Jie Ding

Ganghua Wang, Xun Xian, Jayanth Srinivasa et al.

The growing dependence on machine learning in real-world applications emphasizes the importance of understanding and ensuring its safety. Backdoor attacks pose a significant security risk due to their stealthy nature and potentially serious consequences. Such attacks involve embedding triggers within a learning model with the intention of causing malicious behavior when an active trigger is present while maintaining regular functionality without it. This paper evaluates the effectiveness of any backdoor attack incorporating a constant trigger, by establishing tight lower and upper boundaries for the performance of the compromised model on both clean and backdoor test data. The developed theory answers a series of fundamental but previously underexplored problems, including (1) what are the determining factors for a backdoor attack's success, (2) what is the direction of the most effective backdoor attack, and (3) when will a human-imperceptible trigger succeed. Our derived understanding applies to both discriminative and generative models. We also demonstrate the theory by conducting experiments using benchmark datasets and state-of-the-art backdoor attack scenarios.

An Luo, Jie Ding

As generative models enable rapid creation of high-fidelity images, societal concerns about misinformation and authenticity have intensified. A promising remedy is multi-bit image watermarking, which embeds a multi-bit message into an image so that a verifier can later detect whether the image is generated by someone and further identify the source by decoding the embedded message. Existing approaches often fall short in capacity, resilience to common image distortions, and theoretical justification. To address these limitations, we propose ADD (Add, Dot, Decode), a multi-bit image watermarking method with two stages: learning a watermark to be linearly combined with the multi-bit message and added to the image, and decoding through inner products between the watermarked image and the learned watermark. On the standard MS-COCO benchmark, we demonstrate that for the challenging task of 48-bit watermarking, ADD achieves 100\% decoding accuracy, with performance dropping by at most 2\% under a wide range of image distortions, substantially smaller than the 14\% average drop of state-of-the-art methods. In addition, ADD achieves substantial computational gains, with 2-fold faster embedding and 7.4-fold faster decoding than the fastest existing method. We further provide a theoretical analysis explaining why the learned watermark and the corresponding decoding rule are effective.

Rui Sun, Chenghua Gong, Tianjun Gu et al.

Advancing epidemic dynamics forecasting is vital for targeted interventions and safeguarding public health. Current approaches mainly fall into two categories: mechanism-based and data-driven models. Mechanism-based models are constrained by predefined compartmental structures and oversimplified system assumptions, limiting their ability to model complex real-world dynamics, while data-driven models focus solely on intrinsic data dependencies without physical or epidemiological constraints, risking biased or misleading representations. Although recent studies have attempted to integrate epidemiological knowledge into neural architectures, most of them fail to reconcile explicit physical priors with neural representations. To overcome these obstacles, we introduce Epi$^2$-Net, a Epidemic Forecasting Framework built upon Physics-Inspired Neural Networks. Specifically, we propose reconceptualizing epidemic transmission from the physical transport perspective, introducing the concept of neural epidemic transport. Further, we present a physic-inspired deep learning framework, and integrate physical constraints with neural modules to model spatio-temporal patterns of epidemic dynamics. Experiments on real-world datasets have demonstrated that Epi$^2$-Net outperforms state-of-the-art methods in epidemic forecasting, providing a promising solution for future epidemic containment. The code is available at: https://anonymous.4open.science/r/Epi-2-Net-48CE.

Jin Du, Li Chen, Xun Xian et al.

Reliable causal inference is essential for making decisions in high-stakes areas like medicine, economics, and public policy. However, it remains unclear whether large language models (LLMs) can handle rigorous and trustworthy statistical causal inference. Current benchmarks usually involve simplified tasks. For example, these tasks might only ask LLMs to identify semantic causal relationships or draw conclusions directly from raw data. As a result, models may overlook important statistical pitfalls, such as Simpson's paradox or selection bias. This oversight limits the applicability of LLMs in the real world. To address these limitations, we propose CausalPitfalls, a comprehensive benchmark designed to rigorously evaluate the capability of LLMs in overcoming common causal inference pitfalls. Our benchmark features structured challenges across multiple difficulty levels, each paired with grading rubrics. This approach allows us to quantitatively measure both causal reasoning capabilities and the reliability of LLMs' responses. We evaluate models using two protocols: (1) direct prompting, which assesses intrinsic causal reasoning, and (2) code-assisted prompting, where models generate executable code for explicit statistical analysis. Additionally, we validate the effectiveness of this judge by comparing its scoring with assessments from human experts. Our results reveal significant limitations in current LLMs when performing statistical causal inference. The CausalPitfalls benchmark provides essential guidance and quantitative metrics to advance the development of trustworthy causal reasoning systems.

