Expectation-maximization Framework Research Articles

Learning Representation for Clustering Via Prototype Scattering and Positive Sampling.

Existing deep clustering methods rely on either contrastive or non-contrastive representation learning for downstream clustering task. Contrastive-based methods thanks to negative pairs learn uniform representations for clustering, in which negative pairs, however, may inevitably lead to the class collision issue and consequently compromise the clustering performance. Non-contrastive-based methods, on the other hand, avoid class collision issue, but the resulting non-uniform representations may cause the collapse of clustering. To enjoy the strengths of both worlds, this paper presents a novel end-to-end deep clustering method with prototype scattering and positive sampling, termed ProPos. Specifically, we first maximize the distance between prototypical representations, named prototype scattering loss, which improves the uniformity of representations. Second, we align one augmented view of instance with the sampled neighbors of another view-assumed to be truly positive pair in the embedding space-to improve the within-cluster compactness, termed positive sampling alignment. The strengths of ProPos are avoidable class collision issue, uniform representations, well-separated clusters, and within-cluster compactness. By optimizing ProPos in an end-to-end expectation-maximization framework, extensive experimental results demonstrate that ProPos achieves competing performance on moderate-scale clustering benchmark datasets and establishes new state-of-the-art performance on large-scale datasets. Source code is available at https://github.com/Hzzone/ProPos.

Channel Estimation for Full-Duplex Multi-Antenna Ambient Backscatter Communication Systems

Ambient backscatter communication (AmBC) is a highly promising technology that enables the ubiquitous deployment of low-cost, low-power devices to support the next generation of Internet-of-Things (IoT) applications. This paper addresses channel estimation for full-duplex multi-antenna AmBC systems. This is highly challenging due to the large number of channel parameters resulting from the use of multiple antennas, the presence of self-interference, and the dependence of the backscattering channel on the state of the backscattering device. Considering both pilot-based and semi-blind estimation strategies, we propose three solutions for this problem. The first is the pilot-based maximum-likelihood (ML) estimator. The second is a semi-blind estimator based on the expectation maximization (EM) framework, which provides higher accuracy than the ML, at the cost of higher computational complexity. The third is a semi-blind estimator based on the decision-directed (DD) strategy, which provides a tradeoff between the ML and the EM. Additionally, we derive the exact Cramer-Rao bound (CRB) for pilot-based estimation and the modified CRB for semi-blind estimation. Simulations show that the ML and the EM perform very close to their respective CRBs, and that the semi-blind estimators offer significantly higher estimation accuracy, as well as superior symbol-error-rate performance, compared to the ML estimator.

An expectation-maximization framework for comprehensive prediction of isoform-specific functions.

Advances in RNA sequencing technologies have achieved an unprecedented accuracy in the quantification of mRNA isoforms, but our knowledge of isoform-specific functions has lagged behind. There is a need to understand the functional consequences of differential splicing, which could be supported by the generation of accurate and comprehensive isoform-specific gene ontology annotations. We present isoform interpretation, a method that uses expectation-maximization to infer isoform-specific functions based on the relationship between sequence and functional isoform similarity. We predicted isoform-specific functional annotations for 85617 isoforms of 17900 protein-coding human genes spanning a range of 17430 distinct gene ontology terms. Comparison with a gold-standard corpus of manually annotated human isoform functions showed that isoform interpretation significantly outperforms state-of-the-art competing methods. We provide experimental evidence that functionally related isoforms predicted by isoform interpretation show a higher degree of domain sharing and expression correlation than functionally related genes. We also show that isoform sequence similarity correlates better with inferred isoform function than with gene-level function. Source code, documentation, and resource files are freely available under a GNU3 license at https://github.com/TheJacksonLaboratory/isopretEM and https://zenodo.org/record/7594321.

