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Controllable Recommenders using Deep Generative Models and Disentanglement

In this paper, we consider controllability as a means to satisfy dynamic preferences of users, enabling them to control recommendations such that their current preference is met. While deep models have shown improved performance for collaborative filtering, they are generally not amenable to fine grained control by a user, leading to the development of methods like deep language critiquing. We propose an alternate view, where instead of keyphrase based critiques, a user is provided 'knobs' in a disentangled latent space, with each knob corresponding to an item aspect. Disentanglement here refers to a latent space where generative factors (here, a preference towards an item category like genre) are captured independently in their respective dimensions, thereby enabling predictable manipulations, otherwise not possible in an entangled space. We propose using a (semi-)supervised disentanglement objective for this purpose, as well as multiple metrics to evaluate the controllability and the degree of personalization of controlled recommendations. We show that by updating the disentangled latent space based on user feedback, and by exploiting the generative nature of the recommender, controlled and personalized recommendations can be produced. Through experiments on two widely used collaborative filtering datasets, we demonstrate that a controllable recommender can be trained with a slight reduction in recommender performance, provided enough supervision is provided. The recommendations produced by these models appear to both conform to a user's current preference and remain personalized.


INTRODUCTION
Auto-encoder based architectures have shown impressive performance in collaborative filtering with implicit feedback [19,25,30]. However, these methods may fail to model short term or dynamic preferences of a user. Subsequently, methods to tackle this explicitly problem have been proposed, for example, through conversations via a conversational recommender system [13], or critiquing recommendations using language or keyphrases [18,23,35,37]. In contrast to keyphrases, typically mined from reviews or descriptions (for instance), this work considers building controllable or critique-able recommenders using attribute data for items, which can be used to construct preference distributions at a user level. This is in turn used in the critiquing process or to express a short-term preference, allowing a user to exert control over a recommender in a meaningful manner. For instance, a user who typically watches Action movies, or (as a consequence) exclusively receives Action recommendations, can now explicitly request personalized movies of other genres, like Animation.
Controllability can be achieved by utilizing the generative nature of certain Deep Generative Recommenders [18,23,35,37]. Such models have an encoder which produces a user-latent representation, which is fed to the decoder to predict items for that user. A manipulation of this representation, followed by decoding step using this, should alter recommendations produced by the model. However, since the latent spaces of these models are typically entangled, the outputs produced through such manipulations are likely to be unpredictable or random, making them unusable for this task.
We propose using a disentangled latent space which, in contrast, can be manipulated predictably. A representation is disentangled w.r.t known ground truth variables or generative factors (ex. genres, availability, context, etc), if there is only one latent dimension in the representation that is influenced when this ground truth variable is changed [3,12,20,21].
Prior work tackles critiquing/controllability by modeling a latent space where keyphrases are co-embedded with user/item embeddings. By 'zero-ing' out a certain keyphrase, the corresponding keyphrase embedding is used to update the user representation, producing critiqued recommendations. Our work in contrast doesn't utilize a co-embedding space, and instead the latent space is directly manipulated. This means no addition optimization (like in [18,22]) is required to incorporate (multi-step) critiques. Furthermore, this also allows for 'positive' critiques as well as 'soft' control (gradual, non-binary) instead of only binary critiques.
We propose using supervision to obtain a mapping of a particular factor/aspect to a latent dimension. Since supervision signals might not be available for all users, we experiment with settings where limited data is provided.
In addition, while there have been metrics previously proposed for evaluating controllability/critiquing [32,35,37], these metrics don't explicitly account for the personalization of post-critique recommendations. We propose multiple metrics to evaluate the personalization of critiqued recommendations, measuring both binary critiques as well as 'soft', gradual controllability. To summarize, our contributions are as follows 1 : • We propose using (semi-)supervised disentanglement to learn disentangled representations for controllable, personalized recommendations. Through experiments on two large scale collaborative filtering datasets using 2 types of signals as 'knobs', we show the proposed models produce controllable recommendations, at the cost of a slight reduction in overall recommendation performance. In addition, we experiment with different levels of supervision, and show controllability can be achieved with limited data. • We focus on retaining recommendation performance while achieving effective controllability, and propose several metrics to extensively study (a) the degree of personalization of controlled recommendations (b) whether control is achieved in isolation (i.e if only one factor changes at a time) and (c) the effect of disentanglement on controllability. Using these metrics, we demonstrate that such models are amenable to user control, and the controlled recommendations appear to be personalized to an extent.

