the bottom three rows) fairly reliably outperform those that do not (the top two rows, with Greedy being UCB with 3 O, where is the scaling factor of the variance term in UCB). The observation confirms the benefit of using GPR4DUR to explicitly model uncertainty in a recommender's estimates of user's interests and use this to drive exploration.
7 Conclusion and Discussion
In this paper, we introduced a density-based user representation model, GPR4DUR, marking the first application of Gaussian process regression for user modeling in multi-interest retrieval. This innovative approach inherently captures dynamic user interests, provides uncertainty-awarent proves to be more dimension-efficient than traditional point-based methods. We also establish a new evaluation protocol, developing new metrics specifically tailored to multi-interest retrieval tasks, filling a gap in the current evaluation landscape. Offline experiments validate the adaptability and efficiency of GPR4DUR, and demonstrate significant benefits relative to existing tfth--ffthe-art models. Online simulations further highlight GPR4DUR's s ability to drive user interest exploration by recommendation algorithms that can effectively leverage model uncertainty. The future work and broader impacts of this study are discussed in Appendix (A.9 and Appendix A.10 respectively.
and
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14

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A Appendix
A.1 Notations and Preliminaries
A.1.1 Notations
Table 4: Description of Notation.
Notation
Description
V.C
The of all users, items, and (item) categories.
U, V.V.C
Full embedding matrix of users, items, and categories.
V.
The
's interaction history.
ue V
The history set and holdout set partitioned from V.u
The observed rating scores of items in Vu- The time step when u interacted with v. The length of V..
L
Ey
The length of user history for model input. Item embeddings for items in V.,. The list of retrieved items to
V.
R.
C(-)
The set of categories of all items in the input sequence.
A.1.2 Preliminaries on Gaussian Process Regression
Let X [xi...., Xn. I nxd be set of input points and y (yI.... .n) E RR" be the corresponding output values. A GP is defined as:
I - GP(u,))
(10)
where p(x) is the mean function and k(x, ) is the covariance function (kernel). Given a new point Xx, the joint distribution of the observed outputs and the output at the new point is given by:
[(x) [(xx))
[(X.X)
k(X.x.) A(x.,x.)+ +
[(x]]
k(x..X)
(11)
where (XX is the vector of mean values for the observed data points, K(X, X) the covariance matrix for the observed data points, k(X, x.) is the vector of covariances between the observed data
points and the new input point, and o² and 0, are the noise variances. Without prior observations, μ generally set as 0.
The conditional distribution of f(x,) given the observed data is:
f(x.)ly ((
(12)
with the predictive mean and covariance given by:
f. (xxx) + k(x X) X) -'I] (y H): x.) +0+ k(
(13)
(14)
Fig. 5 presents visual illustration of GPR. The true underlying function is depicted in red, which the function we aim to approximate through GPR. The observations, depicted as black crosses, represent known data points. As expected with GPR, where data points observed, the uncertainty (represented by the shaded region) is minimal, signifying high confidence in predictions at those locations. On the other hand, in areas without observations, the uncertainty increases, reflecting less confidence in the model's 's predictions. The two dashed lines represent samples from the GP posterior. Around observed points, these sampled functions adhere closely the actual data, representing the power and flexibility of GPR in modeling intricate patterns based on sparse data.
A.2 Details for Retrieval List Generation
After obtaining a DUR yn. for E lI using GPR, we generate the retrieval list using the posterior Ia (v) over all unobserved items. The top-N items with the highest values are selected as our retrieval list. We consider two methods for estimating these values.
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1.5
1.0
-0.5
Funcion
Observations
-1.0
Posterio Meen
Samp
1.5
Samp 2
-20
Confiderce
Figure 5: Illustration of Gaussian Process Regression ID. The true function shown red, observations are marked with black crosses, and the dashed lines represent two samples from the GP posterior. The dash-dot line represents the posterior mean, while the shaded region indicates the 95% confidence interval, showcasing the uncertainty associated with the GP predictions.
The first Thompson sampling (TS), a probabilistic method that selects items based on posterior sampling [15]. For each item v in set, we generate sample from the posterior Iu (v(v,, and rank the items using their sampled values. A key advantage of TS its ability to balance the trade-off between exploration and exploitation, improving the diversity of the recommendation list. The sampling and selection process is:
8u, gu(v), Vo $ Tuu
(15)
R2 Top-N(
(16)
where 8u, is the value for item v from user u sampled function, and R., is the final list of retrieved items for user u.
The second method is Upper Confidence Bound (UCB), deterministic method that selects items based their estimated rewards and uncertainties 14 28]. For each item v, compute its upper confidence bound by adding the mean and a confidence interval derived from the variance of the posterior Ia (v); items are ranked using these upper bounds. Unlike TS, UCB tends aggressively promote items with a high degree of posterior uncertainty, giving a different flavor of diversity in the recommendation list. The selection process
by. (v) 3 v var[gn Ve $ Inp
(17)
R₂ Tb,.N(
(18)
where b is the upper confidence bound for w.r.t u's posterior, and B is hyper-paramette that adjusts the exploration-explone trade-off. R, is the final retrieval list.
A.3 Pretraining Strategies
Necessity of Pretraining Item Embeddings with Auxiliary Loss Categories. Without augment- ing the pre-traine pre-training loss with categorical information as in Eq.3i the resulting pre-trained embeddings do not respect category consistency. To illustrate this, compare pre-trained embeddings with and without categorical information (on MovieLens) and show the results Fig. 6
We observe that, without categorical constraints, the learned embeddings do not align with the categorics. There are still overlap between categories (genres) since each movie may belong to multiple genres. Hence, incorporating auxiliary training loss based on item categories is essential for interest-coverage analysis based on the embeddings.