Gen Li, Ganghua Wang, Jie Ding

LASSO regularization is a popular regression tool to enhance the prediction accuracy of statistical models by performing variable selection through the $\ell_1$ penalty, initially formulated for the linear model and its variants. In this paper, the territory of LASSO is extended to two-layer ReLU neural networks, a fashionable and powerful nonlinear regression model. Specifically, given a neural network whose output $y$ depends only on a small subset of input $\boldsymbol{x}$, denoted by $\mathcal{S}^{\star}$, we prove that the LASSO estimator can stably reconstruct the neural network and identify $\mathcal{S}^{\star}$ when the number of samples scales logarithmically with the input dimension. This challenging regime has been well understood for linear models while barely studied for neural networks. Our theory lies in an extended Restricted Isometry Property (RIP)-based analysis framework for two-layer ReLU neural networks, which may be of independent interest to other LASSO or neural network settings. Based on the result, we advocate a neural network-based variable selection method. Experiments on simulated and real-world datasets show promising performance of the variable selection approach compared with existing techniques.

Enmao Diao, Vahid Tarokh, Jie Ding

Recommender Systems (RSs) are operated locally by different organizations in many realistic scenarios. If various organizations can fully share their data and perform computation in a centralized manner, they may significantly improve the accuracy of recommendations. However, collaborations among multiple organizations in enhancing the performance of recommendations are primarily limited due to the difficulty of sharing data and models. To address this challenge, we propose Decentralized Multi-Target Cross-Domain Recommendation (DMTCDR) with Multi-Target Assisted Learning (MTAL) and Assisted AutoEncoder (AAE). Our method can help multiple organizations collaboratively improve their recommendation performance in a decentralized manner without sharing sensitive assets. Consequently, it allows decentralized organizations to collaborate and form a community of shared interest. We conduct extensive experiments to demonstrate that the new method can significantly outperform locally trained RSs and mitigate the cold start problem.

Cheng Chen, Jiaying Zhou, Jie Ding et al.

In the era of big data, many big organizations are integrating machine learning into their work pipelines to facilitate data analysis. However, the performance of their trained models is often restricted by limited and imbalanced data available to them. In this work, we develop an assisted learning framework for assisting organizations to improve their learning performance. The organizations have sufficient computation resources but are subject to stringent data-sharing and collaboration policies. Their limited imbalanced data often cause biased inference and sub-optimal decision-making. In assisted learning, an organizational learner purchases assistance service from an external service provider and aims to enhance its model performance within only a few assistance rounds. We develop effective stochastic training algorithms for both assisted deep learning and assisted reinforcement learning. Different from existing distributed algorithms that need to frequently transmit gradients or models, our framework allows the learner to only occasionally share information with the service provider, but still obtain a model that achieves near-oracle performance as if all the data were centralized.

Jiawei Zhang, Jie Ding, Yuhong Yang

In many applications, we have access to the complete dataset but are only interested in the prediction of a particular region of predictor variables. A standard approach is to find the globally best modeling method from a set of candidate methods. However, it is perhaps rare in reality that one candidate method is uniformly better than the others. A natural approach for this scenario is to apply a weighted $L_2$ loss in performance assessment to reflect the region-specific interest. We propose a targeted cross-validation (TCV) to select models or procedures based on a general weighted $L_2$ loss. We show that the TCV is consistent in selecting the best performing candidate under the weighted $L_2$ loss. Experimental studies are used to demonstrate the use of TCV and its potential advantage over the global CV or the approach of using only local data for modeling a local region. Previous investigations on CV have relied on the condition that when the sample size is large enough, the ranking of two candidates stays the same. However, in many applications with the setup of changing data-generating processes or highly adaptive modeling methods, the relative performance of the methods is not static as the sample size varies. Even with a fixed data-generating process, it is possible that the ranking of two methods switches infinitely many times. In this work, we broaden the concept of the selection consistency by allowing the best candidate to switch as the sample size varies, and then establish the consistency of the TCV. This flexible framework can be applied to high-dimensional and complex machine learning scenarios where the relative performances of modeling procedures are dynamic.

