Ruoming Jin

Phung Lai, Han Hu, NhatHai Phan et al.

In this paper, we show that the process of continually learning new tasks and memorizing previous tasks introduces unknown privacy risks and challenges to bound the privacy loss. Based upon this, we introduce a formal definition of Lifelong DP, in which the participation of any data tuples in the training set of any tasks is protected, under a consistently bounded DP protection, given a growing stream of tasks. A consistently bounded DP means having only one fixed value of the DP privacy budget, regardless of the number of tasks. To preserve Lifelong DP, we propose a scalable and heterogeneous algorithm, called L2DP-ML with a streaming batch training, to efficiently train and continue releasing new versions of an L2M model, given the heterogeneity in terms of data sizes and the training order of tasks, without affecting DP protection of the private training set. An end-to-end theoretical analysis and thorough evaluations show that our mechanism is significantly better than baseline approaches in preserving Lifelong DP. The implementation of L2DP-ML is available at: https://github.com/haiphanNJIT/PrivateDeepLearning.

Khiem Ton, Nhi Nguyen, Mahmoud Nazzal et al.

This paper introduces SGCode, a flexible prompt-optimizing system to generate secure code with large language models (LLMs). SGCode integrates recent prompt-optimization approaches with LLMs in a unified system accessible through front-end and back-end APIs, enabling users to 1) generate secure code, which is free of vulnerabilities, 2) review and share security analysis, and 3) easily switch from one prompt optimization approach to another, while providing insights on model and system performance. We populated SGCode on an AWS server with PromSec, an approach that optimizes prompts by combining an LLM and security tools with a lightweight generative adversarial graph neural network to detect and fix security vulnerabilities in the generated code. Extensive experiments show that SGCode is practical as a public tool to gain insights into the trade-offs between model utility, secure code generation, and system cost. SGCode has only a marginal cost compared with prompting LLMs. SGCode is available at: https://sgcode.codes/.

Dong Li, Yelong Shen, Ruoming Jin et al.

Pre-trained language models have achieved promising success in code retrieval tasks, where a natural language documentation query is given to find the most relevant existing code snippet. However, existing models focus only on optimizing the documentation code pairs by embedding them into latent space, without the association of external knowledge. In this paper, we propose a generation-augmented query expansion framework. Inspired by the human retrieval process - sketching an answer before searching, in this work, we utilize the powerful code generation model to benefit the code retrieval task. Specifically, we demonstrate that rather than merely retrieving the target code snippet according to the documentation query, it would be helpful to augment the documentation query with its generation counterpart - generated code snippets from the code generation model. To the best of our knowledge, this is the first attempt that leverages the code generation model to enhance the code retrieval task. We achieve new state-of-the-art results on the CodeSearchNet benchmark and surpass the baselines significantly.

Xiaopeng Jiang, Thinh On, NhatHai Phan et al.

Mobile apps, such as mHealth and wellness applications, can benefit from deep learning (DL) models trained with mobile sensing data collected by smart phones or wearable devices. However, currently there is no mobile sensing DL system that simultaneously achieves good model accuracy while adapting to user mobility behavior, scales well as the number of users increases, and protects user data privacy. We propose Zone-based Federated Learning (ZoneFL) to address these requirements. ZoneFL divides the physical space into geographical zones mapped to a mobile-edge-cloud system architecture for good model accuracy and scalability. Each zone has a federated training model, called a zone model, which adapts well to data and behaviors of users in that zone. Benefiting from the FL design, the user data privacy is protected during the ZoneFL training. We propose two novel zone-based federated training algorithms to optimize zone models to user mobility behavior: Zone Merge and Split (ZMS) and Zone Gradient Diffusion (ZGD). ZMS optimizes zone models by adapting the zone geographical partitions through merging of neighboring zones or splitting of large zones into smaller ones. Different from ZMS, ZGD maintains fixed zones and optimizes a zone model by incorporating the gradients derived from neighboring zones' data. ZGD uses a self-attention mechanism to dynamically control the impact of one zone on its neighbors. Extensive analysis and experimental results demonstrate that ZoneFL significantly outperforms traditional FL in two models for heart rate prediction and human activity recognition. In addition, we developed a ZoneFL system using Android phones and AWS cloud. The system was used in a heart rate prediction field study with 63 users for 4 months, and we demonstrated the feasibility of ZoneFL in real-life.