BACKGROUND AND RELATED WORK 2.1 Deep Recommender Systems
There have been several works that use Deep Learning for Recommendation [11,31,33,38]. A common theme in several deep models is the use of auto-encoder architectures like the Collaborative Denoising Autoencoder (CDAE) [36] or MultVAE [19]. The latter uses the Variational Autoencoder framework [5,17] for recommendation. Shenbin et al. [30] propose the state-of-the-art RecVAE. Deep Recommender systems however are (typically) black-box models which are difficult to interpret, compared to content-based methods [38].

Disentangled Representation Learning
The use of deep generative recommenders allow for disentangled representations, regaining some interpretability [9,24,34]. Most such models use the VAE framework, where the objective is to reconstruct the input with high probability, with an additional loss term constraining the latent space. By imposing additional constraints, disentangled representations can be learnt. These methods are typically unsupervised and therefore come with limitations [20]: they were found to be very sensitive to hyperparameters, reliably learning unsupervised disentangled representations is a very challenging task.
There have been several works that use disentanglement in recommendation: Ma et al. [25] assume that disentanglement is generated by user behaviours on 'macro' and 'micro' levels, and show that their models outperform non-disentangled baselines. Ma et al. [26] apply disentanglement to the sequential recommendation task, while Wang et al. [34] disentangle diverse user-intents using graph based collaborative filtering; Cui et al. [9] propose DGCF, which have 'implicit' (unknown) and 'explicit' (known) signals that are disentangled using an RNN based model with a two-step method since some computations are non-differentiable. Wang et al. [32] propose using weakly-supervised disentanglement objective on pairs of items. This allows for attribute-based item retrieval, such that items differ more/less on the provided attribute. In contrast to prior work, we use semi-supervised disentanglement, while focusing on using disentanglement for controllability.

Critiquing / Controllable Recommenders
We focus on critiquing for deep recommenders (for a full overview of earlier work in critiquing, see Chapter 13 of [29]). The following paragraphs detail approaches that leverage language or keyphrases for critiquing, followed by other approaches like ours which does not utilize any language/keyphrase. We end this sub-section with a discussion about evaluation metrics.
Recent work has focused on using language or keyphrase based critiquing [18,23,35,37]. Wu et al. [35] propose the Deep Language based Critiquing (DLC) paradigm, where (subjective) keyphrases are treated both as explanations as well as a means for a user to critique recommendations. Here, critiquing is achieved by rejecting or 'zero'-ing out keyphrases which are co-embedded with users. Luo et al. [22] adapt the CE-NCF for multi-step critiquing; [18] use a ranking optimization instead of pairwise re-scoring to rerank items; [23] use a VAE-based model to achieve better training stability and lower computational complexity; [37] propose using Keyphrase Activation Vectors instead of using a second 'head' used in [35], and adapt it for 'positive' critiques. Antognini et al. [2] propose T-RECS, which infers keyphrases from the intersection of user profiles and an item. [1] show that a model under a weaksupervision scheme matches or beats recommendation/explanation and critiquing performance while being much faster. We use supervised disentanglement in the user-latent space instead of a separate embedding space, while not requiring any language data (at the cost of no explanations). Prior work focuses on binary signals ex. reject/accept, while our work considers 'soft' critiques, allowing for a gradual tuning. Note that while we experiment only with unit critiques, compound and/or multi-step critiques is also possible within our proposed models, which we leave for future work.
Wang et al. [32] propose an orthogonal task, where items are retrieved on a 'gradient' given an attribute, focusing on gradual change, similar to our work. Our work focuses on recommendation performance whereas [32] focus on gradient item retrieval. Cen et al. [7] propose ComiRec for sequential recommenders, where control is used to balance diversity and recommendation accuracy, from the perspective of a designer. The method presented in [25] is closest to us, where representations are first altered, followed by a nearest neighbours search over items using a beam search. In contrast, we utilize the generative nature of the model instead of performing nearest neighbour search, in addition to using semisupervised disentanglement. The authors are aware of concurrent work [28] that is close to ours. Since the paper/code was unavailable at the time of experiments/ publication, we leave the evaluation of [28] for future work.
Metrics for critiquing/controllability. Wu et al. [35] propose the Falling MAP for negative critiques. Given a user and a keyphrase (here, genre/tag) this metric measures the difference in MAP values computed on the set of items that have the critiqued keyphrase. If this value is positive, items of the critiqued keyphrase 'falls' down the ranking list, which is desirable. Similarly [37] propose a follow up metric, which accounts for positive critiques as well, comparing the normalized difference of average ratings of items before / after the critique. We note that these metrics don't explicitly model the personalization of post-critique recommendations. In contrast, the proposed metrics explicitly consider this, by measuring performance on against items for which a user's preference is known.

