Alfred O. Hero

Alfred O. Hero, Douglas Cochran

Sensor systems typically operate under resource constraints that prevent the simultaneous use of all resources all of the time. Sensor management becomes relevant when the sensing system has the capability of actively managing these resources; i.e., changing its operating configuration during deployment in reaction to previous measurements. Examples of systems in which sensor management is currently used or is likely to be used in the near future include autonomous robots, surveillance and reconnaissance networks, and waveform-agile radars. This paper provides an overview of the theory, algorithms, and applications of sensor management as it has developed over the past decades and as it stands today.

Zeyu Sun, Monica G. Bobra, Xiantong Wang et al.

We consider the flare prediction problem that distinguishes flare-imminent active regions that produce an M- or X-class flare in the future 24 hours, from quiet active regions that do not produce any flare within $\pm 24$ hours. Using line-of-sight magnetograms and parameters of active regions in two data products covering Solar Cycle 23 and 24, we train and evaluate two deep learning algorithms -- CNN and LSTM -- and their stacking ensembles. The decisions of CNN are explained using visual attribution methods. We have the following three main findings. (1) LSTM trained on data from two solar cycles achieves significantly higher True Skill Scores (TSS) than that trained on data from a single solar cycle with a confidence level of at least 0.95. (2) On data from Solar Cycle 23, a stacking ensemble that combines predictions from LSTM and CNN using the TSS criterion achieves significantly higher TSS than the "select-best" strategy with a confidence level of at least 0.95. (3) A visual attribution method called Integrated Gradients is able to attribute the CNN's predictions of flares to the emerging magnetic flux in the active region. It also reveals a limitation of CNN as a flare prediction method using line-of-sight magnetograms: it treats the polarity artifact of line-of-sight magnetograms as positive evidence of flares.

Theodoros Tsiligkaridis, Brian M. Sadler, Alfred O. Hero

We consider the problem of decentralized 20 questions with noise for multiple players/agents under the minimum entropy criterion in the setting of stochastic search over a parameter space, with application to target localization. We propose decentralized extensions of the active query-based stochastic search strategy that combines elements from the 20 questions approach and social learning. We prove convergence to correct consensus on the value of the parameter. This framework provides a flexible and tractable mathematical model for decentralized parameter estimation systems based on active querying. We illustrate the effectiveness and robustness of the proposed decentralized collaborative 20 questions algorithm for random network topologies with information sharing.

Neophytos Charalambides, Mert Pilanci, Alfred Hero

We generalize the leverage score sampling sketch for $\ell_2$-subspace embeddings, to accommodate sampling subsets of the transformed data, so that the sketching approach is appropriate for distributed settings. This is then used to derive an approximate coded computing approach for first-order methods; known as gradient coding, to accelerate linear regression in the presence of failures in distributed computational networks, \textit{i.e.} stragglers. We replicate the data across the distributed network, to attain the approximation guarantees through the induced sampling distribution. The significance and main contribution of this work, is that it unifies randomized numerical linear algebra with approximate coded computing, while attaining an induced $\ell_2$-subspace embedding through uniform sampling. The transition to uniform sampling is done without applying a random projection, as in the case of the subsampled randomized Hadamard transform. Furthermore, by incorporating this technique to coded computing, our scheme is an iterative sketching approach to approximately solving linear regression. We also propose weighting when sketching takes place through sampling with replacement, for further compression.

Jinghan Jia, Yihua Zhang, Dogyoon Song et al.

Lifelong learning (LL) aims to improve a predictive model as the data source evolves continuously. Most work in this learning paradigm has focused on resolving the problem of 'catastrophic forgetting,' which refers to a notorious dilemma between improving model accuracy over new data and retaining accuracy over previous data. Yet, it is also known that machine learning (ML) models can be vulnerable in the sense that tiny, adversarial input perturbations can deceive the models into producing erroneous predictions. This motivates the research objective of this paper - specification of a new LL framework that can salvage model robustness (against adversarial attacks) from catastrophic forgetting. Specifically, we propose a new memory-replay LL strategy that leverages modern bi-level optimization techniques to determine the 'coreset' of the current data (i.e., a small amount of data to be memorized) for ease of preserving adversarial robustness over time. We term the resulting LL framework 'Data-Efficient Robustness-Preserving LL' (DERPLL). The effectiveness of DERPLL is evaluated for class-incremental image classification using ResNet-18 over the CIFAR-10 dataset. Experimental results show that DERPLL outperforms the conventional coreset-guided LL baseline and achieves a substantial improvement in both standard accuracy and robust accuracy.

Neophytos Charalambides, Hessam Mahdavifar, Mert Pilanci et al.

Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods for speeding up distributed linear regression. We do so by leveraging randomized techniques, while also ensuring security and straggler resiliency in asynchronous distributed computing systems. Specifically, we randomly rotate the basis of the system of equations and then subsample blocks, to simultaneously secure the information and reduce the dimension of the regression problem. In our setup, the basis rotation corresponds to an encoded encryption in an approximate gradient coding scheme, and the subsampling corresponds to the responses of the non-straggling servers in the centralized coded computing framework. This results in a distributive iterative stochastic approach for matrix compression and steepest descent.

Lin Zhou, Alfred Hero

Using the 20 questions estimation framework with query-dependent noise, we study non-adaptive search strategies for a moving target over the unit cube with unknown initial location and velocities under a piecewise constant velocity model. In this search problem, there is an oracle who knows the instantaneous location of the target at any time. Our task is to query the oracle as few times as possible to accurately estimate the location of the target at any specified time. We first study the case where the oracle's answer to each query is corrupted by discrete noise and then generalize our results to the case of additive white Gaussian noise. In our formulation, the performance criterion is the resolution, which is defined as the maximal $L_\infty$ distance between the true locations and estimated locations. We characterize the minimal resolution of an optimal non-adaptive query procedure with a finite number of queries by deriving non-asymptotic and asymptotic bounds. Our bounds are tight in the first-order asymptotic sense when the number of queries satisfies a certain condition and our bounds are tight in the stronger second-order asymptotic sense when the target moves with a constant velocity. To prove our results, we relate the current problem to channel coding, borrow ideas from finite blocklength information theory and construct bounds on the number of possible quantized target trajectories.