Sensitivity to Different Pretraining Strategies. In this work, we use pretrained embeddings for our multi-interest user representation. To ensure a fair comparison, we use the same pretrained embeddings in all other models we compared. To test the impact of the embeddings we add experiments with other pretraining settings. Specifically, we obtain embeddings using matrix factorization (MF) and using YoutubeDNN with varying history lengths. We use the Amazon dataset as an example and measure performance at top-50. The observation is similar on the other two datasets. Other experiment settings are the same presented in the paper. We use the learned
performance,
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Training with category information
Training without category information
Item embeddings align category labels Figure 6: The t-SNE plot for pretrained item embeddings on the MovieLens dataset with and without using auxiliary loss category information.
Item embeddings does not align with category labels
Table Performance comparison different pretraining settings on various metrics, indicates the higher the better; U indicates the lower the better.
Retrieval Task
Ranking Task
Pretraining setting
IC
IR@500
RD& 50
TE
Recall@50 ft nDCG@@50
ComiRec
0.684
0.417
0.523
-0.124
0.865
0.851
MF
GPR4DUR
0.887
0.527
0,501
-0.052
0.882
0.871
YoutubeDNN (max user history=20)
ComiRec
0.709
0.460
0,502
00071
0.878
0.870
GPR4DUR
0.893
0.552
0.426
-0,056
0.892
0.913
YoutubeDNN
ComiRee
0.710
0.463
0.493
-0.040
0.887
0.900
(max user history=50)
GPR4DUR
0.895
0,560
0.423
-0.039
0,908
0.922
YoutubeDNN (max history=100)
ComiRec
0.711
0.465
0.490
-0.039
0.890
0.901
GPR4DUR
0.896
0.423
-0.037
0.910
0.925
embeddings with both ComiRec (one of the strongest baselines) and our GPR4DUR. The results,
shown in Table 5 demonstrate that embeddings from YoutubeDNN outperform those from MF and that longer history leads better performance. These results highlight the effectiveness and robustness of our proposed method across different pretraining settings.
A.4 Dataset Statisties
The statistics the three datasets, Amazon [35. MovieLens [16] and Taobaq is shown Table We report the number of users, number of items, number of total interactions, and density of the three datasets, respectively.
A.5 Hyperparameter Settings and Sensitivity Analysis for GPR Parameter Tuning
In short, we constantly use the radial basis function (RBF) kernel on different datasets due to its superior performance, where is unique for each dataset.
The kernel function, k is tuned from the cosine similarity kernel and the RBF kernel. For the RBF kernel, the standard deviation is tuned from {1e 1e 1, 10, 100). For each dataset, we report one metric on the retrieval task and one metric on the ranking task, both evaluated the top-50. The trend on other metrics is similar.
As shown in Table 7 observe that the RBF kernel outperforms the cosine similarity kernel across various datasets and metrics because better captures non-linear relationships and offers flexibility by mapping inputs into difinteedimeesiionlll space. Additionally, the parameter in the RBF kernel influences model performance-4 larger yields smoother functions for better generalization distances, while smaller detects finer data variations. Dataset-specific optimal values correlate with data sparsity. MovieLens's high density demands a smaller to avoid overfitting due
https:/tiiancii. wwwp::hwwwiiiiiooooooooo htlp://ww.mmmttttssss///nnnnnnnn
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Table 6: The statistics of datasets.
# User
# Item
# Interac.
Density
Amazon
6,223
32,830
4M
0.18%
MovieLens
123,002
12,532
20M
1.27%
Taobao
756,892
570.350
70M
0.01%
Table Hyperparameter Settings and Sensitivity Analysis for GPR Parameter Tuning.
Amazon
MovieLens
Taobao
GPR Parameters
IC@50 fl
Recall @50 fl
IC@50
Recall @S
IC@50 f
Recall @5 |
Cosine
0.809
0.874
0.940
0.710
0,518
0.870
RBF (a le" 3
0.822
0.877
0.963
0.727
0.536
0.872
RBF 1e
0.883
0.892
0.974
0.730
0.587
0.885
RBF
0.895
0.908
0.957
0.725
0,591
0.887
RBF (a 10)
0.887
0.889
0.954
0.723
0.601
0,906
RBF (σ 100)
0.890
0.890
0.954
0.721
0.592
0.899
to capturing detailed variations. contrast, Taobao's low density necessitates a larger a for greater generalization, with Amazon's intermediate sparsity requiring moderate for optimal performance.
A.6 Ablation Analysis on Different Clustering Options
In this section, we provide the ablation analysis on using various clustering algorithms and different number of clusters on the Taobao dataset. Following paper [4]] have selected four distinet clustering algorithms for our comparative analysis: (i) Ward [50]: This hierarchical clustering technique focuses minimizing the variance within each cluster, effectively reducing the overall sum of squared distances across all clusters. (ii) K-Means [51] An iterative clustering algorithm that
aims to minimize the of squared distances from each data point the centroid of its assigned cluster, thereby reducing in-cluster variance. (iii) Spectral Clustering [52]: This method performs clustering based the eigenvectors of the normalized Laplacian, which computed from the affinity matrix, facilitating the division based on the graph's 's inherent structure. (iv) BIRCH [53]: A hierarchical clustering approach that efficiently processes large datasets by incrementally constructing a Clustering Feature Tree, which groups data points based on their proximity and other features.