METHODOLOGY
We present disentanglement of the latent space using semi-supervision as a means to control in Section 3.1. Adapting disentanglement representation learning for this task is explored in detail in Section 3.2.

Control using (semi-)supervised disentanglement
We train a model using a (semi-)supervised disentanglement loss, producing disentangled user representations. During inference, representations for all users are inferred (possibly offline). In the foreground, the representations are manipulated on the fly by increasing/decreasing a 'knob', allowing for granular change. In the background, the mapping of a knob to a latent dimension is utilized to modify the user's representation, which is fed to the decoder to produce controlled recommendations. The following paragraphs motivate the use of disentanglement and semi-supervision to build such a recommender. As mentioned before, the entangled nature of a typical deep recommender renders meaningful manipulation impossible. This is because (a) there is no guarantee that manipulations produce changes in a single generative factor, and (b) it is not apparent which dimension to alter given a factor. Even if we assume (b), predictability is not guaranteed, ex. manipulating the Thriller dimension may increase the number of Thriller movies, but it may inadvertently increase the number of Children movies, which is undesirable.
We propose using supervised disentanglement to tackle these issues. Disentanglement can isolate a generative factor to a single dimension, and altering this dimension (assuming perfect disentanglement) space should produce a change only in this generative factor. Using (semi)-supervised disentanglement addresses two issues: (a) unsupervised disentanglement has several shortcomings [20], which semi-supervision may alleviate; and (b) a particular dimension is now 'tied' to a generative factor, ensuring that the correct dimension is being altered.
These recommendations should ideally be personalized, since they were trained with a reconstruction loss. In essence, a recommender system can be tuned on the fly to express user preferences for the current session. This process is illustrated in Figure 1.
In this paper we opt for preference distributions i.e tag/genre distributions, as generative factors or 'knobs' (see Section 5.1.2), since they are widely available. However, preference distributions are not independent and can also be very noisy [4,10], in contrast to independent and exact generative factors used in disentanglement literature e.g dSprites [27]. Consequently, they may be difficult to learn and/or disentangle. The following section discusses particulars about the models.

Unsupervised and Semi-supervised Disentanglement
In this section, two models, the -VAE [12,19] and the -TCVAE [8], are adapted for the recommendation task using a Multinomial loss [19], resulting in recommenders that can produce disentangled representations. Furthermore, this objective is further supplemented with a semi-supervision loss.

Unsupervised Disentanglement.
The VAE [17] optimizes the marginal (log-)likelihood of the observed data x in expectation over the whole distribution of latent factors z. It assumes that the data is supported on a low dimensional manifold in a high dimensional space. The assumption of a latent code allows us to express the marginal distribution as follows: Since this quantity is intractable, the Evidence Lower Bound is optimized instead [14]: (1) where (z|x) is a variational approximation of the posterior distribution, which is typically a Gaussian distribution. (z), the prior, is usually an isotropic Gaussian: (z) = N (0, 1). Several methods modify this objective to encourage disentanglement: The -VAE [6,12] modifies the VAE loss i.e Equation 1 by adding a -multiplier to the KL term: Disentanglement is encouraged by setting > 1, which further forces the posterior distribution (z|x) to be close to the isotropic prior for every x (as opposed to only on average), imposing statistical independence. However, this involves a trade-off between reconstruction quality and disentanglement [6,12]. While Liang et al. [19] use < 1 for better recommender performance, we opt for >= 1 to encourage disentanglement, and achieve similar/better recommender performance by removing the Dropout layer, following Shenbin et al. [30]. An annealing strategy is used for , following [6,19]. The resulting model, which uses a Multinomial loss (see Section 5.3.2), is termed Mult--VAE .