Byoungwook Jang, Julia Nepper, Marc Chevrette et al.

Recent works in bandit problems adopted lasso convergence theory in the sequential decision-making setting. Even with fully observed contexts, there are technical challenges that hinder the application of existing lasso convergence theory: 1) proving the restricted eigenvalue condition under conditionally sub-Gaussian noise and 2) accounting for the dependence between the context variables and the chosen actions. This paper studies the effect of missing covariates on regret for stochastic linear bandit algorithms. Our work provides a high-probability upper bound on the regret incurred by the proposed algorithm in terms of covariate sampling probabilities, showing that the regret degrades due to missingness by at most $ζ_{min}^2$, where $ζ_{min}$ is the minimum probability of observing covariates in the context vector. We illustrate our algorithm for the practical application of experimental design for collecting gene expression data by a sequential selection of class discriminating DNA probes.

Conrad D. Hougen, Lance M. Kaplan, Magdalena Ivanovska et al.

In second-order uncertain Bayesian networks, the conditional probabilities are only known within distributions, i.e., probabilities over probabilities. The delta-method has been applied to extend exact first-order inference methods to propagate both means and variances through sum-product networks derived from Bayesian networks, thereby characterizing epistemic uncertainty, or the uncertainty in the model itself. Alternatively, second-order belief propagation has been demonstrated for polytrees but not for general directed acyclic graph structures. In this work, we extend Loopy Belief Propagation to the setting of second-order Bayesian networks, giving rise to Second-Order Loopy Belief Propagation (SOLBP). For second-order Bayesian networks, SOLBP generates inferences consistent with those generated by sum-product networks, while being more computationally efficient and scalable.

Conrad D. Hougen, Lance M. Kaplan, Federico Cerutti et al.

When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the probabilities and quantifying the uncertainty in these estimates. We refer to these cases as uncer tain or second-order Bayesian networks. When such data are complete, i.e., all variable values are observed for each instantiation, the conditional probabilities are known to be Dirichlet-distributed. This paper improves the current state-of-the-art approaches for handling uncertain Bayesian networks by enabling them to learn distributions for their parameters, i.e., conditional probabilities, with incomplete data. We extensively evaluate various methods to learn the posterior of the parameters through the desired and empirically derived strength of confidence bounds for various queries.

Chongyu Fan, Jiancheng Liu, Alfred Hero et al.

The trustworthy machine learning (ML) community is increasingly recognizing the crucial need for models capable of selectively 'unlearning' data points after training. This leads to the problem of machine unlearning (MU), aiming to eliminate the influence of chosen data points on model performance, while still maintaining the model's utility post-unlearning. Despite various MU methods for data influence erasure, evaluations have largely focused on random data forgetting, ignoring the vital inquiry into which subset should be chosen to truly gauge the authenticity of unlearning performance. To tackle this issue, we introduce a new evaluative angle for MU from an adversarial viewpoint. We propose identifying the data subset that presents the most significant challenge for influence erasure, i.e., pinpointing the worst-case forget set. Utilizing a bi-level optimization principle, we amplify unlearning challenges at the upper optimization level to emulate worst-case scenarios, while simultaneously engaging in standard training and unlearning at the lower level, achieving a balance between data influence erasure and model utility. Our proposal offers a worst-case evaluation of MU's resilience and effectiveness. Through extensive experiments across different datasets (including CIFAR-10, 100, CelebA, Tiny ImageNet, and ImageNet) and models (including both image classifiers and generative models), we expose critical pros and cons in existing (approximate) unlearning strategies. Our results illuminate the complex challenges of MU in practice, guiding the future development of more accurate and robust unlearning algorithms. The code is available at https://github.com/OPTML-Group/Unlearn-WorstCase.

Chongyu Fan, Yihua Zhang, Jinghan Jia et al.

Large reasoning models (LRMs), such as OpenAI's o1 and DeepSeek-R1, harness test-time scaling to perform multi-step reasoning for complex problem-solving. This reasoning process, executed before producing final answers, is often guided by special juncture tokens or textual segments that prompt self-evaluative reflection. We refer to these transition markers and reflective cues as "reflection tokens" (e.g., "wait", "but", "alternatively"). In this work, we treat reflection tokens as a "resource" and introduce the problem of resource allocation, aimed at improving the test-time compute performance of LRMs by adaptively regulating the frequency and placement of reflection tokens. Through empirical analysis, we show that both excessive and insufficient use of reflection tokens, referred to as over-reflection and under-reflection, can degrade model performance. To better understand and manage this trade-off, we draw an analogy between reflection token usage and learning rate scheduling in optimization. Building on this insight, we propose cyclical reflection token scheduling (termed CyclicReflex), a decoding strategy that dynamically modulates reflection token logits using a position-dependent triangular waveform. Experiments on MATH500, AIME2024/2025, and AMC2023 demonstrate that CyclicReflex consistently improves performance across model sizes (1.5B-8B), outperforming standard decoding and more recent approaches such as TIP (thought switching penalty) and S1. Codes are available at https://github.com/OPTML-Group/CyclicReflex.

Ren Wang, Tianqi Chen, Stephen Lindsly et al.