Ganghua Wang, Jie Ding

With the rapidly increasing ability to collect and analyze personal data, data privacy becomes an emerging concern. In this work, we develop a new statistical notion of local privacy to protect each categorical data that will be collected by untrusted entities. The proposed solution, named subset privacy, privatizes the original data value by replacing it with a random subset containing that value. We develop methods for the estimation of distribution functions and independence testing from subset-private data with theoretical guarantees. We also study different mechanisms to realize the subset privacy and evaluation metrics to quantify the amount of privacy in practice. Experimental results on both simulated and real-world datasets demonstrate the encouraging performance of the developed concepts and methods.

Gen Li, Jie Ding

Multi-layer feedforward networks have been used to approximate a wide range of nonlinear functions. An important and fundamental problem is to understand the learnability of a network model through its statistical risk, or the expected prediction error on future data. To the best of our knowledge, the rate of convergence of neural networks shown by existing works is bounded by at most the order of $n^{-1/4}$ for a sample size of $n$. In this paper, we show that a class of variation-constrained neural networks, with arbitrary width, can achieve near-parametric rate $n^{-1/2+δ}$ for an arbitrarily small positive constant $δ$. It is equivalent to $n^{-1 +2δ}$ under the mean squared error. This rate is also observed by numerical experiments. The result indicates that the neural function space needed for approximating smooth functions may not be as large as what is often perceived. Our result also provides insight to the phenomena that deep neural networks do not easily suffer from overfitting when the number of neurons and learning parameters rapidly grow with $n$ or even surpass $n$. We also discuss the rate of convergence regarding other network parameters, including the input dimension, network layer, and coefficient norm.

Jie Ding, Bangjun Ding

The emerging public awareness and government regulations of data privacy motivate new paradigms of collecting and analyzing data that are transparent and acceptable to data owners. We present a new concept of privacy and corresponding data formats, mechanisms, and theories for privatizing data during data collection. The privacy, named Interval Privacy, enforces the raw data conditional distribution on the privatized data to be the same as its unconditional distribution over a nontrivial support set. Correspondingly, the proposed privacy mechanism will record each data value as a random interval (or, more generally, a range) containing it. The proposed interval privacy mechanisms can be easily deployed through survey-based data collection interfaces, e.g., by asking a respondent whether its data value is within a randomly generated range. Another unique feature of interval mechanisms is that they obfuscate the truth but do not perturb it. Using narrowed range to convey information is complementary to the popular paradigm of perturbing data. Also, the interval mechanisms can generate progressively refined information at the discretion of individuals, naturally leading to privacy-adaptive data collection. We develop different aspects of theory such as composition, robustness, distribution estimation, and regression learning from interval-valued data. Interval privacy provides a new perspective of human-centric data privacy where individuals have a perceptible, transparent, and simple way of sharing sensitive data.

Enmao Diao, Jie Ding, Vahid Tarokh

Federated Learning allows the training of machine learning models by using the computation and private data resources of many distributed clients. Most existing results on Federated Learning (FL) assume the clients have ground-truth labels. However, in many practical scenarios, clients may be unable to label task-specific data due to a lack of expertise or resource. We propose SemiFL to address the problem of combining communication-efficient FL such as FedAvg with Semi-Supervised Learning (SSL). In SemiFL, clients have completely unlabeled data and can train multiple local epochs to reduce communication costs, while the server has a small amount of labeled data. We provide a theoretical understanding of the success of data augmentation-based SSL methods to illustrate the bottleneck of a vanilla combination of communication-efficient FL with SSL. To address this issue, we propose alternate training to `fine-tune global model with labeled data' and `generate pseudo-labels with the global model.' We conduct extensive experiments and demonstrate that our approach significantly improves the performance of a labeled server with unlabeled clients training with multiple local epochs. Moreover, our method outperforms many existing SSFL baselines and performs competitively with the state-of-the-art FL and SSL results.