3.2.3
-TCVAE. Chen et al. [8] show that by imposing a constraint on only a part of the KL divergence term, reconstruction and disentanglement increases compared to the -VAE model. The KL term is decomposed into 3 terms (a) an index-code Mutual Information (MI) term, (b) dimension-wise KL, and (c) a total correlation (TC) term. The index-code MI captures the information between the data and latent variables, based on the empirical data distribution; the dimension-wise KL prevents deviation of the posterior from the prior dimensions; and the TC term encourages statistical independence of the posterior distribution leading to disentanglement. The key idea is that the -VAE constrains all 3 terms, which might harm performance, while only the TC term is penalized in this model. The loss function of the TC-VAE is as follows: where , and are multipliers for the index code MI, the dimension wise KL and the TC term respectively. Following Chen et al. [8], = = 1 is used, is a hyperparameter. The final model, which we term Mult-TCVAE , uses a Multinomial loss (see Section 5.3.2).

Semi-supervised Disentanglement. The distribution (z|x)
can be constrained so that a given dimension of (z) is associated with a ground truth attribute. That is, given a representation (for instance, the mean vector from the posterior) for a data point, ∈ R , and the set of known attributes a ∈ R for that data point, with ≤ , the th dimension of is predictive of the th dimension of a, 1 ≤ ≤ . This is achieved by adding a semisupervised loss : L unsup is either Equation 2 or 3. The binary cross entropy loss is used for [21]: where (.) is the logistic function. Note that the remaining dimensions of z, those that are not supervised, are not constrained by the semi-supervision loss.

EVALUATION METHODOLOGY
In this section we propose an evaluation methodology and a set of metrics that investigates the extent of controllability and personalization of a recommender, described in Section 4.1. We also briefly describe existing metrics for evaluating disentanglement in Section 4.2.

Evaluating Controllability
For ease of discussion, this section assumes a single factor , s.t given a user , and a factor , the set of all items with factor is I , items encountered/rated by a user is I , and items with factor that user has encountered is I ( , ) = I ∩ I (subscripts for z are dropped for brevity in the following descriptions). Note that  an item can have multiple factors e.g a movie can be both Action and Adventure.
Given a user representation z, the dimension corresponding to is obtained by using a mapping function , s.t ( ) is the dimension corresponding to in z, with ( ) ∈ {1, . . . }, with ≤ , where D is the dimensionality of the latent space. In addition, we assume that manipulations of each dimension are in ∈ [0, 1] (0 is minimum). A manipulation entails the replacement of the ( ) dimension with a value indicating the position of a 'knob', producingz. In addition, the top-n items ofx is denoted by top n (x), and the number of items of a factor in the top-n list is denoted by Count(top n (x), ). Finally, the ℎ element of a vector a is denoted by We assume a ranking metric R-MET, computed against a held out set of items. R-MET can be any ranking metric, e.g. NDCG, assuming the relevance of all items except the ones in the holdout set to zero. We consider five metrics in total, with the two metrics, ctrl and irrel , measuring the ranking changes of items of interest versus other items; and three correlation metrics measuring the gradual change observed as a dimension is manipulated: Corr, and (Corr ctrl ,Corr rand ). The metrics measures the change induced when a user prioritizes items of only one factor, reflecting a critique or a short term preference i.e 'show me Animation movies only'. The correlation metrics on the other hand can capture exploratory behaviours or soft preferences ('maybe I will try at Horror movies'), and measures to what extent the recommender is interactive and predictable. These metrics are summarized in Table 1 along with their inputs and holdout sets. Note that all the metrics are averaged across genres and then users.