Ji Liu, Jiaxiang Ren, Ruoming Jin et al.

As a promising paradigm to collaboratively train models with decentralized data, Federated Learning (FL) can be exploited to fine-tune Large Language Models (LLMs). While LLMs correspond to huge size, the scale of the training data significantly increases, which leads to tremendous amounts of computation and communication costs. The training data is generally non-Independent and Identically Distributed (non-IID), which requires adaptive data processing within each device. Although Low Rank Adaptation (LoRA) can significantly reduce the scale of parameters to update in the fine-tuning process, it still takes unaffordable time to transfer the low-rank parameters of all the layers in LLMs. In this paper, we propose a Fisher Information-based Efficient Curriculum Federated Learning framework (FibecFed) with two novel methods, i.e., adaptive federated curriculum learning and efficient sparse parameter update. First, we propose a fisher information-based method to adaptively sample data within each device to improve the effectiveness of the FL fine-tuning process. Second, we dynamically select the proper layers for global aggregation and sparse parameters for local update with LoRA so as to improve the efficiency of the FL fine-tuning process. Extensive experimental results based on 10 datasets demonstrate that FibecFed yields excellent performance (up to 45.35% in terms of accuracy) and superb fine-tuning speed (up to 98.61% faster) compared with 17 baseline approaches).

Ruixin Guo, Ruoming Jin, Xinyu Li et al.

Linear Autoencoders (LAEs) have shown strong performance in state-of-the-art recommender systems. However, this success remains largely empirical, with limited theoretical understanding. In this paper, we investigate the generalizability -- a theoretical measure of model performance in statistical learning -- of multivariate linear regression and LAEs. We first propose a PAC-Bayes bound for multivariate linear regression, extending the earlier bound for single-output linear regression by Shalaeva et al., and establish sufficient conditions for its convergence. We then show that LAEs, when evaluated under a relaxed mean squared error, can be interpreted as constrained multivariate linear regression models on bounded data, to which our bound adapts. Furthermore, we develop theoretical methods to improve the computational efficiency of optimizing the LAE bound, enabling its practical evaluation on large models and real-world datasets. Experimental results demonstrate that our bound is tight and correlates well with practical ranking metrics such as Recall@K and NDCG@K.

Ji Liu, Tianshi Che, Yang Zhou et al.

Federated Learning (FL) has achieved significant achievements recently, enabling collaborative model training on distributed data over edge devices. Iterative gradient or model exchanges between devices and the centralized server in the standard FL paradigm suffer from severe efficiency bottlenecks on the server. While enabling collaborative training without a central server, existing decentralized FL approaches either focus on the synchronous mechanism that deteriorates FL convergence or ignore device staleness with an asynchronous mechanism, resulting in inferior FL accuracy. In this paper, we propose an Asynchronous Efficient Decentralized FL framework, i.e., AEDFL, in heterogeneous environments with three unique contributions. First, we propose an asynchronous FL system model with an efficient model aggregation method for improving the FL convergence. Second, we propose a dynamic staleness-aware model update approach to achieve superior accuracy. Third, we propose an adaptive sparse training method to reduce communication and computation costs without significant accuracy degradation. Extensive experimentation on four public datasets and four models demonstrates the strength of AEDFL in terms of accuracy (up to 16.3% higher), efficiency (up to 92.9% faster), and computation costs (up to 42.3% lower).

Dong Li, Ruoming Jin, Bin Ren

Inspired by the success of contrastive learning, we systematically examine recommendation losses, including listwise (softmax), pairwise (BPR), and pointwise (MSE and CCL) losses. In this endeavor, we introduce InfoNCE+, an optimized generalization of InfoNCE with balance coefficients, and highlight its performance advantages, particularly when aligned with our new decoupled contrastive loss, MINE+. We also leverage debiased InfoNCE to debias pointwise recommendation loss (CCL) as Debiased CCL. Interestingly, our analysis reveals that linear models like iALS and EASE are inherently debiased. Empirical results demonstrates the effectiveness of MINE+ and Debiased-CCL.

Jianfeng Zhu, Julina Maharjan, Xinyu Li et al.

