SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Jinqiu Jin $^{1,*}$  Haoxuan Li $^{2,*}$  Fuli Feng $^{1,\dagger}$  Sihao Ding $^{1}$  Peng Wu $^{3}$  Xiangnan He $^{1}$
$^{2}$ Peking University  $^{3}$ Beijing Technology and Business University
jjq20021015@mail.ustc.edu.cn, hxli@stu.pku.edu.cn, fulifeng93@gmail.com,
dsihao@mail.ustc.edu.cn, pengwu@btbu.edu.cn, xiangnanhe@gmail.com
Item-side group fairness (IGF) requires a recommendation model to treat different item groups similarly, and has a crucial impact on information diffusion, consumption activity, and market equilibrium. Previous IGF notions only focus on the direct utility of the item exposures, i.e., the exposure numbers across different item groups. Nevertheless, the item exposures also facilitate utility gained from the neighboring users via social influence, called social utility, such as information sharing on the social media. To fill this gap, this paper introduces two social attribute-aware IGF metrics, which require similar user social attributes on the exposed items across the different item groups. In light of the trade-off between the direct utility and social utility, we formulate a new multi-objective optimization problem for training recommender models with flexible trade-off while ensuring controllable accuracy. To solve this problem, we develop a gradient-based optimization algorithm and theoretically show that the proposed algorithm can find Pareto optimal solutions with varying trade-off and guaranteed accuracy. Extensive experiments on two real-world datasets validate the effectiveness of our approach. Our codes are available at https://github.com/mitao-cat/nips23_social_igf.
Developing fair recommendation algorithms is crucial to perform reliable information search and decision making, which prevents users' as well as platforms' interests from being sacrificed [1]. One particular aspect of recommendation fairness is item-side group fairness (IGF), which requires a recommendation model to treat different item groups similarly, and the items are grouped based on attributes such as category or brand [2, 3, 4]. Existing IGF frameworks primarily focus on the direct utility of item exposures, requiring a similar number of exposures for different item groups, and can be broadly categorized into two forms: Statistical Parity (SP) [5, 6] and Equal Opportunity (EO) [7].
Nevertheless, the existing IGF notions overlook the social utility of item exposures, as users with different social attributes may produce varying utilities due to the social influence among users. For example, a user's friends may view a recommended micro-video due to sharing activities or public record in the user's timeline. This can lead to unfairness problem in which some item groups benefit more than others though the existing IGF notions are satisfied. Figure 1a illustrates a toy example where item group A receives the same number of exposures as group B, thus satisfying the requirement of the previous SP, while items in group A are recommended to users with greater numbers of friends. This motivates us to consider both direct and social utility for IGF notions.
(a) Previous IGF notions
(b) Social attribute-aware notions
Figure 1: A toy example with item groups A and B to illustrate direct and social utilities of the IGF notions, where "# Exp" is the number of exposed users across the item group, and "# Friends" is the number of friends of the exposed users. The multi-objective optimization considers both utilities.
(c) Multi-objective optimization
In this paper, we first introduce two social attribute-aware IGF metrics, namely Neighborhood SP (NSP) and Neighborhood EO (NEO), which require that users exposed to different item groups have similar total social utility. As shown in Figure 1b, item groups A and B have the same total social utility, which is measured by the number of friends in this toy example. Compared to the previous SP and EO notions, NSP and NEO require similarity in the neighbors of the exposed users, rather than simply requiring the similar number of exposed users across the item groups. However, optimizing only the social attribute-aware IGF metrics may result in varying direct utilities across different item groups, e.g., item groups A and B in Figure 1b have the different number of exposed users. Therefore, it is reasonable to consider both direct and social utility when developing fair recommender models.
To this end, we next formulate a multi-objective optimization problem for training the recommender models with consideration of both direct and social utility, and further require flexibility and controllability of the trade-offs. Specifically, motivated by the previous study [8], we incorporate pre-defined preference regions with varying trade-offs between the direct and social utility into the multi-objective optimization problem, enabling the flexibility to choose the desired trade-offs in practice. Meanwhile, we also incorporate a customizable accuracy constraint for the controllability of the optimization, which leads to a guaranteed recommendation accuracy while satisfying the IGF notions.