A notable deviation from paper 49 is in handling of categories (interests) for training and inference phases; we maintain consistency in categories across both phases, in contrast to their separate categorization. We further refine analysis by tuning the number of clusters from 10, 20, and 50.
Result and analysis. The results presented in the Table indicate a nuanced understanding of the impact of clustering algorithms and the number of clusters retrieval and ranking tasks in infor- mation retrieval systems. Across the board, the differences among the clustering algorithms- -Wadd, K-Means, Spectral, and BIRCH rithm might not be as critical as the configuration of the number of clusters within these algorithms for the tasks at hand.
relatively small, suggesting that the choice of clustering algo-
Notably, as the number of clusters increases from 10 to and then to 50, there is a general trend of improvement in performance metrics. This improvement could be attributed to the algorithms' ability to capture more aine-grained user interests through a larger number clusters, thereby enhancing both retrieval accuracy and ranking precision.
However, the marginal differences observed between the configurations of 20 and 50 clusters across all metrics indicate diminishing returns on further increasing the number of clusters beyond 20. This observation suggests that while increasing the number of clusters to 20 contributes to significant improvements, escalating to 50 clusters does not yield proportionally higher gains. Consequently. this study opts for a configuration of 20 clusters as the optimal balance between performance improvement and computational efficiency. The relatively stable standard deviations across different configurations
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Table 8: Result comparison on Taobao dataset using different cluster options. The Interest Coverage (IC) metric is omitted from this report as its value is significantly influenced by the chosen number of clusters, rendering less relevant for comparative purposes. All reported metrics are evaluated at the top-50. f/ indicates the higher the better; || indicates the lower the better.
Num of clusters
Retrieval Task
Ranking Task
IR@50
ED@50 U
TEI
Rccall@50 f
nDCG@50 π
10
0.602 0,012
0.385 + 0.011
-0.055 + 0.001
0.892 + 0.013
0.920 + 0.012
Ward
20
0.624 + 0.011
0.367 + 0.011
-0.040 + 0.001
0.906 + 0.012
0.936 + 0.011
50
0.625 i 0.011
0.365 1 0.011
-0.041 1 0.001
0.906 : 0.012
0.938 1 0.011
10
0.590 + 0.013
0.392 + 0.011
-0.060 + 0.001
0.885 + 0.013
0.912 + 0.012
M-Meass
20
0.615 0.012
0.370 4 0.011
-0.045 i 0.001
0,900 + 0.012
0,928 + 0.012
50
0.620 0.011
0.368 0.011
-0.046 4 0.001
0.904 + 0.012
0.930 + 0.011
10
0.605 0.012
0.382 = 0.011
-0.533 + 0.001
0.895 = 0.013
0.923 + 0.012
Spectral
20
0.625
0.011
0.366
0.011
-0.039 1 0.001
0.908 1 0.012
0.937 1 0.011
50
0.624 0.011
0.364 0.011
-0.039 = 0.001
0.909 = 0.011
0.936 + 0.012
10
0,580
0.013
0.395
0.012
-0.065 1 0.002
0.880 1 0.014
0.910 + 0.013
BIRCH
20
0.610
0.012
0.372
0.011
-0.050 + 0.001
0.899 + 0.012
0.926 + 0.012
50
0.610 0.011
0.370 = 0.011
-0.051 + 0.001
0.902 + 0.012
0.928 = 0.011
Table 9: Latency and performance comparison across models on the Taobao dataset, which contains 570K items. Training and inference latencies are measured in millisecond (ms). Standard deviation is shown in parentheses. We see that the cost of inference is on par with other methods.
YoutubeDNN
GRU4Rec
BERT4Re:
gSASRec
MIND
ComiRec
CAMI
PIMI
REMI
GPR4DUR (Ours)
Train
153.08
262.28
926.36
492.10
552.37
$75.51
602.38
611.36
732.16
932.00
(std)
(1.93)
(1.20)
(82.39)
(25.63)
(15.50)
(67.32)
(84.31)
(73.02)
(32.97)
(16.27)
Inference
1.33
1.44
49.28
20.05
18.62
18.89
38.24
40.57
49.27
63.67
(std)
(0.76)
(0.81)
(21,47)
(42.07)
(52.25)
(54.57)
(43.18)
(39.65)
(56.33)
(26.38)
TR
0.529
0.533
0.557
0,552
0.552
0.561
0.573
0.566
0.540
0.624
Recall 50
0.875
0.873
0.883
0,884
0,872
0.886
0.891
0.886
0.889
0.906
further support the robustness of our findings, emphasizing the consistency of the performance improvements achieved with an increased number of clusters up to a certain point.
A.7 Latency and Performance Comparison
We show the efficiency comparison (with the performance comparison) across models in Table g For a fair comparison, we run all experiments on a single NVIDIA A100 GPU with TensorFlow framework (version 1.12) without any further optimization on the computation. We choose the Taobao dataset and set the batch as 1.
Result and analysis. In examining the efficiency of various recommendation models, notable differences in training and inference times highlight the diverse computational demands across these models. Models like YoUtubeDNN and GRU4Rec present more efficient profile, offering lower latency during both training and inference phases, while perform the worst on the retrieval and ranking tasks. The variability in model efficiency, as seen in the standard deviations of training and inference times, indicates a potential fluctuation in latency that could impact real-world deployment. Our proposed model, GPR4DUR, stands out with its superior performance on the retrieval task (c.g., measured by wise relevance, IR@50) 50) and the ranking task (c.g., mcasured by recall, Recall @ 50). This suggests that for applications valuing enhanced retrieval and ranking accuracy, the trade-off of increased latency is acceptable. Additionally, GPR4DUR exhibits a low standard deviation in its timing metrics. This consistency in processing times is advantageous for online deployment. It offers a predictable performance, which is crucial for developers when balancing between model efficiency and effectiveness.