4.1.2
metrics. Similar to - [35] and PostCritRatingDiff [37], ctrl measures the change in the ranking as a knob is set to its maximum value. Note, however, that only items not belonging to that the user likes are fed into the model, with the intent to observe if manipulating the ( ) ℎ dimension increases the positions of the held-out items of genre that a user likes. As a consequence, the model has to infer the correct items of to recommend, without knowledge of the users preference towards items of . Furthermore, in contrast to prior metrics, this evaluation is personalized i.e the metric is computed against I ( , ) and not I . The process to compute the metric is detailed below.
First, before the manipulation, items of other genres that the user has liked, I −I ( , ) is used to infer x. R-MET default is computed on this, using I ( , ) as the holdout set, measuring the baseline ranking score of personalized items belonging to . Second, [z] ( ) is set to max indicating a high preference, and decoded to producex. This is used to compute R-MET ctrl on the same holdout, expressing the ranking score of personalized items belonging to after manipulation. The difference between the two metrics is ctrl : The higher the ctrl , the better the ability to produce personalized and controlled recommendations.
The second metric, irrel , is a variation of ctrl . While recommending items of genre before items of other genres is important, it is desirable to recommend items that the user might like, over irrelevant items of . irrel is similar to ctrl , except the holdout set are items of not rated by the user, I − I ( , ) . If irrel is high, items that the user might not like are also being promoted, which may be undesirable. While these two metrics reflect the extent of controllability, granular metrics, reflecting gradual change is presented in the following section.

Correlation Metrics.
The following metrics compute the correlation between changes in ranking metric R-MET and the values of the manipulated dimension. The correlation measure used in the experiments is the Pearson's correlation, we leave non-linear variants to future work.
Corr quantifies the correlation of gradual manipulations (as opposed to setting it to the max value as with ctrl ) with R-MET using I ( , ) as the holdout set. Corr ctrl and Corr rand measure the same correlation with different holdout sets and identical inputs. Corr ctrl uses I ( , ) as the hold out, measuring the effect of manipulation against items of , whereas Corr rand uses I ( , ) which measures the effect of manipulation against items of a random control factor . The input set for the last 2 metrics has neither items of nor . In the ideal case, Corr ctrl should be positive i.e controlling ( ) positively influences items of , but Corr rand should be zero (no change) or negative (decrease, either due to replacement or demotion), meaning items of another factor are not/negatively influenced.
It is our hypothesis that keeping items of irrelevant genres low in the ranking is harder if the genre being controlled is highly correlated with another genre in the data (e.g many Action movies are also tagged Adventure). To measure this, we use two : easy and difficult , where easy is the least co-occurring factor with and difficult conversely frequently co-occurs with producing EasyCorr ctrl , EasyCorr rand , DiffCorr ctrl and DiffCorr rand 2 .

Evaluating Disentanglement
In addition to controllability, disentanglement of the user representations can also be evaluated since the ground truth generative factors are available. Several metrics have been proposed to evaluate disentanglement, such as the Mutual Information Gap (MIG) [8], the -VAE metric [12] or the FactorVAE metric [15]. We evaluate disentanglement with the Mutual Information Gap (MIG) [8], due to ease of implementation, wide applicability and the unbiased nature of the metric for all hyperparameter settings [20]. Given a generative factor, the empirical mutual information (M.I) between the values of the ground truth generative factors and each dimension of encoded samples from the data is computed. The MIG of this generative factor is then the difference between the highest and second highest MI values. This quantity is averaged across all generative factors to obtain the MIG score. A MIG of 1 for a particular generative factor implies that one latent dimension has MI=1, with others having MI=0.

EXPERIMENTS
The datasets, along with the requisite processing steps and generative factors for supervision are described in Section 5.1. The research questions are described in Section 5.2, followed by specifics of models in Section 5.3.

Datasets
In our experiments we use the Million Songs Dataset (MSD) [4] and the Movielens-20M (ML-20M) [10], two widely used collaborative filtering datasets. The steps for preparing the dataset for training are outlined in Section 5.1.1. Preference distributions are constructed as signals for supervision and for evaluating disentanglement/controllability, which is described in Section 5.1.2.

Dataset processing.
Each dataset is processed according to the steps outlined in [19]. The users are split into test, validation and train sets. The test/validation set size for ML-20M is 10,000 users and for MSD is 50,000 users, with 20% of items held-out. The models is trained with the entire train history, and evaluated with the 20% held out set. The data is binarized by keeping ratings of four or higher and only users who have interacted with at least 5 movies are kept.