We further propose a Social attribute-aware Flexible fair recommendation training algorithm with controllable Accuracy (SoFA), for solving the above multi-objective optimization problem. Given a pre-defined preference region, the proposed gradient-based algorithm updates the model parameters within this region to achieve the desired trade-off. On the other hand, when the accuracy loss exceeds a given threshold, the model parameters update direction is changed to achieve the minimum accuracy guarantee. We also theoretically show that SoFA can find Pareto optimal solutions with varying trade-off, meaning the direct and social utility of the trained model is not dominated by any other solutions. Extensive experiments are conducted on two real-world datasets with user social attributes, and the experimental results validate the effectiveness of the proposed training algorithm.
The main contributions of this paper are summarized as follows:
- We propose two social attribute-aware IGF metrics, named NSP and NEO, to study the item exposure utility gained from the user social network.
- We formalize a multi-objective optimization problem to achieve flexible trade-off between the direct utility and social utility with controllable accuracy sacrifice of the recommendation.
- We further propose a gradient-based optimization algorithm to solve the above problem, called SoFA, and theoretically show that SoFA can find Pareto optimal solutions with varying trade-off.
- We conduct extensive experiments on two real-world datasets, revealing that methods ignoring social influence would lead to unfair exposure, and validating the effectiveness of our proposal.
In this section, we present the background about personalized recommendation, item-side group fairness including SP and EO notions, and multi-objective optimization.
Personalized Recommendation. Personalized recommendation aims to select a small subset of items to each user  $u$  based on historical data, with users denoted as  $\mathcal{U} = \{u\}$  and items denoted as
$\mathcal{I} = \{i\}$ . In our study, we focus on a common recommendation scenario known as collaborative filtering (CF) with implicit feedback, where the historical data contains the items that each user has interacted with [9, 10, 11, 12]. Bayesian Personalized Ranking (BPR) [9] is one of the representative CF algorithm modeling the interaction probabilities, by minimizing the pairwise ranking loss
$$
\min  _ {\boldsymbol {\theta}} \mathcal {L} _ {\mathrm {B P R}} (\boldsymbol {\theta}) = - \sum_ {(u, i, j) \in \mathcal {D}} \ln \sigma \left(\hat {y} _ {u, i} - \hat {y} _ {u, j}\right) + \frac {\lambda_ {\boldsymbol {\theta}}}{2} \| \boldsymbol {\theta} \| _ {\mathrm {F}} ^ {2}, \tag {1}
$$
where  $\mathcal{D}$  denotes the historical data for training, including user  $u$ , interacted item  $i$ , and no interacted item  $j$ .  $\sigma(\cdot)$  is the Sigmoid function,  $\theta$  represents the model parameters, and  $\lambda_{\theta}$  is the regularization hyper-parameter to prevent overfitting. The predicted user preference scores  $\hat{y}_{u,i}$  and  $\hat{y}_{u,j}$  for positive item  $i$  and negative item  $j$  can be computed by using the widely-adopted matrix factorization [13].
Item-Side Group Fairness (IGF). The IGF requires fairness of recommendation holds across a set of item groups  $\mathcal{G} = \{g_1, g_2, \dots, g_A\}$ , where each item  $i \in \mathcal{I}$  belongs to one or more groups. The group of an item is correspond to attributes such as genre, brand, or other item characteristics, and denote  $G_{g_a}(i)$  as the indicator function of whether item  $i$  belongs to group  $g_a$ , i.e.,  $G_{g_a}(i) = 1$  if  $i \in g_a$ , otherwise  $G_{g_a}(i) = 0$ . IGF notions aim to ensure fairness across different groups without over-recommending or under-recommending any specific group [14]. The existing IGF notions mainly focus on the exposure levels across different groups, and can be classified into positive rate-based metrics and confusion matrix-based metrics [1]. One particular positive rate-based metric is Statistical Parity (SP) [5, 6], which aims to ensure that each group has an equal likelihood of being recommended and requires the following quantities to be similar across different item groups
