Motivation: A branching processes model yields an unevenly stochastically distributed dataset that consists of sparse and dense regions. This work addresses the problem of precisely evaluating parameters for such a model. Applying a branching processes model to an area such as cancer cell evolution faces a number of obstacles, including high dimensionality and the rare appearance of a result of interest. We take on the ambitious task of obtaining the coefficients of a model that reflects the relationship of driver gene mutations and cancer hallmarks on the basis of personal data regarding variant allele frequencies. Results: An approximate Bayesian computation method based on Isolation Kernel is developed. The method involves the transformation of row data to a Hilbert space (mapping) and the measurement of the similarity between simulated points and maxima weighted Isolation Kernel mapping related to the observation point. We also design a heuristic algorithm for parameter estimation that requires no calculation and is dimension independent. The advantages of the proposed machine learning method are illustrated using multidimensional test data as well as a specific example focused on cancer cell evolution.
Deep-learning (DL) algorithms are becoming the standard for processing ultrasound (US) fetal images. Despite a large number of survey papers already present in this field, most of them are focusing on a broader area of medical-image analysis or not covering all fetal US DL applications. This paper surveys the most recent work in the field, with a total of 145 research papers published after 2017. Each paper is analyzed and commented on from both the methodology and application perspective. We categorized the papers in (i) fetal standard-plane detection, (ii) anatomical-structure analysis, and (iii) biometry parameter estimation. For each category, main limitations and open issues are presented. Summary tables are included to facilitate the comparison among the different approaches. Publicly-available datasets and performance metrics commonly used to assess algorithm performance are summarized, too. This paper ends with a critical summary of the current state of the art on DL algorithms for fetal US image analysis and a discussion on current challenges that have to be tackled by researchers working in the field to translate the research methodology into the actual clinical practice.
We propose a method for covert communications using an IEEE 802.11 OFDM/QAM packet as a carrier. We show how to hide the covert message so that the transmitted signal does not violate the spectral mask specified by the standard, and we determine its impact on the OFDM packet error rate. We show conditions under which the hidden signal is not usable and those under which it can be retrieved with a usable bit error rate (BER). The hidden signal is extracted by cancellation of the OFDM signal in the covert receiver. We explore the effects of the hidden signal on OFDM parameter estimation and the covert signal BER. We conclude with an experiment using Over-The-Air recordings of 802.11 packets, inject the hidden
We consider the problem of controlling an unknown stochastic linear system with quadratic costs - called the adaptive LQ control problem. We re-examine an approach called ''Reward Biased Maximum Likelihood Estimate'' (RBMLE) that was proposed more than forty years ago, and which predates the ''Upper Confidence Bound'' (UCB) method as well as the definition of ''regret'' for bandit problems. It simply added a term favoring parameters with larger rewards to the criterion for parameter estimation. We show how the RBMLE and UCB methods can be reconciled, and thereby propose an Augmented RBMLE-UCB algorithm that combines the penalty of the RBMLE method with the constraints of the UCB method, uniting the two approaches to optimism in the face of uncertainty. We establish that theoretically, this method retains $\Tilde{\mathcal{O}}(\sqrt{T})$ regret, the best-known so far. We further compare the empirical performance of the proposed Augmented RBMLE-UCB and the standard RBMLE (without the augmentation) with UCB, Thompson Sampling, Input Perturbation, Randomized Certainty Equivalence and StabL on many real-world examples including flight control of Boeing 747 and Unmanned Aerial Vehicle. We perform extensive simulation studies showing that the Augmented RBMLE consistently outperforms UCB, Thompson Sampling and StabL by a huge margin, while it is marginally better than Input Perturbation and moderately better than Randomized Certainty Equivalence.
Bayesian neural networks have successfully designed and optimized a robust neural network model in many application problems, including uncertainty quantification. However, with its recent success, information-theoretic understanding about the Bayesian neural network is still at an early stage. Mutual information is an example of an uncertainty measure in a Bayesian neural network to quantify epistemic uncertainty. Still, no analytic formula is known to describe it, one of the fundamental information measures to understand the Bayesian deep learning framework. In this paper, we derive the analytical formula of the mutual information between model parameters and the predictive output by leveraging the notion of the point process entropy. Then, as an application, we discuss the parameter estimation of the Dirichlet distribution and show its practical application in the active learning uncertainty measures by demonstrating that our analytical formula can improve the performance of active learning further in practice.