Adversarial attacks against deep neural networks (DNNs) are continuously evolving, requiring increasingly powerful defense strategies. We develop a novel adversarial defense framework inspired by the adaptive immune system: the Robust Adversarial Immune-inspired Learning System (RAILS). Initializing a population of exemplars that is balanced across classes, RAILS starts from a uniform label distribution that encourages diversity and uses an evolutionary optimization process to adaptively adjust the predictive label distribution in a manner that emulates the way the natural immune system recognizes novel pathogens. RAILS' evolutionary optimization process explicitly captures the tradeoff between robustness (diversity) and accuracy (specificity) of the network, and represents a new immune-inspired perspective on adversarial learning. The benefits of RAILS are empirically demonstrated under eight types of adversarial attacks on a DNN adversarial image classifier for several benchmark datasets, including: MNIST; SVHN; CIFAR-10; and CIFAR-10. We find that PGD is the most damaging attack strategy and that for this attack RAILS is significantly more robust than other methods, achieving improvements in adversarial robustness by $\geq 5.62\%, 12.5\%$, $10.32\%$, and $8.39\%$, on these respective datasets, without appreciable loss of classification accuracy. Codes for the results in this paper are available at https://github.com/wangren09/RAILS.

Ekdeep Singh Lubana, Puja Trivedi, Conrad Hougen et al.

Network pruning in Convolutional Neural Networks (CNNs) has been extensively investigated in recent years. To determine the impact of pruning a group of filters on a network's accuracy, state-of-the-art pruning methods consistently assume filters of a CNN are independent. This allows the importance of a group of filters to be estimated as the sum of importances of individual filters. However, overparameterization in modern networks results in highly correlated filters that invalidate this assumption, thereby resulting in incorrect importance estimates. To address this issue, we propose OrthoReg, a principled regularization strategy that enforces orthonormality on a network's filters to reduce inter-filter correlation, thereby allowing reliable, efficient determination of group importance estimates, improved trainability of pruned networks, and efficient, simultaneous pruning of large groups of filters. When used for iterative pruning on VGG-13, MobileNet-V1, and ResNet-34, OrthoReg consistently outperforms five baseline techniques, including the state-of-the-art, on CIFAR-100 and Tiny-ImageNet. For the recently proposed Early-Bird Ticket hypothesis, which claims networks become amenable to pruning early-on in training and can be pruned after a few epochs to minimize training expenditure, we find OrthoReg significantly outperforms prior work. Code available at https://github.com/EkdeepSLubana/OrthoReg.

Ren Wang, Yuxuan Li, Alfred Hero

Deep learning models have shown considerable vulnerability to adversarial attacks, particularly as attacker strategies become more sophisticated. While traditional adversarial training (AT) techniques offer some resilience, they often focus on defending against a single type of attack, e.g., the $\ell_\infty$-norm attack, which can fail for other types. This paper introduces a computationally efficient multilevel $\ell_p$ defense, called the Efficient Robust Mode Connectivity (EMRC) method, which aims to enhance a deep learning model's resilience against multiple $\ell_p$-norm attacks. Similar to analytical continuation approaches used in continuous optimization, the method blends two $p$-specific adversarially optimal models, the $\ell_1$- and $\ell_\infty$-norm AT solutions, to provide good adversarial robustness for a range of $p$. We present experiments demonstrating that our approach performs better on various attacks as compared to AT-$\ell_\infty$, E-AT, and MSD, for datasets/architectures including: CIFAR-10, CIFAR-100 / PreResNet110, WideResNet, ViT-Base.

Minoh Jeong, Seonho Kim, Alfred Hero

Deterministic embeddings learned by contrastive learning (CL) methods such as SimCLR and SupCon achieve state-of-the-art performance but lack a principled mechanism for uncertainty quantification. We propose Variational Contrastive Learning (VCL), a decoder-free framework that maximizes the evidence lower bound (ELBO) by interpreting the InfoNCE loss as a surrogate reconstruction term and adding a KL divergence regularizer to a uniform prior on the unit hypersphere. We model the approximate posterior $q_θ(z|x)$ as a projected normal distribution, enabling the sampling of probabilistic embeddings. Our two instantiation--VSimCLR and VSupCon--replace deterministic embeddings with samples from $q_θ(z|x)$ and incorporate a normalized KL term into the loss. Experiments on multiple benchmarks demonstrate that VCL mitigates dimensional collapse, enhances mutual information with class labels, and matches or outperforms deterministic baselines in classification accuracy, all the while providing meaningful uncertainty estimates through the posterior model. VCL thus equips contrastive learning with a probabilistic foundation, serving as a new basis for contrastive approaches.

Minoh Jeong, Alfred Hero

Self-supervised contrastive learning (SSCL) has emerged as a powerful paradigm for representation learning and has been studied from multiple perspectives, including mutual information and geometric viewpoints. However, supervised contrastive (SupCon) approaches have received comparatively little attention in this context: for instance, while InfoNCE used in SSCL is known to form a lower bound on mutual information (MI), the relationship between SupCon and MI remains unexplored. To address this gap, we introduce ProjNCE, a generalization of the InfoNCE loss that unifies supervised and self-supervised contrastive objectives by incorporating projection functions and an adjustment term for negative pairs. We prove that ProjNCE constitutes a valid MI bound and affords greater flexibility in selecting projection strategies for class embeddings. Building on this flexibility, we further explore the centroid-based class embeddings in SupCon by exploring a variety of projection methods. Extensive experiments on image and audio datasets demonstrate that ProjNCE consistently outperforms both SupCon and standard cross-entropy training. Our work thus refines SupCon along two complementary perspectives--information-theoretic and projection viewpoints--and offers broadly applicable improvements whenever SupCon serves as the foundational contrastive objective.

Mohammadreza Tavasoli Naeini, Ali Bereyhi, Morteza Noshad et al.