Conclusively, GPR4DUR, along with the other baseline models evaluated, meets the latency require- ments for online application without the need for additional computational and serving optimizations. While GPR4DUR exhibits a higher time cost relative to some baselines, its performance improvement offers compelling advantage.
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Table 10: Result comparison between GPR4DUR and generative recommendation methods that also consider uncertainty. Here we use the Amazon dataset as an example to report the results and we confirm the observation is similar on the other two datasets. indicates the lower the better.
1 indicates the higher the better;
Retrieval Task
Ranking Task
Model
IC@50
IR@50 π
ED@
TEI@50
Recall@50 î aDCG@50
VAECF
0.783
0.482
0.546
-0,082
0.909
0.913
DiffuRec
0.834
0,540
0.442
-0,057
0.892
0.916
DREAM
0.812
0.521
0.460
-0,091
0,889
0.917
GPR4DUR
0.895
0.560
0.423
-0.039
0,908
0.922
A.8
Comparison with Generative Recommendation Methods
We note that some generative recommendation methods also consider user uncertainty, making them potential candidates for comparison with our method. These methods include VAECF (54), which assumes a distribution over user/item representations, and more recently cuffusion-basee recommendation models, DiffuRec (55) and DREAM (56). We do not compare them in the main paper due to (i) different design purpose: these methods are not designed for multi-interest retrieval, which is the focus of this work, and (ūi) different model family: VAECF is parametric model while our model is non-parametric, and diffusion-based methods require an entirely different training procedure and sampling strategies.
To still satisfy this curiosity, we present a comparison between GPR4DUR and the generative recommendation methods on the Amazon dataset for both the retrieval task and ranking task. As shown in Table 10 the results still confirm the effectiveness our model.
A.9
Limitations and Future Work
In Sec. 4.5 we discussed methods to reduce the time complexity of traditional Gaussian Process Regression (GPR). Despite these efforts, the training and inference times presented in Table remain slightly higher than those of recent state-of-the-a methods. Further improving the efficiency of our approach would be intriguing area for future research.
Moreover, the integration of collaborative Gaussian processes offers a promising avenue. Currently, model focuses primarily personalization, using other users only for tuning GPR hyperparame- ters. We hypothesize that leveraging collaborative learning techniques, such as those described in [57], could significantly enhance the performance and effectiveness of our method.
A.10 Broader Impacts
The application of Gaussian Process Regression (GPR) for user modeling in recommendation systems has both positive and negative societal impacts. Below, we outline these impacts in detail.
Positive Societal Impacts. Our approach, GPR4DUR, aims to significantly enhance the personal- ization and efficiency of recommender systems. By effectively capturing the diverse and dynamic interests of users, GPR4DUR can improve user satisfaction and engagement across various online platforms. This could lead to more tailored content delivery, helping users find relevant and interest- ing content more quickly and reducing information overload. Furthermore, the uncertainty- nature our method allows for better ceteraationcxlliitattinn balance, potentially uncovering niche interests and underrepresented content that users might find valuable. This can promote diversity and inclusivity in content consumption, providing a wider range options to users.
Negative Societal Impacts. Despite these positive aspects, there are potential negative societal impacts associated with the deployment our method. One major concern is the potential for reinforcing existing biases in recommendation systems. If the training data reflects societal biases, GPR4DUR might inadvertently perpetuate these biases, leading to unfair treatment of certain user groups. Additionally, the improved personalization capabilities might increase the risk of creating filter bubbles, where users are only exposed to content that reinforces their existing preferences, limiting their exposure to diverse viewpoints.
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Another potential issue is privacy, As GPR4DUR leverages detailed user interaction histories to model preferences. there a risk of sensitive information being inferred or misused. Ensuring robust data protection and adhering to privacy standards is crucial to mitigate this risk.
Mitigation Strategies. To address these potential negative impacts, several mitigation strategies can be employed. Firstly, implementing fairnes--aware algorithms that explicitly account for and mitigate biases during model training can help ensure equitable recommendations across different user groups. Secondly, incorporating mechanisms to introduce serendipity in recommendations can counteract filter bubble effects, exposing users to broader range of content. Lastly, adhering to strict data privacy regulations and employing advanced anonymization techniques can safeguard user data and privacy.
Overall, while GPR4DUR has the potential to significantly improve user modeling and personalization in recommender systems, careful consideration and implementation of mitigation strategies essential to address its broader societal impacts.