Deep learning methods are notoriously data-hungry, which requires a large number of labeled samples. Unfortunately, the large amount of interactive sample labeling efforts has dramatically hindered the application of deep learning methods, especially for 3D modeling tasks, which require heterogeneous samples. To alleviate the work of data annotation for learned 3D modeling of fa\c{c}ades, this paper proposed a semi-supervised adversarial recognition strategy embedded in inverse procedural modeling. Beginning with textured LOD-2 (Level-of-Details) models, we use the classical convolutional neural networks to recognize the types and estimate the parameters of windows from image patches. The window types and parameters are then assembled into procedural grammar. A simple procedural engine is built inside an existing 3D modeling software, producing fine-grained window geometries. To obtain a useful model from a few labeled samples, we leverage the generative adversarial network to train the feature extractor in a semi-supervised manner. The adversarial training strategy can also exploit unlabeled data to make the training phase more stable. Experiments using publicly available fa\c{c}ade image datasets reveal that the proposed training strategy can obtain about 10% improvement in classification accuracy and 50% improvement in parameter estimation under the same network structure. In addition, performance gains are more pronounced when testing against unseen data featuring different fa\c{c}ade styles.
Large information sizes in samples and features can be encoded to speed up the learning of statistical models based on linear algebra and remove unwanted signals. Encoding information can reduce both sample and feature dimension to a smaller representational set. Here two examples are shown on linear mixed models and mixture models speeding up the run time for parameter estimation by a factor defined by the user's choice on dimension reduction (can be linear, quadratic or beyond based on dimension specification).
Most existing Graph Neural Networks (GNNs) are proposed without considering the selection bias in data, i.e., the inconsistent distribution between the training set with test set. In reality, the test data is not even available during the training process, making selection bias agnostic. Training GNNs with biased selected nodes leads to significant parameter estimation bias and greatly impacts the generalization ability on test nodes. In this paper, we first present an experimental investigation, which clearly shows that the selection bias drastically hinders the generalization ability of GNNs, and theoretically prove that the selection bias will cause the biased estimation on GNN parameters. Then to remove the bias in GNN estimation, we propose a novel Debiased Graph Neural Networks (DGNN) with a differentiated decorrelation regularizer. The differentiated decorrelation regularizer estimates a sample weight for each labeled node such that the spurious correlation of learned embeddings could be eliminated. We analyze the regularizer in causal view and it motivates us to differentiate the weights of the variables based on their contribution on the confounding bias. Then, these sample weights are used for reweighting GNNs to eliminate the estimation bias, thus help to improve the stability of prediction on unknown test nodes. Comprehensive experiments are conducted on several challenging graph datasets with two kinds of label selection biases. The results well verify that our proposed model outperforms the state-of-the-art methods and DGNN is a flexible framework to enhance existing GNNs.
Current state of the art acoustic models can easily comprise more than 100 million parameters. This growing complexity demands larger training datasets to maintain a decent generalization of the final decision function. An ideal dataset is not necessarily large in size, but large with respect to the amount of unique speakers, utilized hardware and varying recording conditions. This enables a machine learning model to explore as much of the domain-specific input space as possible during parameter estimation. This work introduces Common Phone, a gender-balanced, multilingual corpus recorded from more than 11.000 contributors via Mozilla's Common Voice project. It comprises around 116 hours of speech enriched with automatically generated phonetic segmentation. A Wav2Vec 2.0 acoustic model was trained with the Common Phone to perform phonetic symbol recognition and validate the quality of the generated phonetic annotation. The architecture achieved a PER of 18.1 % on the entire test set, computed with all 101 unique phonetic symbols, showing slight differences between the individual languages. We conclude that Common Phone provides sufficient variability and reliable phonetic annotation to help bridging the gap between research and application of acoustic models.
Multistage sequential decision-making scenarios are commonly seen in the healthcare diagnosis process. In this paper, an active learning-based method is developed to actively collect only the necessary patient data in a sequential manner. There are two novelties in the proposed method. First, unlike the existing ordinal logistic regression model which only models a single stage, we estimate the parameters for all stages together. Second, it is assumed that the coefficients for common features in different stages are kept consistent. The effectiveness of the proposed method is validated in both a simulation study and a real case study. Compared with the baseline method where the data is modeled individually and independently, the proposed method improves the estimation efficiency by 62\%-1838\%. For both simulation and testing cohorts, the proposed method is more effective, stable, interpretable, and computationally efficient on parameter estimation. The proposed method can be easily extended to a variety of scenarios where decision-making can be done sequentially with only necessary information.
Wireless sensor networks (WSNs) are vulnerable to eavesdropping as the sensor nodes (SNs) communicate over an open radio channel. Intelligent reflecting surface (IRS) technology can be leveraged for physical layer security in WSNs. In this paper, we propose a joint transmit and reflective beamformer (JTRB) design for secure parameter estimation at the fusion center (FC) in the presence of an eavesdropper (ED) in a WSN. We develop a semidefinite relaxation (SDR)-based iterative algorithm, which alternately yields the transmit beamformer at each SN and the corresponding reflection phases at the IRS, to achieve the minimum mean-squared error (MSE) parameter estimate at the FC, subject to transmit power and ED signal-to-noise ratio constraints. Our simulation results demonstrate robust MSE and security performance of the proposed IRS-based JTRB technique.