Generative Factors.
The generative factors considered for both datasets are preference distributions computed for each user using genres (MSD/ML-20M) or tags (MSD only). The number of users, items, generative factors are reported in Table 2. For a user , Genre is computed by calculating the proportion of movies that belong to a genre (or tag), divided by the total number of movies that the user has watched, capturing the (global) preferences of a user towards a genre/tag. Since there are 522362 tags in MSD with many repeats, only the most frequent are picked and grouped

Research Questions
This section details the experimental setup employed in the paper. The evaluation metric for recommender performance throughout this paper is NDCG@100, following [19,30] i.e R-MET is NDCG for all experiments. Controllability for models with 0 supervision cannot be evaluated since (.) is unavailable. In addition, the manipulations (which replaces [z] ( ) ) are produced by using the Inverse CDF of the probability distribution used during training [17].

RQ1 How much supervision is needed for achieving controllability? How does controllability vary across datasets and models?
To investigate this, we train Mult--VAE and Mult--VAE with varying levels of supervision: {0%, 1%, 10%, 50%, 100%}. For each combination of model, signal, level of supervision, we compute the five metrics outlined earlier. To summarize, ctrl evaluates the performance gain when a user sets a knob to its maximum setting, Corr measures the gradual change via a correlation of manipulations and R-MET; the other metrics contrast the controllability of a genre against two control genres. The holdout sets used to compute the metrics above are constructed for 100 users per genre (metrics remain constant beyond 100), while ensuring that there are at least 10/5 items in the input/holdout sets described in Table 1. The number of steps taken in the latent space is 50 for computing the correlation metrics.

RQ2
To what extent does disentanglement affect controllability of models? The relationship between disentanglement and controllability is explored in this section, where we measure if models with disentanglement ( >= 1) perform better than models without ( = 0). Note that = 0 implies no disentanglement, but for the Mult-TCVAE , only the TC constraint is set to 0, i.e which means = 0, = = 1. In addition, we investigate if models that have higher disentanglement (MIG) scores perform better based on recommendation/ controllability metrics. MIG is computed using code from [20] 4 , modified for use in pytorch. Since the exact M.I is intractable, the empirical M.I is computed by discretizing the values, following [8,20]. The number of bins for the discretizer is set to 20, and it is computed for on 10,000 samples from the test set.

RQ3 What effect does introducing controllability into a model have on recommendation performance?
This question deals with the relevance of both controlled and 'default' recommendations. This is paramount, otherwise recommendations can be irrelevant. As such, NDCG@100 is computed for all models, and model selection is done on the basis of recommendation performance on the validation set. We remind the readers that irrel has to be interpreted with ctrl . That is, if irrel is low and ctrl is high, recommended items may be personalized; however, if irrel is higher, the models do exhibit controllability, but the recommended items might not be all personalized. Note that these metrics might be limited since a user might like these items regardless, or, such recommendations might be explicitly sought by the user. Performance for models with no disentanglement ( = 0) and no supervision (% = 0) are also reported.

Experimental Setup
This section details specifics of models being used, along with hyperparameters: N (0, 1)), and a Gaussian distribution for the variational posterior :

Variational Distribution. Both Mult--VAE and Mult-TCVAE use a isotropic Gaussian distribution for a prior ( (z) =
where (x) and 2 (x) are outputs of the encoder network.

Multinomial loss.
We use the Multinomial log-likelihood for , which has been shown to perform well over other losses like the Gaussian/Logistic losses [19]:  5). In addition, = 0 for models with no supervision (%=0), and = 1 otherwise (%>0). To obtain recommendations, items are sorted in the descending order of the likelihood predicted by the decoder.

Model Hyperparameters.
All models use the same neural network with a 3 layer encoder, with dimensions |I| → 600 → 600 → 200 and a single layer decoder which was found optimal for a variety of settings [30]. The outputs of the encoder are two 200 dimensional real vectors representing the mean/log-variance vectors.All models were trained with Adam [16] with a learning rate of 0.001 and a batch size of 500 for 200 epochs for ML-20M and 100 epochs for MSD. For both, we tried ∈ {1, 2.5, 5, 10, 100}, with the 'best' model selected using NDCG@100 computed on the validation set. For the Mult-TCVAE , we set = = 1. Table 3: Results for ML-20M: MIG measures disentanglement, ctrl and Corr measure control, with EasyCorr ctrl , EasyCorr rand , DiffCorr ctrl and DiffCorr rand contrasting control of one genre against another. NDCG and irrel (when contrasted with ctrl ) measure personalization of non-and controlled recommendations respectively. Values in braces are standard errors.