$$
\mathbb {P} (R \mid g = g _ {a}) = \frac {\sum_ {u \in \mathcal {U}} \sum_ {i \in \mathcal {I}} G _ {g _ {a}} (i) \cdot \hat {Y} (u , i)}{\sum_ {u \in \mathcal {U}} \sum_ {i \in \mathcal {I}} G _ {g _ {a}} (i)}, \quad \text {f o r a l l} \quad a = 1, \dots , A, \tag {2}
$$
where  $\hat{Y}(u,i) = \sigma(\hat{y}_{u,i})$  estimates the interaction probability for user  $u$  to item  $i$ , and  $\sum_{i \in \mathcal{I}} G_{g_a}(i)$  is the total number of items belonging to group  $g_a$ . Instead, confusion matrix-based metrics further consider the ground truth labels. For instance, Equal Opportunity (EO) [7] aims to ensure the same true positive rate across different item groups
$$
\mathbb {P} (R \mid g = g _ {a}, y = 1) = \frac {\sum_ {u \in \mathcal {U}} \sum_ {i \in \mathcal {I}} G _ {g _ {a}} (i) \cdot Y (u , i) \cdot \hat {Y} (u , i)}{\sum_ {u \in \mathcal {U}} \sum_ {i \in \mathcal {I}} G _ {g _ {a}} (i) \cdot Y (u , i)}, \quad \text {f o r a l l} \quad a = 1, \dots , A, \tag {3}
$$
where  $Y(u,i)$  is the ground truth label for user  $u$  and item  $i$ , and  $\sum_{i\in \mathcal{I}}G_{ga}(i)Y(u,i)$  computes the total number of items that user  $u$  has interacted with in group  $g_{a}$ . To keep the same value scale for different metrics, we evaluate the IGF of a recommendation model by computing the relative standard deviation of the group probabilities
$$
\mathrm {S P} = \operatorname {r s d} \left(\mathbb {P} (R \mid g = g _ {1}), \dots , \mathbb {P} (R \mid g = g _ {A})\right),
$$
$$
\mathrm {E O} = \operatorname {r s d} \left(\mathbb {P} (R \mid g = g _ {1}, y = 1), \dots , \mathbb {P} (R \mid g = g _ {A}, y = 1)\right), \tag {4}
$$
where  $\mathrm{rsd}(\cdot) = \mathrm{std}(\cdot) / \mathrm{mean}(\cdot)$  calculates the relative standard deviation. The lower the SP and EO values, the fairer the recommender system satisfies the IGF fairness notions.
Multi-Objective Optimization. In many real-world tasks, there might be multiple optimization objectives rather than single one, while these objectives may collaborate or conflict with each other [15, 16]. Multi-objective optimization [17] aims to find a set of solutions that effectively balance the trade-off among these objectives, and it has been widely used in areas such as reinforcement learning [18] and E-commerce [19]. Typically, a multi-objective optimization problem is
$$
\min  _ {\boldsymbol {\theta}} \mathcal {L} (\boldsymbol {\theta}) = \left(\mathcal {L} _ {1} (\boldsymbol {\theta}), \mathcal {L} _ {2} (\boldsymbol {\theta}), \dots , \mathcal {L} _ {M} (\boldsymbol {\theta})\right) ^ {\mathrm {T}}, \tag {5}
$$
where  $(\mathcal{L}_1(\theta),\dots ,\mathcal{L}_M(\theta))$  states the multiple objectives. To solve the multi-objective optimization problem, several population-based and evolutionary algorithm-based methods [20, 21, 22] have been proposed. Nevertheless, they are not efficient in handling large-scale datasets in recommendation. Alternatively, multi-objective gradient descent approaches [23, 24] address this problem by leveraging Karush-Kuhn-Tucker (KKT) conditions [25] to find a gradient direction that reduces all objective values simultaneously. For example, gradient-based steepest descent methods [23] are proposed to seek a descent direction  $d_{t}$  by solving the following optimization problem
$$
\left(\boldsymbol {d} _ {t}, \alpha_ {t}\right) = \underset {\boldsymbol {d}, \alpha \in R} {\arg \min } \alpha + \frac {1}{2} \| \boldsymbol {d} \| ^ {2}, s. t. \nabla \mathcal {L} _ {i} (\boldsymbol {\theta}) ^ {T} \boldsymbol {d} \leq \alpha , i = 1, \dots , M, \tag {6}
$$
then updates the model parameters using gradient descent  $\theta_{t + 1} = \theta_t + \eta d_t$  with step size  $\eta$ . Theoretically, the solutions of the descent direction guarantee that all objective values will decrease, thus achieving the Pareto optimality [26]. To obtain these descent direction solutions, one can employ the widely-adopted multiple gradient descent algorithm (MGDA) [24].