This work invokes the notion of $f$-divergence to introduce a novel upper bound on the Bayes error rate of a general classification task. We show that the proposed bound can be computed by sampling from the output of a parameterized model. Using this practical interpretation, we introduce the Bayes optimal learning threshold (BOLT) loss whose minimization enforces a classification model to achieve the Bayes error rate. We validate the proposed loss for image and text classification tasks, considering MNIST, Fashion-MNIST, CIFAR-10, and IMDb datasets. Numerical experiments demonstrate that models trained with BOLT achieve performance on par with or exceeding that of cross-entropy, particularly on challenging datasets. This highlights the potential of BOLT in improving generalization.

Haonan Zhu, Andre R. Goncalves, Camilo Valdes et al.

This paper proposes a hierarchical Bayesian multitask learning model that is applicable to the general multi-task binary classification learning problem where the model assumes a shared sparsity structure across different tasks. We derive a computationally efficient inference algorithm based on variational inference to approximate the posterior distribution. We demonstrate the potential of the new approach on various synthetic datasets and for predicting human health status based on microbiome profile. Our analysis incorporates data pooled from multiple microbiome studies, along with a comprehensive comparison with other benchmark methods. Results in synthetic datasets show that the proposed approach has superior support recovery property when the underlying regression coefficients share a common sparsity structure across different tasks. Our experiments on microbiome classification demonstrate the utility of the method in extracting informative taxa while providing well-calibrated predictions with uncertainty quantification and achieving competitive performance in terms of prediction metrics. Notably, despite the heterogeneity of the pooled datasets (e.g., different experimental objectives, laboratory setups, sequencing equipment, patient demographics), our method delivers robust results.

Zeyu Sun, Dogyoon Song, Alfred Hero

Recalibrating probabilistic classifiers is vital for enhancing the reliability and accuracy of predictive models. Despite the development of numerous recalibration algorithms, there is still a lack of a comprehensive theory that integrates calibration and sharpness (which is essential for maintaining predictive power). In this paper, we introduce the concept of minimum-risk recalibration within the framework of mean-squared-error (MSE) decomposition, offering a principled approach for evaluating and recalibrating probabilistic classifiers. Using this framework, we analyze the uniform-mass binning (UMB) recalibration method and establish a finite-sample risk upper bound of order $\tilde{O}(B/n + 1/B^2)$ where $B$ is the number of bins and $n$ is the sample size. By balancing calibration and sharpness, we further determine that the optimal number of bins for UMB scales with $n^{1/3}$, resulting in a risk bound of approximately $O(n^{-2/3})$. Additionally, we tackle the challenge of label shift by proposing a two-stage approach that adjusts the recalibration function using limited labeled data from the target domain. Our results show that transferring a calibrated classifier requires significantly fewer target samples compared to recalibrating from scratch. We validate our theoretical findings through numerical simulations, which confirm the tightness of the proposed bounds, the optimal number of bins, and the effectiveness of label shift adaptation.

Neophytos Charalambides, Hessam Mahdavifar, Mert Pilanci et al.

In this work, we propose a method for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a random orthonormal matrix and then subsample in \textit{blocks}, to simultaneously secure the information and reduce the dimension of the regression problem. In our setup, the transformation corresponds to an encoded encryption in an \textit{approximate} gradient coding scheme, and the subsampling corresponds to the responses of the non-straggling workers; in a centralized coded computing network. We focus on the special case of the \textit{Subsampled Randomized Hadamard Transform}, which we generalize to block sampling; and discuss how it can be used to secure the data. We illustrate the performance through numerical experiments.

Davoud Ataee Tarzanagh, Laura Balzano, Alfred O. Hero

Inference of community structure in probabilistic graphical models may not be consistent with fairness constraints when nodes have demographic attributes. Certain demographics may be over-represented in some detected communities and under-represented in others. This paper defines a novel $\ell_1$-regularized pseudo-likelihood approach for fair graphical model selection. In particular, we assume there is some community or clustering structure in the true underlying graph, and we seek to learn a sparse undirected graph and its communities from the data such that demographic groups are fairly represented within the communities. In the case when the graph is known a priori, we provide a convex semidefinite programming approach for fair community detection. We establish the statistical consistency of the proposed method for both a Gaussian graphical model and an Ising model for, respectively, continuous and binary data, proving that our method can recover the graphs and their fair communities with high probability.

Yu Wang, Alfred Hero

In this work, we study the emergence of sparsity and multiway structures in second-order statistical characterizations of dynamical processes governed by partial differential equations (PDEs). We consider several state-of-the-art multiway covariance and inverse covariance (precision) matrix estimators and examine their pros and cons in terms of accuracy and interpretability in the context of physics-driven forecasting when incorporated into the ensemble Kalman filter (EnKF). In particular, we show that multiway data generated from the Poisson and the convection-diffusion types of PDEs can be accurately tracked via EnKF when integrated with appropriate covariance and precision matrix estimators.

Ren Wang, Zhe Xu, Alfred Hero

Deep learning-based Multi-Task Classification (MTC) is widely used in applications like facial attributes and healthcare that warrant strong privacy guarantees. In this work, we aim to protect sensitive information in the inference phase of MTC and propose a novel Multi-Trigger-Key (MTK) framework to achieve the privacy-preserving objective. MTK associates each secured task in the multi-task dataset with a specifically designed trigger-key. The true information can be revealed by adding the trigger-key if the user is authorized. We obtain such an MTK model by training it with a newly generated training set. To address the information leakage malaise resulting from correlations among different tasks, we generalize the training process by incorporating an MTK decoupling process with a controllable trade-off between the protective efficacy and the model performance. Theoretical guarantees and experimental results demonstrate the effectiveness of the privacy protection without appreciable hindering on the model performance.