Large Language Models (LLMs) are increasingly deployed in roles requiring nuanced psychological understanding, such as emotional support agents, counselors, and decision-making assistants. However, their ability to interpret human personality traits, a critical aspect of such applications, remains unexplored, particularly in ecologically valid conversational settings. While prior work has simulated LLM "personas" using discrete Big Five labels on social media data, the alignment of LLMs with continuous, ground-truth personality assessments derived from natural interactions is largely unexamined. To address this gap, we introduce a novel benchmark comprising semi-structured interview transcripts paired with validated continuous Big Five trait scores. Using this dataset, we systematically evaluate LLM performance across three paradigms: (1) zero-shot and chain-of-thought prompting with GPT-4.1 Mini, (2) LoRA-based fine-tuning applied to both RoBERTa and Meta-LLaMA architectures, and (3) regression using static embeddings from pretrained BERT and OpenAI's text-embedding-3-small. Our results reveal that all Pearson correlations between model predictions and ground-truth personality traits remain below 0.26, highlighting the limited alignment of current LLMs with validated psychological constructs. Chain-of-thought prompting offers minimal gains over zero-shot, suggesting that personality inference relies more on latent semantic representation than explicit reasoning. These findings underscore the challenges of aligning LLMs with complex human attributes and motivate future work on trait-specific prompting, context-aware modeling, and alignment-oriented fine-tuning.

Jianfeng Zhu, Hailong Jiang, Yulan Wang et al.

Early substance use during adolescence increases the risk of later substance use disorders and mental health problems, yet the emotional and contextual factors driving these behaviors remain poorly understood. This study analyzed 23000 substance-use related posts and an equal number of non-substance posts from Reddit's r/teenagers community (2018-2022). Posts were annotated for six discrete emotions (sadness, anger, joy, guilt, fear, disgust) and contextual factors (family, peers, school) using large language models (LLMs). Statistical analyses compared group differences, and interpretable machine learning (SHAP) identified key predictors of substance-use discussions. LLM-assisted thematic coding further revealed latent psychosocial themes linking emotions with contexts. Negative emotions, especially sadness, guilt, fear, and disgust, were significantly more common in substance-use posts, while joy dominated non-substance discussions. Guilt and shame diverged in function: guilt often reflected regret and self-reflection, whereas shame reinforced risky behaviors through peer performance. Peer influence emerged as the strongest contextual factor, closely tied to sadness, fear, and guilt. Family and school environments acted as both risk and protective factors depending on relational quality and stress levels. Overall, adolescent substance-use discussions reflected a dynamic interplay of emotion, social context, and coping behavior. By integrating statistical analysis, interpretable models, and LLM-based thematic exploration, this study demonstrates the value of mixed computational approaches for uncovering the emotional and contextual mechanisms underlying adolescent risk behavior.

Jianfeng Zhu, Ruoming Jin, Karin G. Coifman

Large Language Models (LLMs) such as OpenAI's GPT-4 and Meta's LLaMA offer a promising approach for scalable personality assessment from open-ended language. However, inferring personality traits remains challenging, and earlier work often relied on synthetic data or social media text lacking psychometric validity. We introduce a real-world benchmark of 555 semi-structured interviews with BFI-10 self-report scores for evaluating LLM-based personality inference. Three state-of-the-art LLMs (GPT-4.1 Mini, Meta-LLaMA, and DeepSeek) were tested using zero-shot prompting for BFI-10 item prediction and both zero-shot and chain-of-thought prompting for Big Five trait inference. All models showed high test-retest reliability, but construct validity was limited: correlations with ground-truth scores were weak (max Pearson's $r = 0.27$), interrater agreement was low (Cohen's $κ< 0.10$), and predictions were biased toward moderate or high trait levels. Chain-of-thought prompting and longer input context modestly improved distributional alignment, but not trait-level accuracy. These results underscore limitations in current LLM-based personality inference and highlight the need for evidence-based development for psychological applications.

Kieu Dang, Phung Lai, NhatHai Phan et al.