3 Social Attributes-Aware IGF
Existing IGF notions such as SP and EO define the utility of recommending an item to a user only depends on the exposure and interaction numbers. For example, if item  $i_1$  and item  $i_2$  are recommended to user  $u_1$  and user  $u_2$  respectively, then both  $i_1$  and  $i_2$  have the same utility when  $\hat{Y}(u_1, i_1) = \hat{Y}(u_2, i_2)$ . However, they overlook the social attributes of users. Considering that the user social network plays a crucial role in click or conversion behaviors in real-world recommendation scenarios [27], recommending to users with distinct social attributes may lead to diverse item utilities.
To bridge this gap, we propose social attribute-aware IGF metrics as the extension of previously widely used SP and EO notions. Denote the neighbors (such as friends or followers) of user  $u$  as  $\mathcal{N}_u$ , for each user  $v \in \mathcal{N}_u$ , let  $R_v(i) > 0$  be the utility of item  $i$  gained from user  $v$  via the social influence of user  $u$ , when the item  $i$  is recommended to the user  $u$ . Therefore, for positive rate-based metrics and confusion matrix-based metrics, the following quantities are required to be similar
$$
\mathrm {N R} \left(g = g _ {a}\right) = \frac {\sum_ {u \in \mathcal {U}} \sum_ {i \in \mathcal {I}} G _ {g _ {a}} (i) \cdot \hat {Y} (u , i) \sum_ {v \in \mathcal {N} _ {u}} R _ {v} (i)}{\sum_ {u \in \mathcal {U}} \sum_ {i \in \mathcal {I}} G _ {g _ {a}} (i)}, \quad \text {f o r a l l} \quad a = 1, \dots , A,
$$
$$
\operatorname {N R} \left(g = g _ {a}, y = 1\right) = \frac {\sum_ {u \in \mathcal {U}} \sum_ {i \in \mathcal {I}} G _ {g _ {a}} (i) \cdot Y (u , i) \cdot \hat {Y} (u , i) \sum_ {v \in \mathcal {N} _ {u}} R _ {v} (i)}{\sum_ {u \in \mathcal {U}} \sum_ {i \in \mathcal {I}} G _ {g _ {a}} (i) \cdot Y (u , i)}, \quad \text {f o r a l l} \quad a = 1, \dots , A, \tag {7}
$$
where the sum of utilities from the social network  $\sum_{v\in \mathcal{N}_u}R_v$  are multiplied by the interaction probability  $\hat{Y} (u,i)$  to measure the total social utility. Similar to Eq. (4), we then compute the Neighborhood  $SP$  and Neighborhood  $EO$  by the relative standard deviations
$$
\mathrm {N S P} = \operatorname {r s d} \left(\mathrm {N R} \left(g = g _ {1}\right), \dots , \mathrm {N R} \left(g = g _ {A}\right)\right),
$$
$$
\mathrm {N E O} = \operatorname {r s d} \left(\mathrm {N R} \left(g = g _ {1}, y = 1\right), \dots , \mathrm {N R} \left(g = g _ {A}, y = 1\right)\right). \tag {8}
$$
Further Discussion. For the existing and the proposed IGF notions, the former including SP and EO focus on the direct utility obtained through recommendation exposures to users, whereas the latter including SP and EO emphasize the social utility gained from the user social network. Since these metrics emphasize different aspects, optimizing one IGF notion alone does not guarantee the optimality of the other IGF notion. Figures 1a and 1b illustrate this with a toy example: if we solely optimize SP, it does not guarantee the achievement of the other IGF notion, i.e., NSP, and vise versa. Since both IGF metrics are important, it is desirable to optimize both SP (EO) and NSP (NEO) simultaneously from the prospective of multi-objective optimization, as illustrated in Figure 1c.
4.1 Multi-Objective Optimization Problem Formulation
The optimization objective for training a fair recommendation model under IGF notions is to minimize both SP (EO) and NSP (NEO), so as to obtain similar direct utility and similar social utility simultaneously. Building upon prior studies [8, 28], we formulate the fair recommendation training task as a multi-objective optimization problem, where each optimization objective corresponds to a pre-defined IGF metric. Without loss of generality, let the number of IGF metrics used as optimization objectives be  $M$ , then we aim to obtain Pareto optimal solutions among these IGF metrics.