Enmao Diao, Jie Ding, Vahid Tarokh

Collaborations among multiple organizations, such as financial institutions, medical centers, and retail markets in decentralized settings are crucial to providing improved service and performance. However, the underlying organizations may have little interest in sharing their local data, models, and objective functions. These requirements have created new challenges for multi-organization collaboration. In this work, we propose Gradient Assisted Learning (GAL), a new method for multiple organizations to assist each other in supervised learning tasks without sharing local data, models, and objective functions. In this framework, all participants collaboratively optimize the aggregate of local loss functions, and each participant autonomously builds its own model by iteratively fitting the gradients of the overarching objective function. We also provide asymptotic convergence analysis and practical case studies of GAL. Experimental studies demonstrate that GAL can achieve performance close to centralized learning when all data, models, and objective functions are fully disclosed.

Yuan Yang, Jie Ding

Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time series from different scales. This naturally motivated us to propose a new concept referred to as the scale-based inference. The basic idea is that more accurate prediction can be made by exploiting scale information of a time series. We first propose a nonparametric predictor based on $k$-nearest neighbors with an optimally chosen $k$ for a single time series. Based on that, we focus on a specific but important type of scale information, the resolution/sampling rate of time series data. We then propose an algorithm to sequentially predict time series using past data at various resolutions. We prove that asymptotically the algorithm produces the mean prediction error that is no larger than the best possible algorithm at any single resolution, under some optimally chosen parameters. Finally, we establish the general formulations for scale inference, and provide further motivating examples. Experiments on both synthetic and real data illustrate the potential applicability of our approaches to a wide range of time series models.

Jiaying Zhou, Xun Xian, Na Li et al.

The rapid development in data collecting devices and computation platforms produces an emerging number of agents, each equipped with a unique data modality over a particular population of subjects. While the predictive performance of an agent may be enhanced by transmitting other data to it, this is often unrealistic due to intractable transmission costs and security concerns. While the predictive performance of an agent may be enhanced by transmitting other data to it, this is often unrealistic due to intractable transmission costs and security concerns. In this paper, we propose a method named ASCII for an agent to improve its classification performance through assistance from other agents. The main idea is to iteratively interchange an ignorance value between 0 and 1 for each collated sample among agents, where the value represents the urgency of further assistance needed. The method is naturally suitable for privacy-aware, transmission-economical, and decentralized learning scenarios. The method is also general as it allows the agents to use arbitrary classifiers such as logistic regression, ensemble tree, and neural network, and they may be heterogeneous among agents. We demonstrate the proposed method with extensive experimental studies.

Enmao Diao, Jie Ding, Vahid Tarokh

Federated Learning (FL) is a method of training machine learning models on private data distributed over a large number of possibly heterogeneous clients such as mobile phones and IoT devices. In this work, we propose a new federated learning framework named HeteroFL to address heterogeneous clients equipped with very different computation and communication capabilities. Our solution can enable the training of heterogeneous local models with varying computation complexities and still produce a single global inference model. For the first time, our method challenges the underlying assumption of existing work that local models have to share the same architecture as the global model. We demonstrate several strategies to enhance FL training and conduct extensive empirical evaluations, including five computation complexity levels of three model architecture on three datasets. We show that adaptively distributing subnetworks according to clients' capabilities is both computation and communication efficient.

Xinran Wang, Yu Xiang, Jun Gao et al.

In this work, we propose information laundering, a novel framework for enhancing model privacy. Unlike data privacy that concerns the protection of raw data information, model privacy aims to protect an already-learned model that is to be deployed for public use. The private model can be obtained from general learning methods, and its deployment means that it will return a deterministic or random response for a given input query. An information-laundered model consists of probabilistic components that deliberately maneuver the intended input and output for queries to the model, so the model's adversarial acquisition is less likely. Under the proposed framework, we develop an information-theoretic principle to quantify the fundamental tradeoffs between model utility and privacy leakage and derive the optimal design.

Xun Xian, Xinran Wang, Mingyi Hong et al.

In recent years, there have been many cloud-based machine learning services, where well-trained models are provided to users on a pay-per-query scheme through a prediction API. The emergence of these services motivates this work, where we will develop a general notion of model privacy named imitation privacy. We show the broad applicability of imitation privacy in classical query-response MLaaS scenarios and new multi-organizational learning scenarios. We also exemplify the fundamental difference between imitation privacy and the usual data-level privacy.