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Reviews:
[{"review_id": "dV6fSnmtIv", "reviewer": "Reviewer_F9WH", "summary": "The authors propose GPR4DUR, which incorporates uncertainty-awareness and scales well to large numbers of users.  This method leverages Gaussian process regression (GPR) to effectively capture the diverse and dynamic interests of users without the need for manual tuning. Through experiments with real-world offline datasets and online simulations, the authors demonstrate that GPR4DUR can adapt to user interest variability and efficiently balance the exploration-exploitation trade-off by utilizing model uncertainty. The paper also presents new evaluation protocols and metrics for multi-interest retrieval, showing the adaptability and efficiency of GPR4DUR in capturing a user's multiple interests and recommending items that span those interests, including niche ones.", "questions": "- Is there greater uncertainty associated with a user's niche interests? Or, how does the uncertainty differ between items of varying popularity and users with different interaction patterns?\n\n- In the tuning of GPR parameters, would using different parameters for different users yield better results?", "limitations": "Yes", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "- The authors ingeniously apply Gaussian Processes (GP) to characterize the diversity and density of user interests, incorporating a measure of uncertainty that proves especially efficacious in identifying and capturing niche user interests with precision.\n\n- The researchers have designed a comprehensive suite of evaluation metrics tailored for multi-interest contexts. These metrics, which encompass interest matching, interest coverage, and multi-interest balance, are poised to serve as a robust framework for guiding future research endeavors in this domain.\n\n- The authors have validated the outstanding performance of GPR4DUR in both offline and online settings.", "weaknesses": "- As mentioned in section 4.5 of the document, GPR4DUR is more suited for the ranking stage of large-scale recommendation systems. However, the ranking stage often involves a variety of user features, such as user embeddings, to achieve more accurate ranking results. Yet, this paper only utilizes the user's historical interactions.\n\n- The article still lacks an analysis of the relationship between multiple interests and uncertainty.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your positive feedback and appreciation of our method's novelty and in-depth analysis. We address your main concerns below.\n\n**W1 Clarification on the focus of our work**\n\nAs mentioned in our paper (lines 119, 139, 212-213), our approach focuses on the retrieval phase and is best suited to scenarios with millions or tens of millions of items, of which O(100) items are retrieved for downstream ranking. The ranking stage is not our focus. Rich user features can be used in the ranking stage, as you rightly observe, to achieve more accurate ranking results if such auxiliary information is available in the dataset. We do note, however, that our method performs competitively in the ranking phase (Table 2), even though our main focus is on retrieval. Finally, user embeddings are also based on a user’s historical interactions, so our approach still uses the same raw information.\n\n**W2+Q1 Relationship between interests and uncertainty**\n \nThanks for the question. If we are interpreting it correctly, for items with fewer observations, such as items in niche interests interacted with by few users, the mean prediction will be close to the prior while the variance (uncertainty) will be high (see the toy example in Figure 2). This is due to the nature of GPR. If we misinterpreted your question, please let us know.\n\n**Q2 GPR parameter tuning**\n\nIt is indeed possible to tune the GPR parameters for each user, but this requires a holdout set with sufficient data per user. In our experiments, we have no more than 160 interactions per user, so we leverage collaborative information for tuning the hyperparameters of the GPR.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "dbUrB299aL", "reviewer": "Reviewer_r5NL", "summary": "The research problem addressed in this study revolves around the challenge of effectively capturing user interests to enhance the quality of personalized recommendations. Traditional methods often struggle to model users with diverse interests accurately, leading to suboptimal recommendations.\n\nThe authors emphasize the limitations of existing user modeling techniques, such as collaborative filtering and matrix factorization, which may not adequately capture the multi-interest nature of users. To address this gap, the paper introduces the concept of Density-based User Representations (DURs) and proposes the GPR4DUR approach, which leverages Gaussian Process Regression to create more nuanced user representations based on the density of user interactions.", "questions": "Could the authors provide more details on the selection criteria for the real-world offline datasets used in the experiments? What specific characteristics were considered in choosing these datasets, and how do these characteristics make them particularly suitable for evaluating the effectiveness of the GPR4DUR approach?\n\nIn the online experiments involving simulated users, what specific metrics were employed to assess the effectiveness of the GPR4DUR recommendation policies? Can the authors detail the methodology used to simulate user interactions and describe how the performance of GPR4DUR was evaluated in this online setting?\n\nConsidering the emphasis on scalability, how does the computational complexity of GPR4DUR compare to traditional user modeling methods as the number of users and items increases? Have there been specific experiments conducted to analyze the scalability of GPR4DUR across different dataset sizes? What were the findings regarding the impact of increasing data volume on system performance?\n\nHow does GPR4DUR address and mitigate biases during the model training process to ensure equitable recommendations across diverse user groups? Can the authors elaborate on the specific mechanisms or algorithms implemented within GPR4DUR to promote fairness and reduce potential biases in the recommendation outcomes?", "limitations": "The authors have adequately addressed the limitations and identified no potential negative societal impacts of their work.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tIntroducing the concept of Density-based User Representations (DURs) as a more effective way to capture user interests.\n2.\tProposing the GPR4DUR approach, which utilizes Gaussian Process Regression to create personalized user representations based on interaction density.", "weaknesses": "1. A clearer articulation of the specific advancements or enhancements that Gaussian Process Regression for Density-based User Representation (GPR4DUR) provides over traditional methods—particularly in terms of adaptability.