Yasin Yilmaz, Mehmet Aktukmak, Alfred O. Hero

The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do not readily extend to heterogeneous data that are a combination of numerical and categorical variables, e.g., arising from linked GPS and text data. In this paper, we are interested in learning probabilistic generative models from high-dimensional heterogeneous data in an unsupervised fashion. The learned generative model provides latent unified representations that capture the factors common to the multiple dimensions of the data, and thus enable fusing multimodal data for various machine learning tasks. Following a Bayesian approach, we propose a general framework that combines disparate data types through the natural parameterization of the exponential family of distributions. To scale the model inference to millions of instances with thousands of features, we use the Laplace-Bernstein approximation for posterior computations involving nonlinear link functions. The proposed algorithm is presented in detail for the commonly encountered heterogeneous datasets with real-valued (Gaussian) and categorical (multinomial) features. Experiments on two high-dimensional and heterogeneous datasets (NYC Taxi and MovieLens-10M) demonstrate the scalability and competitive performance of the proposed algorithm on different machine learning tasks such as anomaly detection, data imputation, and recommender systems.

Ren Wang, Tianqi Chen, Philip Yao et al.

K-Nearest Neighbor (kNN)-based deep learning methods have been applied to many applications due to their simplicity and geometric interpretability. However, the robustness of kNN-based classification models has not been thoroughly explored and kNN attack strategies are underdeveloped. In this paper, we propose an Adversarial Soft kNN (ASK) loss to both design more effective kNN attack strategies and to develop better defenses against them. Our ASK loss approach has two advantages. First, ASK loss can better approximate the kNN's probability of classification error than objectives proposed in previous works. Second, the ASK loss is interpretable: it preserves the mutual information between the perturbed input and the in-class-reference data. We use the ASK loss to generate a novel attack method called the ASK-Attack (ASK-Atk), which shows superior attack efficiency and accuracy degradation relative to previous kNN attacks. Based on the ASK-Atk, we then derive an ASK-\underline{Def}ense (ASK-Def) method that optimizes the worst-case training loss induced by ASK-Atk. Experiments on CIFAR-10 (ImageNet) show that (i) ASK-Atk achieves $\geq 13\%$ ($\geq 13\%$) improvement in attack success rate over previous kNN attacks, and (ii) ASK-Def outperforms the conventional adversarial training method by $\geq 6.9\%$ ($\geq 3.5\%$) in terms of robustness improvement.

Ren Wang, Tianqi Chen, Stephen Lindsly et al.

Biomimetics has played a key role in the evolution of artificial neural networks. Thus far, in silico metaphors have been dominated by concepts from neuroscience and cognitive psychology. In this paper we introduce a different type of biomimetic model, one that borrows concepts from the immune system, for designing robust deep neural networks. This immuno-mimetic model leads to a new computational biology framework for robustification of deep neural networks against adversarial attacks. Within this Immuno-Net framework we define a robust adaptive immune-inspired learning system (Immuno-Net RAILS) that emulates, in silico, the adaptive biological mechanisms of B-cells that are used to defend a mammalian host against pathogenic attacks. When applied to image classification tasks on benchmark datasets, we demonstrate that Immuno-net RAILS results in improvement of as much as 12.5% in adversarial accuracy of a baseline method, the DkNN-robustified CNN, without appreciable loss of accuracy on clean data.

Yu Wang, Alfred Hero

We propose a new graphical model inference procedure, called SG-PALM, for learning conditional dependency structure of high-dimensional tensor-variate data. Unlike most other tensor graphical models the proposed model is interpretable and computationally scalable to high dimension. Physical interpretability follows from the Sylvester generative (SG) model on which SG-PALM is based: the model is exact for any observation process that is a solution of a partial differential equation of Poisson type. Scalability follows from the fast proximal alternating linearized minimization (PALM) procedure that SG-PALM uses during training. We establish that SG-PALM converges linearly (i.e., geometric convergence rate) to a global optimum of its objective function. We demonstrate the scalability and accuracy of SG-PALM for an important but challenging climate prediction problem: spatio-temporal forecasting of solar flares from multimodal imaging data.

Ren Wang, Tianqi Chen, Stephen Lindsly et al.

Adversarial attacks against deep neural networks are continuously evolving. Without effective defenses, they can lead to catastrophic failure. The long-standing and arguably most powerful natural defense system is the mammalian immune system, which has successfully defended against attacks by novel pathogens for millions of years. In this paper, we propose a new adversarial defense framework, called the Robust Adversarial Immune-inspired Learning System (RAILS). RAILS incorporates an Adaptive Immune System Emulation (AISE), which emulates in silico the biological mechanisms that are used to defend the host against attacks by pathogens. We use RAILS to harden Deep k-Nearest Neighbor (DkNN) architectures against evasion attacks. Evolutionary programming is used to simulate processes in the natural immune system: B-cell flocking, clonal expansion, and affinity maturation. We show that the RAILS learning curve exhibits similar diversity-selection learning phases as observed in our in vitro biological experiments. When applied to adversarial image classification on three different datasets, RAILS delivers an additional 5.62%/12.56%/4.74% robustness improvement as compared to applying DkNN alone, without appreciable loss of accuracy on clean data.

Sijia Liu, Pin-Yu Chen, Bhavya Kailkhura et al.

Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning applications. It is used for solving optimization problems similarly to gradient-based methods. However, it does not require the gradient, using only function evaluations. Specifically, ZO optimization iteratively performs three major steps: gradient estimation, descent direction computation, and solution update. In this paper, we provide a comprehensive review of ZO optimization, with an emphasis on showing the underlying intuition, optimization principles and recent advances in convergence analysis. Moreover, we demonstrate promising applications of ZO optimization, such as evaluating robustness and generating explanations from black-box deep learning models, and efficient online sensor management.