Large Language Models (LLMs) have transformed natural language processing, demonstrating impressive capabilities across diverse tasks. However, deploying these models introduces critical risks related to intellectual property violations and potential misuse, particularly as adversaries can imitate these models to steal services or generate misleading outputs. We specifically focus on model stealing attacks, as they are highly relevant to proprietary LLMs and pose a serious threat to their security, revenue, and ethical deployment. While various watermarking techniques have emerged to mitigate these risks, it remains unclear how far the community and industry have progressed in developing and deploying watermarks in LLMs. To bridge this gap, we aim to develop a comprehensive systematization for watermarks in LLMs by 1) presenting a detailed taxonomy for watermarks in LLMs, 2) proposing a novel intellectual property classifier to explore the effectiveness and impacts of watermarks on LLMs under both attack and attack-free environments, 3) analyzing the limitations of existing watermarks in LLMs, and 4) discussing practical challenges and potential future directions for watermarks in LLMs. Through extensive experiments, we show that despite promising research outcomes and significant attention from leading companies and community to deploy watermarks, these techniques have yet to reach their full potential in real-world applications due to their unfavorable impacts on model utility of LLMs and downstream tasks. Our findings provide an insightful understanding of watermarks in LLMs, highlighting the need for practical watermarks solutions tailored to LLM deployment.

Hailong Jiang, Jianfeng Zhu, Yao Wan et al.

Intermediate Representations (IRs) play a critical role in compiler design and program analysis, yet their comprehension by Large Language Models (LLMs) remains underexplored. In this paper, we present an explorative empirical study evaluating the capabilities of six state-of-the-art LLMs: GPT-4, GPT-3, DeepSeek, Gemma 2, Llama 3, and Code Llama, in understanding IRs. Specifically, we assess model performance across four core tasks: control flow graph reconstruction, decompilation, code summarization, and execution reasoning. While LLMs exhibit competence in parsing IR syntax and identifying high-level structures, they consistently struggle with instruction-level reasoning, especially in control flow reasoning, loop handling, and dynamic execution. Common failure modes include misinterpreting branching instructions, omitting critical operations, and relying on heuristic reasoning rather than precise instruction-level logic. Our findings highlight the need for IR-specific enhancements in LLM design. We recommend fine-tuning on structured IR datasets and integrating control-flow-sensitive architectures to improve model effectiveness. All experimental data and source code are publicly available at

Ruixin Guo, Xinyu Li, Hao Zhou et al.

Linear autoencoders (LAEs) have gained increasing popularity in recommender systems due to their simplicity and strong empirical performance. Most LAE models, including the Emphasized Denoising Linear Autoencoder (EDLAE) introduced by (Steck, 2020), use quadratic loss during training. However, the original EDLAE only provides closed-form solutions for the hyperparameter choice $b = 0$, which limits its capacity. In this work, we generalize EDLAE objective into a Decoupled Expected Quadratic Loss (DEQL). We show that DEQL simplifies the process of deriving EDLAE solutions and reveals solutions in a broader hyperparameter range $b > 0$, which were not derived in Steck's original paper. Additionally, we propose an efficient algorithm based on Miller's matrix inverse theorem to ensure the computational tractability for the $b > 0$ case. Empirical results on benchmark datasets show that the $b > 0$ solutions provided by DEQL outperform the $b = 0$ EDLAE baseline, demonstrating that DEQL expands the solution space and enables the discovery of models with better testing performance.

Xiang Li, Gagan Agrawal, Ruoming Jin et al.

We consider the problem of constructing embeddings of large attributed graphs and supporting multiple downstream learning tasks. We develop a graph embedding method, which is based on extending deep metric and unbiased contrastive learning techniques to 1) work with attributed graphs, 2) enabling a mini-batch based approach, and 3) achieving scalability. Based on a multi-class tuplet loss function, we present two algorithms -- DMT for semi-supervised learning and DMAT-i for the unsupervised case. Analyzing our methods, we provide a generalization bound for the downstream node classification task and for the first time relate tuplet loss to contrastive learning. Through extensive experiments, we show high scalability of representation construction, and in applying the method for three downstream tasks (node clustering, node classification, and link prediction) better consistency over any single existing method.

Xiang Li, Gagan Agrawal, Rajiv Ramnath et al.

Graph-level representations (and clustering/classification based on these representations) are required in a variety of applications. Examples include identifying malicious network traffic, prediction of protein properties, and many others. Often, data has to stay in isolated local systems (i.e., cannot be centrally shared for analysis) due to a variety of considerations like privacy concerns, lack of trust between the parties, regulations, or simply because the data is too large to be shared sufficiently quickly. This points to the need for federated learning for graph-level representations, a topic that has not been explored much, especially in an unsupervised setting. Addressing this problem, this paper presents a new framework we refer to as Federated Contrastive Learning of Graph-level Representations (FCLG). As the name suggests, our approach builds on contrastive learning. However, what is unique is that we apply contrastive learning at two levels. The first application is for local unsupervised learning of graph representations. The second level is to address the challenge associated with data distribution variation (i.e. the ``Non-IID issue") when combining local models. Through extensive experiments on the downstream task of graph-level clustering, we demonstrate FCLG outperforms baselines (which apply existing federated methods on existing graph-level clustering methods) with significant margins.