RESULTS
The results of all experiments on ML-20M is reported in Table 3, on MSD (Tag) in Table 4 and finally on MSD (Genre) in Table 5. The results indicate that while increasing supervision generally tends to increase controllability, too much supervision can sometimes harm controllability, or alternatively increase controllability at the cost of more non-personalized recommendations (Section 6.1). The degree of supervision required for controllability varies across models/datasets/signals. In addition, adding a disentanglement objective helps across all metrics, but there appears to be no conclusive trend between degree of disentanglement and controllability (Section 6.2). Finally, controlled recommendations seem to be more personalized for ML-20M compared to MSD, where more non-personalized items get recommended (Section 6.3). We discuss each result in detail in the sections that follow.

Semi-Supervision and Controllability
Surprisingly, apparent control over recommendations seems to be achieved with as little as 10% of data for both datasets, as measured by high Corr and ctrl . In addition, these values increase as supervision is increased to 50% for all data and models. Supervision beyond that, however, can produce mixed results; for instance, Mult--VAE trained on 100% of ML-20M scores worse on ctrl and Corr. In contrast, for MSD(Genre) and MSD(Tag) (with the exception of Mult--VAE for 100%), ctrl increases with supervision. These trends also hold for the = 0 models. Therefore, in most cases, supervision increases apparent controllability.  Given a model which scores high on ctrl (or Corr), finer grained RandCorr metrics can be analyzed, to check if changing a knob inadvertently changes other genres 5 . Increasing supervision for ML-20M makes models score better on DiffCorr rand (i.e more negative), while only slightly decreasing DiffCorr ctrl , indicating that supervision can help with similar genres in particular. While supervision initially improves EasyCorr rand , 100% supervision actually worsens it slightly from 50%. Therefore, for ML-20M, supervision can help the model avoid confusing similar genres, at the (slight) cost of controlling dissimilar genres, especially if fully supervised.
For MSD (Genre), we first note that values of EasyCorr rand and DiffCorr rand are positive for this dataset, indicating that other genres are also being manipulated. Increasing supervision increases EasyCorr ctrl and DiffCorr ctrl i.e help control, while EasyCorr rand and DiffCorr rand tend to become worse, indicating confusion among other genres. While EasyCorr ctrl and DiffCorr ctrl becomes worse with 100% supervision, EasyCorr rand and DiffCorr rand improve, indicating that full supervision can help with confusion. In conclusion, for MSD (Genre), increasing supervision generally improves control, at the cost of other genres being also recommended, which improves with 100% supervision for MSD(Genre).
In MSD (Tag), supervision generally increases EasyCorr ctrl and DiffCorr ctrl . For the Mult-TCVAE , increasing supervision to 100% makes the model score better on DiffCorr rand , but worse on EasyCorr rand . In contrast, for increasing supervision to 100% for the Mult--VAE makes the model score worse on both DiffCorr rand and EasyCorr rand . For the MSD (Tag) dataset, therefore, while supervision increases controllability, too much can cause confusion between tags.
In summary, while an increase in supervision generally increases controllability across datasets and models, and additionally reduces confusion between factors, too much supervision can harm performance by causing other genres to also be recommended alongside the one being controlled. 5 Note that EasyCorr ctrl (or EasyCorr rand ) cannot be compared with DiffCorr ctrl (or DiffCorr rand ), as the inputs for computing these metrics can be very different. In addition, we observed that a lot of values of EasyCorr rand (at user/genre level) are equal to 0.

Disentanglement and Controllability
This section discusses if disentanglement ( >= 1) models are necessary, and if increased disentanglement as measured by the MIG score contributes to controllability.