Pareto Dominance. A solution  $\pmb{\theta}_{1}$  dominates another solution  $\pmb{\theta}_{2}$  if  $\mathcal{L}_i(\pmb{\theta}_1) \leq \mathcal{L}_i(\pmb{\theta}_2)$ ,  $\forall i = 1, \dots, M$  and  $\mathcal{L}(\pmb{\theta}_1) = (\mathcal{L}_1(\pmb{\theta}_1), \dots, \mathcal{L}_M(\pmb{\theta}_1))^{\mathrm{T}} \neq \mathcal{L}(\pmb{\theta}_2) = (\mathcal{L}_1(\pmb{\theta}_2), \dots, \mathcal{L}_M(\pmb{\theta}_2))^{\mathrm{T}}$ .
Pareto Optimality. A solution  $\theta$  is a Pareto optimal solution if  $\theta$  is not dominated by any other solutions. The set of the Pareto optimal solutions is called as Pareto optimal set.
It is now attractive to formulate the trade-off between different IGF metrics as a multi-objective optimization problem, then obtain a Pareto-optimal solution between these metrics. However, due to the well-known accuracy sacrifice for improving fairness [14], directly solving the above problem without considering recommendation accuracy may lead to a significant reduction in recommendation quality. To ensure controllable recommendation accuracy during the optimization process, we introduce an accuracy constraint that penalizes instances with the accuracy loss (e.g., BPR loss) exceeding a pre-defined threshold. Formally, the multi-objective optimization problem is
$$
\min  _ {\boldsymbol {\theta}} \mathcal {L} (\boldsymbol {\theta}) = \left(\mathcal {L} _ {1} (\boldsymbol {\theta}), \mathcal {L} _ {2} (\boldsymbol {\theta}), \dots , \mathcal {L} _ {M} (\boldsymbol {\theta})\right) ^ {\mathrm {T}}, \text {s . t .} \mathcal {L} _ {\mathrm {B P R}} (\boldsymbol {\theta}) \leq \xi , \tag {9}
$$
where  $\xi$  is the pre-defined accuracy threshold, and  $\xi$  should be set to exceed the loss of a recommendation model trained using only BPR loss to ensure the existence of feasible solutions.
Furthermore, in real-world recommendation scenarios, the two types of IGF metrics that consider direct and social effects, respectively, may require different proportions of trade-offs. For example, a recommender system designed for social media applications may place more emphasis on the social utility than the direct utility. Therefore, it is meaningful to find flexible Pareto-optimal solutions to the multi-objective optimization problem with varying trade-offs. Following the previous work [8], we decompose the optimization problem into  $N$  subproblems using a set of pre-defined unit preference vectors  $\boldsymbol{s}_1,\boldsymbol{s}_2,\dots ,\boldsymbol{s}_N\in R_+^M$ , and define the  $N$  preference regions  $\Omega_1,\Omega_2,\ldots ,\Omega_N$  as follows
$$
\Omega_ {n} = \left\{\mathcal {L} (\boldsymbol {\theta}) \in R _ {+} ^ {M} \mid \boldsymbol {s} _ {j} ^ {T} \mathcal {L} (\boldsymbol {\theta}) \leq \boldsymbol {s} _ {n} ^ {T} \mathcal {L} (\boldsymbol {\theta}), \forall j = 1, \dots , N \right\}, \tag {10}
$$
where  $\mathcal{L}(\pmb{\theta}) \in \Omega_n$  if and only if  $\mathcal{L}(\pmb{\theta})$  forms the smallest acute angle with  $s_n$ , resulting in the largest inner product  $s_n^T \mathcal{L}(\pmb{\theta})$  among all  $s_1^T \mathcal{L}(\pmb{\theta}), s_2^T \mathcal{L}(\pmb{\theta}), \ldots, s_N^T \mathcal{L}(\pmb{\theta})$ . To ensure that the solution  $\tilde{\mathcal{L}}(\pmb{\theta})$  obtained from the optimization phase falls within the preference region  $\Omega_n$ , we further impose a constraint that penalizes the distance of the obtained solution from this preference region
$$
\min  _ {\boldsymbol {\theta}} \mathcal {L} (\boldsymbol {\theta}) = \left(\mathcal {L} _ {1} (\boldsymbol {\theta}), \mathcal {L} _ {2} (\boldsymbol {\theta}), \dots , \mathcal {L} _ {M} (\boldsymbol {\theta})\right) ^ {\mathrm {T}}
$$
$$
s. t. \mathcal {G} _ {j} (\boldsymbol {\theta}) = \left(\boldsymbol {s} _ {j} - \boldsymbol {s} _ {n}\right) ^ {T} \mathcal {L} (\boldsymbol {\theta}) \leq 0, \forall j = 1, \dots , N, \tag {11}
$$
$$
\mathcal {L} _ {\mathrm {B P R}} (\boldsymbol {\theta}) \leq \xi .