Ruoming Jin, Dong Li

In this paper, we perform a systemic examination of the recommendation losses, including listwise (softmax), pairwise(BPR), and pointwise (mean-squared error, MSE, and Cosine Contrastive Loss, CCL) losses through the lens of contrastive learning. We introduce and study both debiased InfoNCE and mutual information neural estimator (MINE), for the first time, under the recommendation setting. We also relate and differentiate these two losses with the BPR loss through the lower bound analysis. Furthermore, we present the debiased pointwise loss (for both MSE and CCL) and theoretically certify both iALS and EASE, two of the most popular linear models, are inherently debiased. The empirical experimental results demonstrate the effectiveness of the debiased losses and newly introduced mutual-information losses outperform the existing (biased) ones.

Xiang Li, Dong Li, Ruoming Jin et al.

Web-based interactions can be frequently represented by an attributed graph, and node clustering in such graphs has received much attention lately. Multiple efforts have successfully applied Graph Convolutional Networks (GCN), though with some limits on accuracy as GCNs have been shown to suffer from over-smoothing issues. Though other methods (particularly those based on Laplacian Smoothing) have reported better accuracy, a fundamental limitation of all the work is a lack of scalability. This paper addresses this open problem by relating the Laplacian smoothing to the Generalized PageRank and applying a random-walk based algorithm as a scalable graph filter. This forms the basis for our scalable deep clustering algorithm, RwSL, where through a self-supervised mini-batch training mechanism, we simultaneously optimize a deep neural network for sample-cluster assignment distribution and an autoencoder for a clustering-oriented embedding. Using 6 real-world datasets and 6 clustering metrics, we show that RwSL achieved improved results over several recent baselines. Most notably, we show that RwSL, unlike all other deep clustering frameworks, can continue to scale beyond graphs with more than one million nodes, i.e., handle web-scale. We also demonstrate how RwSL could perform node clustering on a graph with 1.8 billion edges using only a single GPU.

Xiaopeng Jiang, Han Hu, Vijaya Datta Mayyuri et al.

This article presents the design, implementation, and evaluation of FLSys, a mobile-cloud federated learning (FL) system, which can be a key component for an open ecosystem of FL models and apps. FLSys is designed to work on smart phones with mobile sensing data. It balances model performance with resource consumption, tolerates communication failures, and achieves scalability. In FLSys, different DL models with different FL aggregation methods can be trained and accessed concurrently by different apps. Furthermore, FLSys provides advanced privacy preserving mechanisms and a common API for third-party app developers to access FL models. FLSys adopts a modular design and is implemented in Android and AWS cloud. We co-designed FLSys with a human activity recognition (HAR) model. HAR sensing data was collected in the wild from 100+ college students during a 4-month period. We implemented HAR-Wild, a CNN model tailored to mobile devices, with a data augmentation mechanism to mitigate the problem of non-Independent and Identically Distributed data. A sentiment analysis model is also used to demonstrate that FLSys effectively supports concurrent models. This article reports our experience and lessons learned from conducting extensive experiments using simulations, Android/Linux emulations, and Android phones that demonstrate FLSys achieves good model utility and practical system performance.

Dong Li, Ruoming Jin, Jing Gao et al.

Recently, Rendle has warned that the use of sampling-based top-$k$ metrics might not suffice. This throws a number of recent studies on deep learning-based recommendation algorithms, and classic non-deep-learning algorithms using such a metric, into jeopardy. In this work, we thoroughly investigate the relationship between the sampling and global top-$K$ Hit-Ratio (HR, or Recall), originally proposed by Koren[2] and extensively used by others. By formulating the problem of aligning sampling top-$k$ ($SHR@k$) and global top-$K$ ($HR@K$) Hit-Ratios through a mapping function $f$, so that $SHR@k\approx HR@f(k)$, we demonstrate both theoretically and experimentally that the sampling top-$k$ Hit-Ratio provides an accurate approximation of its global (exact) counterpart, and can consistently predict the correct winners (the same as indicate by their corresponding global Hit-Ratios).

Ruoming Jin, Dong Li, Benjamin Mudrak et al.