A Theoretical Model Characterizing Tangle Evolution in IOTA Blockchain Network

IOTA blockchain system is lightweight without heavy proof-of-work mining phases, which is considered a promising service platform of Internet of Things applications. IOTA organizes ledger data in a directed acyclic graph (DAG), called Tangle, rather a chain structure as in traditional blockchains. With arriving messages, IOTA tangle grows in a special way, as multiple messages can be attached to the tangle at different locations in parallel. Hence, the network dynamics of an operational IOTA system would justify a thorough study, which is currently unexplored in the literature. In this article, we present the first theoretical modeling for the evolving IOTA tangle based on stochastic analysis. After analyzing snapshots of the real-world IOTA ledger data, our key finding suggests that IOTA tangle follows a rather atypical double Pareto Lognormal (dPLN) degree distribution. In contrast, typical power-law and exponential distributions do not accurately reflect the fact. For model parameter estimation, we further realize that using generic optimization solvers cannot yield quality fitting results. Thus, we design an alternative algorithm based on expectation-maximization (EM) framework. We evaluate the proposed model and fitting algorithm with official data provided by the IOTA Foundation. Quantitative comparisons confirm the fitting quality of our proposed model and algorithm. The whole analysis reveals a deeper understanding of the internal mechanism of the IOTA network.

Reconstructing Sparse Multiplex Networks with Application to Covert Networks

Network structure provides critical information for understanding the dynamic behavior of complex systems. However, the complete structure of real-world networks is often unavailable, thus it is crucially important to develop approaches to infer a more complete structure of networks. In this paper, we integrate the configuration model for generating random networks into an Expectation-Maximization-Aggregation (EMA) framework to reconstruct the complete structure of multiplex networks. We validate the proposed EMA framework against the Expectation-Maximization (EM) framework and random model on several real-world multiplex networks, including both covert and overt ones. It is found that the EMA framework generally achieves the best predictive accuracy compared to the EM framework and the random model. As the number of layers increases, the performance improvement of EMA over EM decreases. The inferred multiplex networks can be leveraged to inform the decision-making on monitoring covert networks as well as allocating limited resources for collecting additional information to improve reconstruction accuracy. For law enforcement agencies, the inferred complete network structure can be used to develop more effective strategies for covert network interdiction.

A Generalized GraphEM for Sparse Time-Varying Dynamical Systems

We consider the problem of joint parameter estimation and smoothing in structured linear systems using the expectation maximization (EM) framework. Specifically, we explore how partially known sparsity structures in the estimation model can be leveraged to improve the computation speed and performance of the considered EM approaches. We use these ideas to generalize a recently proposed GraphEM algorithm to a linear time-varying setting, where the sparsity structures may vary in time. We obtain a biconvex form of the majorizing function in the M-step, which is minimized subject to an l1-regularization using a Douglas-Rachford proximal splitting algorithm. Numerical results using a satellite positioning example shows significant improvements in the estimation errors and an F1-score that quantifies model sparsity.

Adaptive Smoothing with Ambiguity Fixation for GNSS Post-Processing

We propose a complete post-processing solution for GNSS (global navigation satellite system) positioning leveraging linear-regression Kalman filtering methods, employed in a Rauch-Tung-Striebel (RTS) smoothing context, where the model parameters are adapted in an expectation maximization (EM) framework. In particular, we (i) discuss the effects of using different moment approximations in the smoother; (ii) demonstrate that it is advantageous to fixate the integer ambiguities on the smoothing posterior; and (iii) show that the proposed method is viable for a wide range of GNSS measurement models, including single difference, double difference, and ionosphere-free combinations of the multi-band GNSS observations.

A Robust and Flexible EM Algorithm for Mixtures of Elliptical Distributions with Missing Data

This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when compared to other popular approaches such as those based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -nearest neighbors or on multiple imputations by chained equations. However, Gaussian mixture models are known to be non-robust to heterogeneous data, which can lead to poor estimation performance when the data is contaminated by outliers or have non-Gaussian distributions. To overcome this issue, a new EM algorithm is investigated for mixtures of elliptical distributions with the property of handling potential missing data. This paper shows that this problem reduces to the estimation of a mixture of angular Gaussian distributions under generic assumptions ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , each sample is drawn from a mixture of elliptical distributions, which is possibly different for one sample to another). In that case, the complete-data likelihood associated with mixtures of elliptical distributions is well adapted to the EM framework with missing data thanks to its conditional distribution, which is shown to be a multivariate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> -distribution. Experimental results on synthetic data demonstrate that the proposed algorithm is robust to outliers and can be used with non-Gaussian data. Furthermore, experiments conducted on real-world datasets show that this algorithm is very competitive when compared to other classical imputation methods.