Abram Magner, Mayank Baranwal, Alfred O. Hero

Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of the embeddings of their sample graphs. In particular, the graph models that we consider arise from graphons, which are the most general possible parameterizations of infinite exchangeable graph models and which are the central objects of study in the theory of dense graph limits. We exhibit an infinite class of graphons that are well-separated in terms of cut distance and are indistinguishable by a GCN with nonlinear activation functions coming from a certain broad class if its depth is at least logarithmic in the size of the sample graph. These results theoretically match empirical observations of several prior works. Finally, we show a converse result that for pairs of graphons satisfying a degree profile separation property, a very simple GCN architecture suffices for distinguishability. To prove our results, we exploit a connection to random walks on graphs.

Yu Wang, Byoungwook Jang, Alfred Hero

This paper introduces the Sylvester graphical lasso (SyGlasso) that captures multiway dependencies present in tensor-valued data. The model is based on the Sylvester equation that defines a generative model. The proposed model complements the tensor graphical lasso (Greenewald et al., 2019) that imposes a Kronecker sum model for the inverse covariance matrix by providing an alternative Kronecker sum model that is generative and interpretable. A nodewise regression approach is adopted for estimating the conditional independence relationships among variables. The statistical convergence of the method is established, and empirical studies are provided to demonstrate the recovery of meaningful conditional dependency graphs. We apply the SyGlasso to an electroencephalography (EEG) study to compare the brain connectivity of alcoholic and nonalcoholic subjects. We demonstrate that our model can simultaneously estimate both the brain connectivity and its temporal dependencies.

Abram Magner, Mayank Baranwal, Alfred O. Hero

Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish between different random graph models (corresponding to different class-conditional distributions in a classification problem) on the basis of the embeddings of their sample graphs. In particular, the graph models that we consider arise from graphons, which are the most general possible parameterizations of infinite exchangeable graph models and which are the central objects of study in the theory of dense graph limits. We give a precise characterization of the set of pairs of graphons that are indistinguishable by a GCN with nonlinear activation functions coming from a certain broad class if its depth is at least logarithmic in the size of the sample graph. This characterization is in terms of a degree profile closeness property. Outside this class, a very simple GCN architecture suffices for distinguishability. We then exhibit a concrete, infinite class of graphons arising from stochastic block models that are well-separated in terms of cut distance and are indistinguishable by a GCN. These results theoretically match empirical observations of several prior works. To prove our results, we exploit a connection to random walks on graphs. Finally, we give empirical results on synthetic and real graph classification datasets, indicating that indistinguishable graph distributions arise in practice.

Salimeh Yasaei Sekeh, Madan Ravi Ganesh, Shurjo Banerjee et al.

Online Streaming Feature Selection (OSFS) is a sequential learning problem where individual features across all samples are made available to algorithms in a streaming fashion. In this work, firstly, we assert that OSFS's main assumption of having data from all the samples available at runtime is unrealistic and introduce a new setting where features and samples are streamed concurrently called OSFS with Streaming Samples (OSFS-SS). Secondly, the primary OSFS method, SAOLA utilizes an unbounded mutual information measure and requires multiple comparison steps between the stored and incoming feature sets to evaluate a feature's importance. We introduce Geometric Online Adaption, an algorithm that requires relatively less feature comparison steps and uses a bounded conditional geometric dependency measure. Our algorithm outperforms several OSFS baselines including SAOLA on a variety of datasets. We also extend SAOLA to work in the OSFS-SS setting and show that GOA continues to achieve the best results. Thirdly, the current paradigm of the OSFS algorithm comparison is flawed. Algorithms are measured by comparing the number of features used and the accuracy obtained by the learner, two properties that are fundamentally at odds with one another. Without fixing a limit on either of these properties, the qualities of features obtained by different algorithms are incomparable. We try to rectify this inconsistency by fixing the maximum number of features available to the learner and comparing algorithms in terms of their accuracy. Additionally, we characterize the behaviour of SAOLA and GOA on feature sets derived from popular deep convolutional featurizers.

Morteza Noshad, Li Xu, Alfred Hero

We address the problem of learning to benchmark the best achievable classifier performance. In this problem the objective is to establish statistically consistent estimates of the Bayes misclassification error rate without having to learn a Bayes-optimal classifier. Our learning to benchmark framework improves on previous work on learning bounds on Bayes misclassification rate since it learns the {\it exact} Bayes error rate instead of a bound on error rate. We propose a benchmark learner based on an ensemble of $ε$-ball estimators and Chebyshev approximation. Under a smoothness assumption on the class densities we show that our estimator achieves an optimal (parametric) mean squared error (MSE) rate of $O(N^{-1})$, where $N$ is the number of samples. Experiments on both simulated and real datasets establish that our proposed benchmark learning algorithm produces estimates of the Bayes error that are more accurate than previous approaches for learning bounds on Bayes error probability.

Brandon Oselio, Amir Sadeghian, Silvio Savarese et al.

Directed information (DI) is a useful tool to explore time-directed interactions in multivariate data. However, as originally formulated DI is not well suited to interactions that change over time. In previous work, adaptive directed information was introduced to accommodate non-stationarity, while still preserving the utility of DI to discover complex dependencies between entities. There are many design decisions and parameters that are crucial to the effectiveness of ADI. Here, we apply ideas from ensemble learning in order to alleviate this issue, allowing for a more robust estimator for exploratory data analysis. We apply these techniques to interaction estimation in a crowded scene, utilizing the Stanford drone dataset as an example.

Joel W. LeBlanc, Brian J. Thelen, Alfred O. Hero

Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally convergent algorithm has found the globally optimal solution. When the problem is formulated in terms of maximizing the likelihood function under a statistical model for the measurements, one can construct a statistical test that a local maximum is in fact the global maximum. A one-sided test is proposed for the case that the statistical model is a member of the generalized location family of probability distributions, a condition often satisfied in imaging and other inverse problems. We propose a general method for improving the accuracy of the test by reparameterizing the likelihood function to embed its domain into a higher dimensional parameter space. We show that the proposed global maximum testing method results in improved accuracy and reduced computation for a physically-motivated joint-inverse problem arising in camera-blur estimation.