\n\n2. Discussing the scalability of the GPR4DUR approach with larger datasets and its computational efficiency would help to assess the practical applicability of the technique.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your positive feedback and appreciation of our method's novelty, soundness, and presentation. We address your main concerns below and will add details and clarifications in the paper as needed.\n\n**W1 The advancements of GPR4DUR over prior baselines**\n\nOur proposed method, GPR4DUR, advances traditional methods in all three aspects described in the introduction: (1) *Adaptability*, (2) *Uncertainty-awareness*, and (3) *Efficiency*. We elaborate on these below and will update the discussion in the paper to make these contributions more evident.\n\n - *Adaptability*: To demonstrate our method's adaptability to different user interest patterns, we evaluated it on two interest-wise metrics and two exposure-related metrics for the retrieval phase (Table 1) and two classical relevance metrics for the ranking phase (Table 2) across three widely used datasets. Our results indicate that, compared to prior SOTA MUR methods that use multiple points to represent a user, our GPR-based method can better capture user interests with a higher coverage ratio and retrieve more relevant items. This demonstrates that our method is more adaptable to different users regardless of their interest patterns.\n\n - *Uncertainty-awareness*: Section 6 details our experiments and analysis, showing that GPR4DUR can effectively capture users' dynamic interests in an online setting. We highlight that traditional heuristic, SUR, and MUR methods (baselines in Section 5.4) do not model uncertainty and always use a deterministic approach to compute the relevance score between a user and an item. The ability of our method to capture uncertainty stems from the inherent nature of Gaussian Processes.\n\n - *Efficiency*: Lines 362-369 and Figure 4 provide the experiment and analysis. GPR4DUR achieves competitive performance with low-dimensional item embeddings, while traditional methods perform poorly with low dimensions.\n\n**W2+Q1+Q3 Datasets and computational efficiency**\n\nWe selected the three datasets due to their varying size and sparsity, different domains, and widespread adoption in the recommendation community, ensuring that our empirical results are generalizable. The Taobao dataset, containing 70 million user-item interactions, is considered large in the community. The dataset statistics are shown in Table 6, Appendix A.4. In general, our method consistently achieves better performance compared to baselines across different datasets as shown in Section 5.\nComputational efficiency is discussed in Section 4.5 where we provide empirical results in Table 9, Appendix A.7. In summary, GPR4DUR, along with the other baseline models evaluated, meets the latency requirements for real-world applications without needing additional computational and serving optimizations. While GPR4DUR exhibits a higher time cost than some baselines, its performance improvement offers a compelling advantage. The dataset used in this experiment is the largest one in this paper, i.e., the Taobao dataset. We acknowledge that further improving the efficiency of our approach would be an intriguing area for future research (see discussion in Section 4.5).\n\n**Q2 Clarification on the online simulation**\n\nThe metric we report is interest coverage (see lines 397-399 and the caption of Table 3), which is the same as the interest-wise coverage (IC) (see line 262). We will better clarify this in the final manuscript. To report the values in Table 3, we compute a “cumulative” version of interest coverage by reporting the IC@10 (i.e., line 406, we recommend the top-10 items per user at each iteration) averaged across all users on all previously recommended items prior to the current iteration. Thus, Table 3 shows that using our proposed method with Thompson sampling, an average of 98% of interests can be covered for each user after 10 iterations in this online simulation experiment, outperforming methods without uncertainty.\n\nFor the method used to simulate user interactions, we adopt the method cited in line 380: *“... we follow [46], first running a Markov Chain using a predefined user interest transition matrix to obtain the user’s interest interactions for S = 10 steps.”* Due to character restrictions, it is challenging to describe the full process in detail here. We refer the reviewer to Section 3.2 and Appendix A of the paper [46] for a comprehensive explanation. We will add more exposition of this method in the Appendix.\n\n[46]: Mehta et al. Density Weighting for Multi-Interest Personalized Recommendation.\n\n**Q4 Mechanisms to promote fairness and reduce bias**\n\nThe ability of our proposed GPR4DUR to promote fairness and reduce potential biases is due to the inherent nature of Gaussian Process Regression (GPR) for capturing uncertainty. For items with fewer observations, such as items corresponding to niche interests interacted with by few users, the mean prediction will be close to the prior while the variance (uncertainty) will be high (see the toy example in Figure 2). Thus, when using UCB to sample items to generate the retrieval list (Section 4.2), items of niche interests still have a chance to be selected. We thus observe that our method has a low value on Exposure Deviation and a high value on Tail Exposure Improvement. Moreover, this “fairness” in the item exposure can also promote “fairness” in user satisfaction, since those users who generally like niche interests have a higher chance of finding the items they prefer.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Ot0XzUfewF", "reviewer": "Reviewer_Eeve", "summary": "The paper introduces density-based user representations (DURs) using Gaussian process regression (GPR) to address limitations in existing user modeling methods for personalized recommender systems. The proposed GPR4DUR approach effectively captures user interest variability, incorporates uncertainty-awareness, and scales well, as demonstrated by experiments with realworld datasets and simulated users. This method balances exploration and exploitation, enhancing multi-interest recommendations without manual tuning.", "questions": "1 For some simple collaborative signal modeling, can your method also achieve good performance improvement on it?\n\n2 Is there a more detailed definition or explanation of density-based? \n\n3 Figure 1 is not well explained. What do the x-axis and y-axis represent? How to understand the value range? Is normalization performed? The SUR and MUR graphs look the same. What do the color of the points mean? \n\n4 The explanation on line 35 is too abstract. How to understand since interests generally have high variability across users. Is there a strict mathematical definition to explain this problem?\n\n5 Lines 40-42, this three words are too abstract. Is there a more detailed explanation or explanation in mathematical formulas? Why can Gaussian process solve these three points?