Off-Grid Based DOA Estimation Algorithm Using Auto-Regression (1) Sparse Bayesian Learning with Linear Interpolation Model

On-grid approaches for DOA estimation majorly exhibits the problem of grid mismatch. Coarse grid leads to reduced estimation accuracy and dense grid leads to increased algorithm complexity and performance degradation due to highly correlated array manifold matrix. In this paper, a fixed off-grid DOA estimation algorithm is proposed to overcome this grid mismatch problem. Firstly, a sparsity based linear interpolation model for array manifold matrix is proposed to avoid the above limitation by introducing a bias parameter into the estimation framework. To solve this model, an Auto-regression (1) (AR (1)) based sparse Bayesian learning algorithm is proposed. To exploit the temporal correlation property of unknown DOA spatial spectrum in a MMV case, we develop this AR (1) model along with SBL to estimate the unknown DOA spectrum and expectation maximization (EM) framework to update the hyper-parameters. The results section shows that the proposed algorithm enjoys good estimation resolution and accuracy in the cases of fewer snapshots available, highly correlated signal sources, very low SNR and very closely spaced sources.

Clustered Sparse Bayesian Learning Based Channel Estimation for Millimeter-Wave Massive MIMO Systems

In this article, we present two clustered sparse Bayesian learning (Cluster-SBL) channel estimation algorithms for millimeter-wave (mmWave) massive multiple-input-multiple-output (MIMO) systems. Different from prior literature, channel path correlations at both the transmitter and the receiver are considered and exploited for estimation performance enhancement. Specifically, we first propose a Kronecker product-based multivariate Gaussian (KP-Gaussian) prior model for mmWave massive MIMO channels, which captures not only sparsity but also the widely existing clustering channel property in mmWave communications. Then, a channel approximation method is derived and leveraged to overcome the challenge caused by channel priors' uncertainty due to the varying propagation environments and improve the robustness of the channel estimation algorithm against channel sparsity. After that, the Cluster-SBL channel estimation algorithm, which is developed based on the expectation maximization (EM) framework and has superior estimation accuracy and high robustness, is proposed. Moreover, to reduce the computation complexity in the channel estimation for practical applications, we also propose an efficient Cluster-SBL (eCluster-SBL) channel estimation algorithm. It is highly beneficial to mmWave massive MIMO systems, especially when the angular resolution is relatively high. Numerical results reveal that, compared with the existing compressed sensing-based and Bayesian criterion-based algorithms, the proposed two channel estimation algorithms exhibit the better performance from both the aspect of estimation accuracy and the aspect of robustness.

Fast combined-frequency phase extraction for phase shifting profilometry.

Due to the nonlinearity in phase shifting profilometry (PSP) system, the captured images are often distorted with fringe harmonics, resulting in inaccurate phase map and measurement. Considering the fact that the phase error can be significantly reduced by modeling high-order fringe harmonics, this work formulates the phase extraction problem - with different frequency images and high-order fringe harmonic model - as a maximum likelihood estimation (MLE). To optimize it efficiently, we thus propose a combined-frequency phase extraction (CFPE) solution by introducing a latent phase map and incorporating the famous expectation-maximization (EM) framework. As a result, our CFPE method only needs ∼5% execution time of a high-order baseline, whilst keeps the high-order accuracy. Tested on synthetic images as well as practical measurements, our CFPE method demonstrated its performance improvement of efficiency and accuracy. In addition, our detailed implementation with experimental arrangement is also provided for interested researchers.

ScanMix: Learning from Severe Label Noise via Semantic Clustering and Semi-Supervised Learning

We propose a new training algorithm, ScanMix, that explores semantic clustering and semi-supervised learning (SSL) to allow superior robustness to severe label noise and competitive robustness to non-severe label noise problems, in comparison to the state of the art (SOTA) methods. ScanMix is based on the expectation maximisation framework, where the E-step estimates the latent variable to cluster the training images based on their appearance and classification results, and the M-step optimises the SSL classification and learns effective feature representations via semantic clustering. We present a theoretical result that shows the correctness and convergence of ScanMix, and an empirical result that shows that ScanMix has SOTA results on CIFAR-10/-100 (with symmetric, asymmetric and semantic label noise), Red Mini-ImageNet (from the Controlled Noisy Web Labels), Clothing1M and WebVision. In all benchmarks with severe label noise, our results are competitive to the current SOTA.