Pin-Yu Chen, Sutanay Choudhury, Luke Rodriguez et al.

Lateral movement attacks are a serious threat to enterprise security. In these attacks, an attacker compromises a trusted user account to get a foothold into the enterprise network and uses it to attack other trusted users, increasingly gaining higher and higher privileges. Such lateral attacks are very hard to model because of the unwitting role that users play in the attack and even harder to detect and prevent because of their low and slow nature. In this paper, a theoretical framework is presented for modeling lateral movement attacks and for proposing a methodology for designing resilient cyber systems against such attacks. The enterprise is modeled as a tripartite graph capturing the interaction between users, machines, and applications, and a set of procedures is proposed to harden the network by increasing the cost of lateral movement. Strong theoretical guarantees on system resilience are established and experimentally validated for large enterprise networks.

Byoungwook Jang, Alfred Hero

We propose a new topic modeling procedure that takes advantage of the fact that the Latent Dirichlet Allocation (LDA) log likelihood function is asymptotically equivalent to the logarithm of the volume of the topic simplex. This allows topic modeling to be reformulated as finding the probability simplex that minimizes its volume and encloses the documents that are represented as distributions over words. A convex relaxation of the minimum volume topic model optimization is proposed, and it is shown that the relaxed problem has the same global minimum as the original problem under the separability assumption and the sufficiently scattered assumption introduced by Arora et al. (2013) and Huang et al. (2016). A locally convergent alternating direction method of multipliers (ADMM) approach is introduced for solving the relaxed minimum volume problem. Numerical experiments illustrate the benefits of our approach in terms of computation time and topic recovery performance.

Salimeh Yasaei Sekeh, Alfred O. Hero

Feature selection and reducing the dimensionality of data is an essential step in data analysis. In this work, we propose a new criterion for feature selection that is formulated as conditional information between features given the labeled variable. Instead of using the standard mutual information measure based on Kullback-Leibler divergence, we use our proposed criterion to filter out redundant features for the purpose of multiclass classification. This approach results in an efficient and fast non-parametric implementation of feature selection as it can be directly estimated using a geometric measure of dependency, the global Friedman-Rafsky (FR) multivariate run test statistic constructed by a global minimal spanning tree (MST). We demonstrate the advantages of our proposed feature selection approach through simulation. In addition the proposed feature selection method is applied to the MNIST data set.

Alexander Jung, Alfred O. Hero, Alexandru Mara et al.

We propose and analyze a method for semi-supervised learning from partially-labeled network-structured data. Our approach is based on a graph signal recovery interpretation under a clustering hypothesis that labels of data points belonging to the same well-connected subset (cluster) are similar valued. This lends naturally to learning the labels by total variation (TV) minimization, which we solve by applying a recently proposed primal-dual method for non-smooth convex optimization. The resulting algorithm allows for a highly scalable implementation using message passing over the underlying empirical graph, which renders the algorithm suitable for big data applications. By applying tools of compressed sensing, we derive a sufficient condition on the underlying network structure such that TV minimization recovers clusters in the empirical graph of the data. In particular, we show that the proposed primal-dual method amounts to maximizing network flows over the empirical graph of the dataset. Moreover, the learning accuracy of the proposed algorithm is linked to the set of network flows between data points having known labels. The effectiveness and scalability of our approach is verified by numerical experiments.

Salimeh Yasaei Sekeh, Brandon Oselio, Alfred O. Hero

In the context of supervised learning, meta learning uses features, metadata and other information to learn about the difficulty, behavior, or composition of the problem. Using this knowledge can be useful to contextualize classifier results or allow for targeted decisions about future data sampling. In this paper, we are specifically interested in learning the Bayes error rate (BER) based on a labeled data sample. Providing a tight bound on the BER that is also feasible to estimate has been a challenge. Previous work[1] has shown that a pairwise bound based on the sum of Henze-Penrose (HP) divergence over label pairs can be directly estimated using a sum of Friedman-Rafsky (FR) multivariate run test statistics. However, in situations in which the dataset and number of classes are large, this bound is computationally infeasible to calculate and may not be tight. Other multi-class bounds also suffer from computationally complex estimation procedures. In this paper, we present a generalized HP divergence measure that allows us to estimate the Bayes error rate with log-linear computation. We prove that the proposed bound is tighter than both the pairwise method and a bound proposed by Lin [2]. We also empirically show that these bounds are close to the BER. We illustrate the proposed method on the MNIST dataset, and show its utility for the evaluation of feature reduction strategies. We further demonstrate an approach for evaluation of deep learning architectures using the proposed bounds.

Salimeh Yasaei Sekeh, Morteza Noshad, Kevin R. Moon et al.

Bounding the best achievable error probability for binary classification problems is relevant to many applications including machine learning, signal processing, and information theory. Many bounds on the Bayes binary classification error rate depend on information divergences between the pair of class distributions. Recently, the Henze-Penrose (HP) divergence has been proposed for bounding classification error probability. We consider the problem of empirically estimating the HP-divergence from random samples. We derive a bound on the convergence rate for the Friedman-Rafsky (FR) estimator of the HP-divergence, which is related to a multivariate runs statistic for testing between two distributions. The FR estimator is derived from a multicolored Euclidean minimal spanning tree (MST) that spans the merged samples. We obtain a concentration inequality for the Friedman-Rafsky estimator of the Henze-Penrose divergence. We validate our results experimentally and illustrate their application to real datasets.

Inyong Yun, Cheolkon Jung, Xinran Wang et al.