\n\n6 Line 36, why is uncertainty regarding a user’s interests not well-modeled by these methods, diminishing their ability to perform effective online exploration.", "limitations": "The core motivation is not clearly explained, and it is difficult for the author to understand how the proposed method solves the problems of existing methods. This paper is not recommended for acceptance.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1 The authors present a density-based approach for representing users in personalized multi-interest retrieval, incorporating Gaussian process regression for more sophisticated user modeling.\n\n2 The paper introduces four novel evaluation protocols tailored for the multi-interest retrieval task.\n\n3 The proposed method, GPR4DUR, is thoroughly validated through extensive experimentation on real-world datasets, showcasing its efficacy in the field.", "weaknesses": "1 The difference between SUR and MUR is not clearly explained. Why MUR is better, is there a reasonable explanation or proof? The author should explain this in detail in the introduction section.\n\n2 The adaptability and uncertainty that the author repeatedly emphasizes, what is the specific manifestation in the recommendation scenario. Whether their modeling of user representation is meaningful, they should provide specific definitions, clear assumptions and more specific explanations.\n\n3 The core motivation of the paper is not clear. For example, in line 33, the author did not explain why manually selecting clusters will limit the adaptability of MUR. How to understand the variability of interests across users? Why this type of method cannot simulate uncertainty well?\n\n4 The paper intro is vague and abstract, and it is hard for readers to establish a connection between the motivation and the proposed method.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for taking the time to review our paper. We address your main concerns below.\n\n**W1+Q2+Q3 Clarification on the difference of SUR, MUR, DUR**\n\nSUR uses a single point (K=1) in the embedding space to represent a user, while MUR uses multiple points (K>1, e.g., K=4 in MaxMF) to represent a user. We believe this distinction is clearly explained in the introduction and also in the name of these two categories (lines 24-26, 30-32). MUR generally outperforms SUR because users often have multiple interests, which are better captured by multiple points in the embedding space. This has been shown by previous works on MUR which we cited. For example, a user interested in documentary, horror, action, and comedy movies is more accurately represented by multiple points, each reflecting a different interest, as mentioned in line 31.\n\nRegarding Figure 1, lines 67-70 and the figure caption clarify that it is a t-SNE visualization of the prediction scores between a user and all items, reduced from an original embedding size (i.e., 64) to 2D. The x-axis and y-axis do not have specific meanings but form a 2D embedding space. The score, defined as *“the inner-product between user and item embeddings”* (lines 67-68), is represented by the color bar in each subfigure, with more “red” indicating higher scores and more “blue” indicating lower scores. While the subfigures for SUR and MUR look similar because both are point-based methods, the high-score region (red) in MUR is larger than in SUR, covering more small triangles (as described in line 70), indicating that MUR captures more user interests.\n\nFor DUR (Density-based User Representation), it uses a function over the item embedding space to encode user preferences (lines 45-47). The mathematical definition of DUR is provided in Section 4.1.\n\n**W4+Q5 Clarification on adaptability, uncertainty-awareness, efficiency**\n\n - **W2+W3+Q4 - *Adaptability***\n\nIn real-world systems, users have varying interests. For example, some users only like comedy movies, while others have broader interests. A user may also have different preferences depending on their mood and other contexts. This variability is what we refer to as \"interests generally have high variability across users\" (lines 35-36). This is also verified in our datasets, and we provide an analysis in \"Performance across User Groups\" (lines 350-360), where users are grouped based on the number of interests. Therefore, manually choosing a constant number of clusters (K) across all users is suboptimal. Deriving a personalized K is also hard since we do not know the exact number of interests a user may have, and new interests may emerge.\n\nWe are unsure what the reviewer means regards to “the specific manifestation in the recommendation scenario” as well as the concerns on “whether their modeling of user representation is meaningful”. Our DUR method is well-defined and well-motivated to solve the limitations of prior methods for capturing user’s multiple interests with Gaussian process regression. Also, we evaluate our method using three widely used datasets, comparing with 11 baselines in Section 5 and three generative recommendation methods in Appendix A.8, across four retrieval metrics (Table 1) and two ranking metrics (Table 2). The consistent superiority of our method demonstrates its ability to capture diverse user interests and improve retrieval and recommendation quality. Thus, our method has both theoretical grounding and empirical support for the improvements it offers.\n\n - **W2+Q6 - *Uncertainty-awareness***\n\nThe SUR and MUR methods cited in paragraphs 2 and 3 of the introduction do not consider uncertainty in user preferences as part of their model design. We also describe this in the second paragraph of the related work (lines 105-110, Section 2), noting that these methods use a deterministic approach to compute the relevance score between a user and an item. Capturing uncertainty is crucial for online exploration in recommendation systems as it balances exploiting known preferences and exploring new items, leading to improved personalization and adaptability to changing preferences. The ability of our method to capture uncertainty comes from the inherent nature of Gaussian Processes.\n\n- **Q5 - *Efficiency***\n\nEfficiency, as mentioned in lines 43-44, relates to avoiding high-dimensional embeddings. Lines 362-369 and Figure 4 detail our experiments and analysis. GPR4DUR achieves competitive performance with low-dimensional item embeddings, while traditional methods perform poorly with low dimensions.\n\n**Q1 Clarification on “simple collaborative signal modeling”**\n\nWe are unsure what “simple collaborative signal modeling” refers to. If the reviewer is referring to methods like Matrix Factorization, we highlight that our comparisons include 11 baselines (Section 5.4), most of which do use collaborative filtering signals and are more powerful than Matrix Factorization (for example, YoutubeDNN). The comparison with these stronger and state-of-the-art methods demonstrates the effectiveness and efficiency of our approach. If the reviewer has something else in mind, we would be happy to respond to any clarification.