Comparison with baselines. Models without disentanglement
= 0, generally score worse in most respects, compared to models with disentanglement. For the ML-20M dataset, = 0 models have comparable controllability scores compared with models with disentanglement. However, this comes at a drastic reduction in recommender performance i.e the best NDCG (0.2904) among the baselines is worse than the lowest NDCG among models with disentanglement (0.3675). This is also seen for the MSD (Genre) datasets, although the performance drop is smaller. For both the MSD datasets, however, the gap observed in the controllability performance of entangled/disentangled models is much greater than the gap in the ML-20M dataset, indicating that disentanglement is necessary for controllability in these datasets. Overall, models with disentanglement perform better than models without disentanglement. The next section compares the degree of disentanglement with controllability.

Does increased disentanglement help?
For the ML-20M dataset, increased disentanglement results in lower recommendation (NDCG) performance. ML-20M models with high MIG scores perform better on ctrl , although this doesn't seem to be necessary for Mult-TCVAE with % = 50, which scores high on many metrics despite having a low MIG score. For the MSD (Genre) models, a jump in MIG is accompanied by large increases in ctrl and irrel . However, as the values of MIG scores here are either high or near zero, it's difficult to make concrete conclusions about the precise relationship between disentanglement scores and controllability. We note, however, that Mult-TCVAE , which achieves better disentanglement [8] in general, seems to perform better on the ML-20M and MSD (Tag) dataset while achieving the highest MIG scores, while Mult--VAE performs better and achieves the highest MIG score for MSG (Genre).

Controlled Recommendation Performance
We first note that as the amount of supervision, and consequently, controllability increases, average recommender performance (NDCG) decreases. However, we argue that the benefits might outweigh the cost, as this drop is relatively small while providing control for users (or practitioners). While NDCG measures performance of non-controlled recommendations, the degree of personalization of controlled recommendations can be measured by comparing ctrl and irrel .
The results vary depending on the model or dataset. For instance, since ctrl is much higher than irrel for Mult--VAE with 100% supervision on the ML-20M, we can conclude that it recommends personalized items instead of random items that a user might like. However, the opposite is true for Mult-TCVAE , as ctrl and irrel are at a similar level, which means that the items recommended on controlling a genre might not be as personalized to the user. Mult-TCVAE produces the highest ctrl scores for the ML-20M and MSD(Tag) datasets, while Mult--VAE produces the highest ctrl scores for MSD (Genre). In addition, while ctrl is higher (more items of that genre are being pushed to the top), irrel is also very high in MSD (Genre), which mean recommendations are controllable, but might not be personalized. However, as data sparsity increases, irrel might be overestimated because of missing relevance judgements, as evidenced by high irrel for almost all models trained on MSD. In addition to incompleteness, this evaluation also does not account for the exploratory/interactive/serendipitous nature of controllable recommendations.
In summary, controlled recommendations appear to be personalized, as evidenced by high scores of ctrl , showing that users can exert control and expect personalized recommendations to an extent. However, other items of the given genre might also be recommended, which is especially true for the MSD dataset.

CONCLUSION
We showed that controllable recommendations can be achieved by leveraging the generative nature of recommenders. (Semi-)supervised disentanglement is used both to tie a generative factor to a known dimension, and to enforce disentanglement. Consequently, manipulating a dimension produces controlled recommendations, allowing a user to express short-term/dynamic preferences, or to explore these recommendations in an interactive manner. We experimented with genre/tag distributions as supervision signals on two datasets. We proposed metrics to measure the extent of controllability in addition to the degree of personalization of controlled recommendations. Using these metrics, we showed that a user can control recommendations, while retaining personalization to an extent. We showed that such control comes only at a slight reduction in recommendation performance, but might require different degrees of supervision depending on the data, model or signals used.
While the experiments here detail controlling only a single dimension, multiple dimensions can be manipulated allowing for greater or more nuanced control, which we leave for future work. In addition, the dimensionality of the supervision signal is limited by the dimensionality of the latent space, which limits the applicability to large sets of knobs. Evaluating the personalization of controlled recommendations presents a challenge as outlined in the previous section, which we plan to pursue in the future. In addition, this method can be used to 'boost' recommendations of items belonging to a particular category, for instance, if items of category X are being under-recommended (possibly due biases), they can be boosted to compensate for it.