Tianyang Xie, Jie Ding

An emerging number of modern applications involve forecasting time series data that exhibit both short-time dynamics and long-time seasonality. Specifically, time series with multiple seasonality is a difficult task with comparatively fewer discussions. In this paper, we propose a two-stage method for time series with multiple seasonality, which does not require pre-determined seasonality periods. In the first stage, we generalize the classical seasonal autoregressive moving average (ARMA) model in multiple seasonality regime. In the second stage, we utilize an appropriate criterion for lag order selection. Simulation and empirical studies show the excellent predictive performance of our method, especially compared to a recently popular `Facebook Prophet' model for time series.

Khalil Elkhalil, Ali Hasan, Jie Ding et al.

It has been conjectured that the Fisher divergence is more robust to model uncertainty than the conventional Kullback-Leibler (KL) divergence. This motivates the design of a new class of robust generative auto-encoders (AE) referred to as Fisher auto-encoders. Our approach is to design Fisher AEs by minimizing the Fisher divergence between the intractable joint distribution of observed data and latent variables, with that of the postulated/modeled joint distribution. In contrast to KL-based variational AEs (VAEs), the Fisher AE can exactly quantify the distance between the true and the model-based posterior distributions. Qualitative and quantitative results are provided on both MNIST and celebA datasets demonstrating the competitive performance of Fisher AEs in terms of robustness compared to other AEs such as VAEs and Wasserstein AEs.

Chenglong Ye, Reza Ghanadan, Jie Ding

In collaborative learning, learners coordinate to enhance each of their learning performances. From the perspective of any learner, a critical challenge is to filter out unqualified collaborators. We propose a framework named meta clustering to address the challenge. Unlike the classical problem of clustering data points, meta clustering categorizes learners. Assuming each learner performs a supervised regression on a standalone local dataset, we propose a Select-Exchange-Cluster (SEC) method to classify the learners by their underlying supervised functions. We theoretically show that the SEC can cluster learners into accurate collaboration sets. Empirical studies corroborate the theoretical analysis and demonstrate that SEC can be computationally efficient, robust against learner heterogeneity, and effective in enhancing single-learner performance. Also, we show how the proposed approach may be used to enhance data fairness. Supplementary materials for this article are available online.

Jiaying Zhou, Jie Ding, Kean Ming Tan et al.

We consider a distributed learning setting where each agent/learner holds a specific parametric model and data source. The goal is to integrate information across a set of learners to enhance the prediction accuracy of a given learner. A natural way to integrate information is to build a joint model across a group of learners that shares common parameters of interest. However, the underlying parameter sharing patterns across a set of learners may not be a priori known. Misspecifying the parameter sharing patterns or the parametric model for each learner often yields a biased estimation and degrades the prediction accuracy. We propose a general method to integrate information across a set of learners that is robust against misspecifications of both models and parameter sharing patterns. The main crux is to sequentially incorporate additional learners that can enhance the prediction accuracy of an existing joint model based on user-specified parameter sharing patterns across a set of learners. Theoretically, we show that the proposed method can data-adaptively select the most suitable way of parameter sharing and thus enhance the predictive performance of any particular learner of interest. Extensive numerical studies show the promising performance of the proposed method.

Xun Xian, Xinran Wang, Jie Ding et al.

In an increasing number of AI scenarios, collaborations among different organizations or agents (e.g., human and robots, mobile units) are often essential to accomplish an organization-specific mission. However, to avoid leaking useful and possibly proprietary information, organizations typically enforce stringent security constraints on sharing modeling algorithms and data, which significantly limits collaborations. In this work, we introduce the Assisted Learning framework for organizations to assist each other in supervised learning tasks without revealing any organization's algorithm, data, or even task. An organization seeks assistance by broadcasting task-specific but nonsensitive statistics and incorporating others' feedback in one or more iterations to eventually improve its predictive performance. Theoretical and experimental studies, including real-world medical benchmarks, show that Assisted Learning can often achieve near-oracle learning performance as if data and training processes were centralized.

Jiawei Zhang, Jie Ding, Yuhong Yang

In recent years, many non-traditional classification methods, such as Random Forest, Boosting, and neural network, have been widely used in applications. Their performance is typically measured in terms of classification accuracy. While the classification error rate and the like are important, they do not address a fundamental question: Is the classification method underfitted? To our best knowledge, there is no existing method that can assess the goodness-of-fit of a general classification procedure. Indeed, the lack of a parametric assumption makes it challenging to construct proper tests. To overcome this difficulty, we propose a methodology called BAGofT that splits the data into a training set and a validation set. First, the classification procedure to assess is applied to the training set, which is also used to adaptively find a data grouping that reveals the most severe regions of underfitting. Then, based on this grouping, we calculate a test statistic by comparing the estimated success probabilities and the actual observed responses from the validation set. The data splitting guarantees that the size of the test is controlled under the null hypothesis, and the power of the test goes to one as the sample size increases under the alternative hypothesis. For testing parametric classification models, the BAGofT has a broader scope than the existing methods since it is not restricted to specific parametric models (e.g., logistic regression). Extensive simulation studies show the utility of the BAGofT when assessing general classification procedures and its strengths over some existing methods when testing parametric classification models.