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "cPU9YLHlUD", "reviewer": "Reviewer_icLv", "summary": "This work presents a novel method for user representation in retrieval and recommendation systems. The authors propose a density-based approach that leverages the density of user interactions to enhance the representation of users. This method is aimed at improving the performance of retrieval and recommendation systems by better capturing the underlying user preferences and behaviors. The paper includes detailed experiments and evaluations demonstrating the effectiveness of the proposed approach compared to existing methods.", "questions": "Please refer to the Weaknesses section.", "limitations": "The authors have acknowledged several limitations in their work, especially the potential challenges in scalability.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "S1. The paper introduces a unique density-based user representation method that is novel in its approach. This originality is reflected in the way the authors have redefined user representation by focusing on the density of user interactions, which is a creative and fresh perspective in the field of recommendation systems.\n\nS2. The quality of the research is high, as evidenced by the thorough experimentation and detailed evaluations. The authors have conducted extensive tests to validate their method, comparing it with several baselines and showing significant improvements in performance.\n\nS3. The paper is well-written and clearly structured. The authors have provided comprehensive explanations of their methodology, including detailed mathematical formulations and algorithmic steps. The experimental results are presented in a clear and understandable manner.", "weaknesses": "W1. The proposed method uses item categories as auxiliary information, while most of the baselines only consider user-item interaction information. This may lead to unfair comparisons. \n\nW2. Some important baselines are missing. Specifically, STOSA[1], DT4Rec[2], and BERD+[3] use Gaussian distribution to model the uncertainty of user preferences in sequential recommendation, which are highly relevant to this work.\n\nW3. The Interest-wise Relevance (IR) metric might not be reliable, as it relies on the learned item embeddings which may be inaccurate.\n\nW4. The manuscript contains some typos. For example, on line 124, 'a RS' should be 'an RS'. On line 155, there should be an 'is' before the covariance function.\n\n\n\nReferences:\n\n[1] \tZiwei Fan, Zhiwei Liu, Yu Wang, Alice Wang, Zahra Nazari, Lei Zheng, Hao Peng, Philip S. Yu. Sequential Recommendation via Stochastic Self-Attention. WWW 2022: 2036-2047.\n\n[2] Ziwei Fan, Zhiwei Liu, Shen Wang, Lei Zheng, Philip S. Yu. Modeling Sequences as Distributions with Uncertainty for Sequential Recommendation. CIKM 2021: 3019-3023.\n\n[3] Yatong Sun, Xiaochun Yang, Zhu Sun, Bin Wang. BERD+: A Generic Sequential Recommendation Framework by Eliminating Unreliable Data with Item- and Attribute-level Signals. ACM Trans. Inf. Syst. 42(2): 41:1-41:33 (2024).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your positive feedback and appreciation of our method's novelty, soundness, and presentation. We address your main concerns below.\n\n**W1 Clarification on using the item categories**\n\nWe would like to clarify that many strong baselines we are comparing use the category information, such as MIND, ComiRec, and CAMI (short for Category-Aware Multi-Interest), thus we believe our comparison is fair. We avoid modifying other baselines which do not leverage category information. We view this as an inherent limitation of these approaches, as such information is fruitful and often easily available in real-world systems. \n\nAdditionally, we emphasize that using category information during item pretraining is necessary, as shown in Figure 6, Appendix A.3. Pretraining without the item-category auxiliary loss in Eq. (5) leads to misaligned item embeddings.\n\n**W2 Clarification on baselines**\n\nWe acknowledge that the cited works are relevant to user modeling in terms of capturing uncertainty. We appreciate the reviewer for pointing out these works and will add them in the related work section in our final manuscript.\n\nOur task is multi-interest retrieval (lines 115-116, lines 139-142), thus most state-of-the-art baselines we are comparing to are designed for this task, such as all MUR baselines. The focus of the works pointed out by the reviewer differs somewhat from ours: they each focus on the ranking phase rather than the retrieval phase (e.g., paper [1] and [2] pointed out by the reviewer use cut-off relevance metrics merely at lengths one and five to measure the ranking performance), and none of them have the goal of finding a collection of items that can cover a user’s multiple interests. Additionally, our method is non-parametric without additional transformer layers or feed-forward layers, which is also a big difference in the model architecture compared to the works pointed out by the reviewer. Given the 11 baselines in our experiment section, the 3 generative recommendation methods (including some very recent ones) in Table 10, Appendix A.8, and the different focus of the work pointed out by the reviewer, we believe our experiments convincingly show the effectiveness and efficiency of our method.\n\n**W3 Reliability of the IR metric**\n\nThanks for pointing this out: we considered this during our design and will make this more explicit in the discussion. As shown in lines 271-273, *“To obtain ground-truth similarities between items, and to mitigate the influence of the chosen pre-trained model, we pretrain the item embeddings using YoutubeDNN with a higher dimension size (d = 256) …”* Considering that YoutubeDNN is a mature method that has shown its success and reliability in one of the largest real-world recommendation platforms, we think it is reasonable to pretrain YoutubeDNN with a high dimension size to obtain reliable item embeddings. Our results on other metrics (IC, ED, TEI, Recall, nDCG) also demonstrate the superiority of our method over prior baselines on the multi-interest retrieval, showing a similar trend as the IR metric.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The paper proposes a method called GPR4DUR for multi-interest recommendation and retrieval by using Gaussian process regression and density-based user representation.

Reviewers mostly agree on the following contribution of the paper:
* using Gaussian Processes (GP) and density-based user representation to capture multi-interest of users and providing a measure of uncertainty on the recommendation is novel (all reviewers), 
* performance study is comprehensive (F9WH, Eeve, icLv)
* design new evaluation metrics tailored for multi-interest contexts (F9WH, Eeve)

The reviewers raised questions on scalability, clarity on adaptability and comparing with more relevant baselines etc.. Some of them are addressed during rebuttal. The authors are advised to incorporate these additional analysis and results in the final version.
Decision: Accept (poster)