Pedestrians in videos have a wide range of appearances such as body poses, occlusions, and complex backgrounds, and there exists the proposal shift problem in pedestrian detection that causes the loss of body parts such as head and legs. To address it, we propose part-level convolutional neural networks (CNN) for pedestrian detection using saliency and boundary box alignment in this paper. The proposed network consists of two sub-networks: detection and alignment. We use saliency in the detection sub-network to remove false positives such as lamp posts and trees. We adopt bounding box alignment on detection proposals in the alignment sub-network to address the proposal shift problem. First, we combine FCN and CAM to extract deep features for pedestrian detection. Then, we perform part-level CNN to recall the lost body parts. Experimental results on various datasets demonstrate that the proposed method remarkably improves accuracy in pedestrian detection and outperforms existing state-of-the-arts in terms of log average miss rate at false position per image (FPPI).

Hye Won Chung, Ji Oon Lee, Doyeon Kim et al.

Consider a query-based data acquisition problem that aims to recover the values of $k$ binary variables from parity (XOR) measurements of chosen subsets of the variables. Assume the response model where only a randomly selected subset of the measurements is received. We propose a method for designing a sequence of queries so that the variables can be identified with high probability using as few ($n$) measurements as possible. We define the query difficulty $\bar{d}$ as the average size of the query subsets and the sample complexity $n$ as the minimum number of measurements required to attain a given recovery accuracy. We obtain fundamental trade-offs between recovery accuracy, query difficulty, and sample complexity. In particular, the necessary and sufficient sample complexity required for recovering all $k$ variables with high probability is $n = c_0 \max\{k, (k \log k)/\bar{d}\}$ and the sample complexity for recovering a fixed proportion $(1-δ)k$ of the variables for $δ=o(1)$ is $n = c_1\max\{k, (k \log(1/δ))/\bar{d}\}$, where $c_0, c_1>0$.

Hafiz Tiomoko Ali, Sijia Liu, Yasin Yilmaz et al.

We propose a method for simultaneously detecting shared and unshared communities in heterogeneous multilayer weighted and undirected networks. The multilayer network is assumed to follow a generative probabilistic model that takes into account the similarities and dissimilarities between the communities. We make use of a variational Bayes approach for jointly inferring the shared and unshared hidden communities from multilayer network observations. We show that our approach outperforms state-of-the-art algorithms in detecting disparate (shared and private) communities on synthetic data as well as on real genome-wide fibroblast proliferation dataset.

Elizabeth Hou, Alfred O. Hero

In many real-world applications, data is not collected as one batch, but sequentially over time, and often it is not possible or desirable to wait until the data is completely gathered before analyzing it. Thus, we propose a framework to sequentially update a maximum margin classifier by taking advantage of the Maximum Entropy Discrimination principle. Our maximum margin classifier allows for a kernel representation to represent large numbers of features and can also be regularized with respect to a smooth sub-manifold, allowing it to incorporate unlabeled observations. We compare the performance of our classifier to its non-sequential equivalents in both simulated and real datasets.

Morteza Noshad, Yu Zeng, Alfred O. Hero

The Mutual Information (MI) is an often used measure of dependency between two random variables utilized in information theory, statistics and machine learning. Recently several MI estimators have been proposed that can achieve parametric MSE convergence rate. However, most of the previously proposed estimators have the high computational complexity of at least $O(N^2)$. We propose a unified method for empirical non-parametric estimation of general MI function between random vectors in $\mathbb{R}^d$ based on $N$ i.i.d. samples. The reduced complexity MI estimator, called the ensemble dependency graph estimator (EDGE), combines randomized locality sensitive hashing (LSH), dependency graphs, and ensemble bias-reduction methods. We prove that EDGE achieves optimal computational complexity $O(N)$, and can achieve the optimal parametric MSE rate of $O(1/N)$ if the density is $d$ times differentiable. To the best of our knowledge EDGE is the first non-parametric MI estimator that can achieve parametric MSE rates with linear time complexity. We illustrate the utility of EDGE for the analysis of the information plane (IP) in deep learning. Using EDGE we shed light on a controversy on whether or not the compression property of information bottleneck (IB) in fact holds for ReLu and other rectification functions in deep neural networks (DNN).

Farshad Harirchi, Doohyun Kim, Omar A. Khalil et al.

Chemical kinetic mechanisms can be represented by sets of elementary reactions that are easily translated into mathematical terms using physicochemical relationships. The schematic representation of reactions captures the interactions between reacting species and products. Determining the minimal chemical interactions underlying the dynamic behavior of systems is a major task. In this paper, we introduce a novel approach for the identification of the influential reactions in chemical reaction networks for combustion applications, using a data-driven sparse-learning technique. The proposed approach identifies a set of influential reactions using species concentrations and reaction rates, with minimal computational cost without requiring additional data or simulations. The new approach is applied to analyze the combustion chemistry of H2 and C3H8 in a constant-volume homogeneous reactor. The influential reactions identified by the sparse-learning method are consistent with the current kinetics knowledge of chemical mechanisms. Additionally, we show that a reduced version of the parent mechanism can be generated as a combination of the influential reactions identified at different times and conditions and that for both H2 and C3H8 this reduced mechanism performs closely to the parent mechanism as a function of ignition delay over a wide range of conditions. Our results demonstrate the potential of the sparse-learning approach as an effective and efficient tool for mechanism analysis and mechanism reduction.

Farshad Harirchi, Omar A. Khalil, Sijia Liu et al.

In this paper, we propose an optimization-based sparse learning approach to identify the set of most influential reactions in a chemical reaction network. This reduced set of reactions is then employed to construct a reduced chemical reaction mechanism, which is relevant to chemical interaction network modeling. The problem of identifying influential reactions is first formulated as a mixed-integer quadratic program, and then a relaxation method is leveraged to reduce the computational complexity of our approach. Qualitative and quantitative validation of the sparse encoding approach demonstrates that the model captures important network structural properties with moderate computational load.