Yuhao Su, Jie Ding

Using ensemble methods for regression has been a large success in obtaining high-accuracy prediction. Examples are Bagging, Random forest, Boosting, BART (Bayesian additive regression tree), and their variants. In this paper, we propose a new perspective named variable grouping to enhance the predictive performance. The main idea is to seek for potential grouping of variables in such way that there is no nonlinear interaction term between variables of different groups. Given a sum-of-learner model, each learner will only be responsible for one group of variables, which would be more efficient in modeling nonlinear interactions. We propose a two-stage method named variable grouping based Bayesian additive regression tree (GBART) with a well-developed python package gbart available. The first stage is to search for potential interactions and an appropriate grouping of variables. The second stage is to build a final model based on the discovered groups. Experiments on synthetic and real data show that the proposed method can perform significantly better than classical approaches.

Suya Wu, Enmao Diao, Jie Ding et al.

Motivated by the ever-increasing demands for limited communication bandwidth and low-power consumption, we propose a new methodology, named joint Variational Autoencoders with Bernoulli mixture models (VAB), for performing clustering in the compressed data domain. The idea is to reduce the data dimension by Variational Autoencoders (VAEs) and group data representations by Bernoulli mixture models (BMMs). Once jointly trained for compression and clustering, the model can be decomposed into two parts: a data vendor that encodes the raw data into compressed data, and a data consumer that classifies the received (compressed) data. In this way, the data vendor benefits from data security and communication bandwidth, while the data consumer benefits from low computational complexity. To enable training using the gradient descent algorithm, we propose to use the Gumbel-Softmax distribution to resolve the infeasibility of the back-propagation algorithm when assessing categorical samples.

Jianyou Wang, Michael Xue, Ryan Culhane et al.

Speech Emotion Recognition (SER) has emerged as a critical component of the next generation human-machine interfacing technologies. In this work, we propose a new dual-level model that predicts emotions based on both MFCC features and mel-spectrograms produced from raw audio signals. Each utterance is preprocessed into MFCC features and two mel-spectrograms at different time-frequency resolutions. A standard LSTM processes the MFCC features, while a novel LSTM architecture, denoted as Dual-Sequence LSTM (DS-LSTM), processes the two mel-spectrograms simultaneously. The outputs are later averaged to produce a final classification of the utterance. Our proposed model achieves, on average, a weighted accuracy of 72.7% and an unweighted accuracy of 73.3%---a 6% improvement over current state-of-the-art unimodal models---and is comparable with multimodal models that leverage textual information as well as audio signals.

Cat P. Le, Yi Zhou, Jie Ding et al.

Classical supervised classification tasks search for a nonlinear mapping that maps each encoded feature directly to a probability mass over the labels. Such a learning framework typically lacks the intuition that encoded features from the same class tend to be similar and thus has little interpretability for the learned features. In this paper, we propose a novel supervised learning model named Supervised-Encoding Quantizer (SEQ). The SEQ applies a quantizer to cluster and classify the encoded features. We found that the quantizer provides an interpretable graph where each cluster in the graph represents a class of data samples that have a particular style. We also trained a decoder that can decode convex combinations of the encoded features from similar and different clusters and provide guidance on style transfer between sub-classes.

Enmao Diao, Jie Ding, Vahid Tarokh

Recurrent Neural Network (RNN) and its variations such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU), have become standard building blocks for learning online data of sequential nature in many research areas, including natural language processing and speech data analysis. In this paper, we present a new methodology to significantly reduce the number of parameters in RNNs while maintaining performance that is comparable or even better than classical RNNs. The new proposal, referred to as Restricted Recurrent Neural Network (RRNN), restricts the weight matrices corresponding to the input data and hidden states at each time step to share a large proportion of parameters. The new architecture can be regarded as a compression of its classical counterpart, but it does not require pre-training or sophisticated parameter fine-tuning, both of which are major issues in most existing compression techniques. Experiments on natural language modeling show that compared with its classical counterpart, the restricted recurrent architecture generally produces comparable results at about 50\% compression rate. In particular, the Restricted LSTM can outperform classical RNN with even less number of parameters.