$$
By letting the preference vectors be uniformly distributed in  $R_{+}^{M}$ , we can obtain flexible Pareto optimal solutions with varying trade-offs. Each subproblem corresponds to a unique Pareto-optimal solution in a specific preference region, which can reflect different attention to the direct and social utilities. Finally, we can select the desired Pareto optimal solution for diverse recommendation scenarios to satisfy both the flexible trade-offs and the controllable prediction accuracy.
4.2 Gradient-Based Flexible and Controllable Fair Recommendation Training
Finding the Initial Solution. For more efficient finding a solution to the multi-objective problem that falls within the specified preference region, we first find a feasible initial solution that satisfies all the constraints of that preference region. Specifically, for a randomly generated initial solution  $\pmb{\theta}_r$ , we define the set of indices that violate the constraints as  $I_{\epsilon}(\pmb{\theta}_r) = \{j = 1,\dots ,N\mid \mathcal{G}_j(\pmb{\theta}_r)\geq -\epsilon \}$ , where  $\epsilon$  is a small value to deal with solutions near the boundary. Then we can compute a descending direction  $\pmb{d}_r$  that reduces all the values of  $\{\mathcal{G}_j(\pmb{\theta}_r)|j\in I_\epsilon (\pmb{\theta}_r)\}$  by solving the optimization problem
$$
\left(\boldsymbol {d} _ {r}, \alpha_ {r}\right) = \underset {\boldsymbol {d}, \alpha \in R} {\arg \min } \alpha + \frac {1}{2} \| \boldsymbol {d} \| ^ {2}, s. t. \nabla \mathcal {G} _ {j} \left(\boldsymbol {\theta} _ {r}\right) ^ {T} \boldsymbol {d} \leq \alpha , j \in I _ {\epsilon} \left(\boldsymbol {\theta} _ {r}\right). \tag {12}
$$
The gradient-based update rule can be expressed as  $\pmb{\theta}_{r_{t + 1}} = \pmb{\theta}_{r_t} + \eta_r\pmb{d}_{r_t}$ , where  $\eta_r$  denotes the step size, and will stop when a feasible solution is found or the maximum iteration number is reached.
Solving the Subproblem. Given the feasible initial solution  $\theta_0$ , we next propose a gradient-based learning approach to solve the multi-objective optimization problem in Eq. (11). Specifically, we compute the update direction  $d_t$  from  $\theta_t$  to  $\theta_{t+1}$  by solving the following optimization problem
$$
\begin{array}{l} (\boldsymbol{d}_{t},\alpha_{t}) = \operatorname *{arg  min}_{\boldsymbol {d},\alpha \in R}\alpha +\frac{1}{2}\| \boldsymbol {d}\|^{2} \\ s. t. \nabla \mathcal {L} _ {i} \left(\boldsymbol {\theta} _ {t}\right) ^ {T} \boldsymbol {d} \leq \alpha , i = 1, \dots , M, \tag {13} \\ \nabla \mathcal {G} _ {j} (\boldsymbol {\theta} _ {t}) ^ {T} \boldsymbol {d} \leq \alpha , j \in I _ {\epsilon} (\boldsymbol {\theta} _ {t}), \\ \nabla \mathcal {L} _ {\mathrm {B P R}} (\boldsymbol {\theta} _ {t}) ^ {T} \boldsymbol {d} \leq \alpha , \text {i f} \mathcal {L} _ {\mathrm {B P R}} (\boldsymbol {\theta} _ {t}) \geq \xi . \\ \end{array}
$$
The Lagrange function of the above optimization problem is