Since the recent study (Krichene and Rendle 2020) done by Krichene and Rendle on the sampling-based top-k evaluation metric for recommendation, there has been a lot of debates on the validity of using sampling to evaluate recommendation algorithms. Though their work and the recent work (Li et al.2020) have proposed some basic approaches for mapping the sampling-based metrics to their global counterparts which rank the entire set of items, there is still a lack of understanding and consensus on how sampling should be used for recommendation evaluation. The proposed approaches either are rather uninformative (linking sampling to metric evaluation) or can only work on simple metrics, such as Recall/Precision (Krichene and Rendle 2020; Li et al. 2020). In this paper, we introduce a new research problem on learning the empirical rank distribution, and a new approach based on the estimated rank distribution, to estimate the top-k metrics. Since this question is closely related to the underlying mechanism of sampling for recommendation, tackling it can help better understand the power of sampling and can help resolve the questions of if and how should we use sampling for evaluating recommendation. We introduce two approaches based on MLE (MaximalLikelihood Estimation) and its weighted variants, and ME(Maximal Entropy) principals to recover the empirical rank distribution, and then utilize them for metrics estimation. The experimental results show the advantages of using the new approaches for evaluating recommendation algorithms based on top-k metrics.

NhatHai Phan, Minh Vu, Yang Liu et al.

In this paper, we propose a novel Heterogeneous Gaussian Mechanism (HGM) to preserve differential privacy in deep neural networks, with provable robustness against adversarial examples. We first relax the constraint of the privacy budget in the traditional Gaussian Mechanism from (0, 1] to (0, \infty), with a new bound of the noise scale to preserve differential privacy. The noise in our mechanism can be arbitrarily redistributed, offering a distinctive ability to address the trade-off between model utility and privacy loss. To derive provable robustness, our HGM is applied to inject Gaussian noise into the first hidden layer. Then, a tighter robustness bound is proposed. Theoretical analysis and thorough evaluations show that our mechanism notably improves the robustness of differentially private deep neural networks, compared with baseline approaches, under a variety of model attacks.

NhatHai Phan, My T. Thai, Han Hu et al.

In this paper, we aim to develop a scalable algorithm to preserve differential privacy (DP) in adversarial learning for deep neural networks (DNNs), with certified robustness to adversarial examples. By leveraging the sequential composition theory in DP, we randomize both input and latent spaces to strengthen our certified robustness bounds. To address the trade-off among model utility, privacy loss, and robustness, we design an original adversarial objective function, based on the post-processing property in DP, to tighten the sensitivity of our model. A new stochastic batch training is proposed to apply our mechanism on large DNNs and datasets, by bypassing the vanilla iterative batch-by-batch training in DP DNNs. An end-to-end theoretical analysis and evaluations show that our mechanism notably improves the robustness and scalability of DP DNNs.

Yelong Shen, Ruoming Jin, Jianshu Chen et al.

Co-occurrence Data is a common and important information source in many areas, such as the word co-occurrence in the sentences, friends co-occurrence in social networks and products co-occurrence in commercial transaction data, etc, which contains rich correlation and clustering information about the items. In this paper, we study co-occurrence data using a general energy-based probabilistic model, and we analyze three different categories of energy-based model, namely, the $L_1$, $L_2$ and $L_k$ models, which are able to capture different levels of dependency in the co-occurrence data. We also discuss how several typical existing models are related to these three types of energy models, including the Fully Visible Boltzmann Machine (FVBM) ($L_2$), Matrix Factorization ($L_2$), Log-BiLinear (LBL) models ($L_2$), and the Restricted Boltzmann Machine (RBM) model ($L_k$). Then, we propose a Deep Embedding Model (DEM) (an $L_k$ model) from the energy model in a \emph{principled} manner. Furthermore, motivated by the observation that the partition function in the energy model is intractable and the fact that the major objective of modeling the co-occurrence data is to predict using the conditional probability, we apply the \emph{maximum pseudo-likelihood} method to learn DEM. In consequence, the developed model and its learning method naturally avoid the above difficulties and can be easily used to compute the conditional probability in prediction. Interestingly, our method is equivalent to learning a special structured deep neural network using back-propagation and a special sampling strategy, which makes it scalable on large-scale datasets. Finally, in the experiments, we show that the DEM can achieve comparable or better results than state-of-the-art methods on datasets across several application domains.