Jie Ding, Vahid Tarokh, Yuhong Yang

In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are employed, a crucial step is to select the most appropriate model or method from a set of candidates. Model selection is a key ingredient in data analysis for reliable and reproducible statistical inference or prediction, and thus central to scientific studies in fields such as ecology, economics, engineering, finance, political science, biology, and epidemiology. There has been a long history of model selection techniques that arise from researches in statistics, information theory, and signal processing. A considerable number of methods have been proposed, following different philosophies and exhibiting varying performances. The purpose of this article is to bring a comprehensive overview of them, in terms of their motivation, large sample performance, and applicability. We provide integrated and practically relevant discussions on theoretical properties of state-of- the-art model selection approaches. We also share our thoughts on some controversial views on the practice of model selection.

Jie Ding, Mohammad Noshad, Vahid Tarokh

Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable autoregressive (AR) processes. We introduce a new model selection technique based on Gap statistics to learn the appropriate number of AR filters needed to model a time series. We define a new distance measure between stable AR filters and draw a reference curve that is used to measure how much adding a new AR filter improves the performance of the model, and then choose the number of AR filters that has the maximum gap with the reference curve. To that end, we propose a new method in order to generate uniform random stable AR filters in root domain. Numerical results are provided demonstrating the performance of the proposed approach.

Jie Ding, Vahid Tarokh, Yuhong Yang

We introduce a new criterion to determine the order of an autoregressive model fitted to time series data. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information criterion. When the data is generated from a finite order autoregression, the Bayesian information criterion is known to be consistent, and so is the new criterion. When the true order is infinity or suitably high with respect to the sample size, the Akaike information criterion is known to be efficient in the sense that its prediction performance is asymptotically equivalent to the best offered by the candidate models; in this case, the new criterion behaves in a similar manner. Different from the two classical criteria, the proposed criterion adaptively achieves either consistency or efficiency depending on the underlying true model. In practice where the observed time series is given without any prior information about the model specification, the proposed order selection criterion is more flexible and robust compared with classical approaches. Numerical results are presented demonstrating the adaptivity of the proposed technique when applied to various datasets.

Jie Ding, Abdelmadjid Bouabdallah, Vahid Tarokh

With the development of wireless communication technologies which considerably contributed to the development of wireless sensor networks (WSN), we have witnessed an ever-increasing WSN based applications which induced a host of research activities in both academia and industry. Since most of the target WSN applications are very sensitive, security issue is one of the major challenges in the deployment of WSN. One of the important building blocks in securing WSN is key management. Traditional key management solutions developed for other networks are not suitable for WSN since WSN networks are resource (e.g. memory, computation, energy) limited. Key pre-distribution algorithms have recently evolved as efficient alternatives of key management in these networks. In the key pre-distribution systems, secure communication is achieved between a pair of nodes either by the existence of a key allowing for direct communication or by a chain of keys forming a key-path between the pair. In this paper, we propose methods which bring prior knowledge of network characteristics and application constraints into the design of key pre-distribution schemes, in order to provide better security and connectivity while requiring less resources. Our methods are based on casting the prior information as a graph. Motivated by this idea, we also propose a class of quasi-symmetric designs referred here to as g-designs. These produce key pre-distribution schemes that significantly improve upon the existing constructions based on unital designs. We give some examples, and point out open problems for future research.

Jie Ding, Mohammad Noshad, Vahid Tarokh

In this work, we consider the class of multi-state autoregressive processes that can be used to model non-stationary time-series of interest. In order to capture different autoregressive (AR) states underlying an observed time series, it is crucial to select the appropriate number of states. We propose a new model selection technique based on the Gap statistics, which uses a null reference distribution on the stable AR filters to check whether adding a new AR state significantly improves the performance of the model. To that end, we define a new distance measure between AR filters based on mean squared prediction error (MSPE), and propose an efficient method to generate random stable filters that are uniformly distributed in the coefficient space. Numerical results are provided to evaluate the performance of the proposed approach.