Joint Rigid Registration of Multiple Generalized Point Sets With Anisotropic Positional Uncertainties in Image-Guided Surgery

In medical image analysis (MIA) and computer-assisted surgery (CAS), aligning two multiple point sets (PSs) together is an essential but also a challenging problem. For example, rigidly aligning multiple point sets into one common coordinate frame is a prerequisite for statistical shape modelling (SSM). Accurately aligning the pre-operative space with the intra-operative space in CAS is very crucial to successful interventions. In this article, we formally formulate the multiple generalized point set registration problem (MGPSR) in a probabilistic manner, where both the positional and the normal vectors are used. The six-dimensional vectors consisting of both positional and normal vectors are called as generalized points. In the formulated model, all the generalized PSs to be registered are considered to be the realizations of underlying unknown hybrid mixture models (HMMs). By assuming the independence of the positional and orientational vectors (i.e., the normal vectors), the probability density function (PDF) of an observed generalized point is computed as the product of Gaussian and Fisher distributions. Furthermore, to consider the anisotropic noise in surgical navigation, the positional error is assumed to obey a multi-variate Gaussian distribution. Finally, registering PSs is formulated as a maximum likelihood (ML) problem, and solved under the expectation maximization (EM) technique. By using more enriched information (i.e., the normal vectors), our algorithm is more robust to outliers. By treating all PSs equally, our algorithm does not bias towards any PS. To validate the proposed approach, extensive experiments have been conducted on surface points extracted from CT images of (i) a human femur bone model; (ii) a human pelvis bone model. Results demonstrate our algorithm’s high accuracy, robustness to noise and outliers. Note to Practitioners—This paper was motivated by solving the problem of registering two or more PSs. Most existing registration approaches use only the positional information associated with each point, and thus lacks robustness to noise and outliers. Three significant improvements are brought by our proposed approach. First, the normal vectors that can be extracted from the point sets are utilized in the registration. Second, the positional error distribution is assumed to be anisotropic and inhomogeneous. Third, all the PSs to be registered are treated equally that means no PS is considered as the model one. The registration problem is cast into a maximum likelihood (ML) problem and solved under the expectation maximization (EM) framework. We have demonstrated through extensive experiments that the proposed registration approach achieves significantly improved accuracy, robustness to noise and outliers. The algorithm is particularly suitable for biomedical applications involving the registration procedures, such as image-guided surgery.

Graph prototypical contrastive learning

Unsupervised graph representation learning methods based on contrastive learning have drawn increasing attention and achieved promising performance. Most of these methods only model instance-level feature similarity while ignoring the underlying semantic structure of the whole data. In this paper, we propose a Graph Prototypical Contrastive Learning (GPCL) framework for unsupervised graph representation learning. Besides modeling instance-level feature similarity, GPCL explores the underlying semantic structure of the whole data. Specifically, we introduce an instance-prototype contrastive objective to learn representations that are invariant to intra-class variance and discriminative to inter-class variance. Meanwhile, a prototype-prototype contrastive objective is proposed to encourage clustering consistency between instances in the same cluster and their augmentations. To optimize the model, we formulate GPCL as an online Expectation–Maximization framework. We iteratively perform E-step to estimate the posterior probability of prototype assignments through online clustering and M-step to optimize model parameters through graph prototypical contrastive learning. We evaluate GPCL on various graph benchmarks, and the experimental results verify the superiority of our method.

Learning Large Graph-Based MDPs With Historical Data

Weconsider learning the dynamics and measurement model parameters of a graph-based Markov decision process (GMDP) given a history of measurements. Graph-based models have been used in modeling many data-based applications, such as recognition tasks, disease epidemics, forest wildfires, freeway traffic, and social networks. We leverage the expectation–maximization framework and develop an algorithm that optimizes the measurement likelihood and has favorable complexity for large models. In contrast to prior work, we directly consider GMDPs with significantly large discrete state spaces, arbitrary coupling structure, and long measurement sequences. We also consider a special structural property called Anonymous Influence, which we use to test hypotheses and gain insights into the data. We demonstrate the effectiveness of our learning algorithm by considering two real-world data sets on the 2020 Novel Coronavirus (COVID-19) pandemic in California and on user interactions on Twitter. Our results show that the learned GMDP models better explain the data compared to an uncoupled model assumption.

Point Cloud Registration Leveraging Structural Regularity in Manhattan World

Point cloud registration is an essential technique for many tasks including autonomous navigation, augmented/virtual reality and scene reconstruction. In man-made environments, abundant plane features with structural regularities are commonly seen, which is actually beneficial for point cloud registration. This paper presents an accurate and robust registration method that formulates the registration problem as a maximum likelihood estimation (MLE) problem where the useful structure information is also leveraged. To align two point sets efficiently, one point set is first represented as a Gaussian mixture models (GMM) tree, and then the Manhattan frame (MF) with dominant planes is estimated and the degenerated nodes corresponding to the dominant planes in the GMM tree are clustered to embody the structure information. The proposed MLE problem is solved by an Expectation Maximization (EM) framework. In the E step, the probabilistic data association between the GMM and another point set is first estimated and then refined by aligning the MF and planes. In the M step, an optimization problem using Mahalanobis distance is solved. Experimental results on both indoor room and hybrid man-made environments show that the proposed method not only achieves a good balance between accuracy and speed, but also provides robust and accurate performance in sequence registration process. The source code is available on our Github <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> .

Reward-Weighted Regression Converges to a Global Optimum

Reward-Weighted Regression (RWR) belongs to a family of widely known iterative Reinforcement Learning algorithms based on the Expectation-Maximization framework. In this family, learning at each iteration consists of sampling a batch of trajectories using the current policy and fitting a new policy to maximize a return-weighted log-likelihood of actions. Although RWR is known to yield monotonic improvement of the policy under certain circumstances, whether and under which conditions RWR converges to the optimal policy have remained open questions. In this paper, we provide for the first time a proof that RWR converges to a global optimum when no function approximation is used, in a general compact setting. Furthermore, for the simpler case with finite state and action spaces we prove R-linear convergence of the state-value function to the optimum.

Deep Unsupervised Hashing with Latent Semantic Components

Deep unsupervised hashing has been appreciated in the regime of image retrieval. However, most prior arts failed to detect the semantic components and their relationships behind the images, which makes them lack discriminative power. To make up the defect, we propose a novel Deep Semantic Components Hashing (DSCH), which involves a common sense that an image normally contains a bunch of semantic components with homology and co-occurrence relationships. Based on this prior, DSCH regards the semantic components as latent variables under the Expectation-Maximization framework and designs a two-step iterative algorithm with the objective of maximum likelihood of training data. Firstly, DSCH constructs a semantic component structure by uncovering the fine-grained semantics components of images with a Gaussian Mixture Modal~(GMM), where an image is represented as a mixture of multiple components, and the semantics co-occurrence are exploited. Besides, coarse-grained semantics components, are discovered by considering the homology relationships between fine-grained components, and the hierarchy organization is then constructed. Secondly, DSCH makes the images close to their semantic component centers at both fine-grained and coarse-grained levels, and also makes the images share similar semantic components close to each other. Extensive experiments on three benchmark datasets demonstrate that the proposed hierarchical semantic components indeed facilitate the hashing model to achieve superior performance.

Towards Off-Policy Learning for Ranking Policies with Logged Feedback

Probabilistic learning to rank (LTR) has been the dominating approach for optimizing the ranking metric, but cannot maximize long-term rewards. Reinforcement learning models have been proposed to maximize user long-term rewards by formulating the recommendation as a sequential decision-making problem, but could only achieve inferior accuracy compared to LTR counterparts, primarily due to the lack of online interactions and the characteristics of ranking. In this paper, we propose a new off-policy value ranking (VR) algorithm that can simultaneously maximize user long-term rewards and optimize the ranking metric offline for improved sample efficiency in a unified Expectation-Maximization (EM) framework. We theoretically and empirically show that the EM process guides the leaned policy to enjoy the benefit of integration of the future reward and ranking metric, and learn without any online interactions. Extensive offline and online experiments demonstrate the effectiveness of our methods

EM-Driven Unsupervised Learning for Efficient Motion Segmentation.

In this paper, we present a CNN-based fully unsupervised method for motion segmentation from optical flow. We assume that the input optical flow can be represented as a piecewise set of parametric motion models, typically, affine or quadratic motion models. The core idea of our work is to leverage the Expectation-Maximization (EM) framework in order to design in a well-founded manner a loss function and a training procedure of our motion segmentation neural network that does not require either ground-truth or manual annotation. However, in contrast to the classical iterative EM, once the network is trained, we can provide a segmentation for any unseen optical flow field in a single inference step and without estimating any motion models. We investigate different loss functions including robust ones and propose a novel efficient data augmentation technique on the optical flow field, applicable to any network taking optical flow as input. In addition, our method is able by design to segment multiple motions. Our motion segmentation network was tested on four benchmarks, DAVIS2016, SegTrackV2, FBMS59, and MoCA, and performed very well, while being fast at test time.