Goal: To achieve-high quality comprehensive feature extraction from physiological signals that enables precise physiological parameter estimation despite evolving waveform morphologies. Methods: We propose Boosted-SpringDTW, a probabilistic framework that leverages dynamic time warping (DTW) and minimal domain-specific heuristics to simultaneously segment physiological signals and identify fiducial points that represent cardiac events. An automated dynamic template adapts to evolving waveform morphologies. We validate Boosted-SpringDTW performance with a benchmark PPG dataset whose morphologies include subject- and respiratory-induced variation. Results: Boosted-SpringDTW achieves precision, recall, and F1-scores over 0.96 for identifying fiducial points and mean absolute error values less than 11.41 milliseconds when estimating IBI. Conclusion: Boosted-SpringDTW improves F1-Scores compared to two baseline feature extraction algorithms by 35 percent on average for fiducial point identification and mean percent difference by 16 percent on average for IBI estimation. Significance: Precise hemodynamic parameter estimation with wearable devices enables continuous health monitoring throughout a patients' daily life.
Linear and Quadratic Discriminant Analysis are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not robust. To fill this gap, this paper presents a new robust discriminant analysis where each data point is drawn by its own arbitrary Elliptically Symmetrical (ES) distribution and its own arbitrary scale parameter. Such a model allows for possibly very heterogeneous, independent but non-identically distributed samples. After deriving a new decision rule, it is shown that maximum-likelihood parameter estimation and classification are very simple, fast and robust compared to state-of-the-art methods.
In this paper, we present a crash frequency data augmentation method based on Conditional Generative Adversarial Networks to improve crash frequency models. The proposed method is evaluated by comparing the performance of Base SPFs (developed using original data) and Augmented SPFs (developed using original data plus synthesised data) in terms of hotspot identification performance, model prediction accuracy, and dispersion parameter estimation accuracy. The experiments are conducted using simulated and real-world crash data sets. The results indicate that the synthesised crash data by CGAN have the same distribution as the original data and the Augmented SPFs outperforms Base SPFs in almost all aspects especially when the dispersion parameter is low.
Oscillator output generally has phase noise causing the output power spectral density (PSD) to disperse around a Dirac delta function. In this paper, the AWGN channel is considered, where the sent signal accompanying with phase noise is added to the channel Gaussian noise and received at the receiver. Conventional channel estimation algorithms such as least mean square (LMS) and mean MSE criterion are not suitable for this channel estimation. We (i) analyze this phase noise channel estimation with information theoretic learning (ITL) criterion, i.e., maximum correntropy criterion (MCC), leading to robustness in the channel estimator's steady state behavior; and (ii) improve the convergence rate by combining MSE and MCC as a novel mixed-LMS algorithm.
Multinomial Logit (MNL) is one of the most popular discrete choice models and has been widely used to model ranking data. However, there is a long-standing technical challenge of learning MNL from many real-world ranking data: exact calculation of the MNL likelihood of \emph{partial rankings} is generally intractable. In this work, we develop a scalable method for approximating the MNL likelihood of general partial rankings in polynomial time complexity. We also extend the proposed method to learn mixture of MNL. We demonstrate that the proposed methods are particularly helpful for applications to choice-based network formation modeling, where the formation of new edges in a network is viewed as individuals making choices of their friends over a candidate set. The problem of learning mixture of MNL models from partial rankings naturally arises in such applications. And the proposed methods can be used to learn MNL models from network data without the strong assumption that temporal orders of all the edge formation are available. We conduct experiments on both synthetic and real-world network data to demonstrate that the proposed methods achieve more accurate parameter estimation and better fitness of data compared to conventional methods.
The design of a globally convergent position observer for feature points from visual information is a challenging problem, especially for the case with only inertial measurements and without assumptions of uniform observability, which remained open for a long time. We give a solution to the problem in this paper assuming that only the bearing of a feature point, and biased linear acceleration and rotational velocity of a robot -- all in the body-fixed frame -- are available. Further, in contrast to existing related results, we do not need the value of the gravitational constant either. The proposed approach builds upon the parameter estimation-based observer recently developed in (Ortega et al., Syst. Control Lett., vol.85, 2015) and its extension to matrix Lie groups in our previous work. Conditions on the robot trajectory under which the observer converges are given, and these are strictly weaker than the standard persistency of excitation and uniform complete observability conditions. Finally, as an illustration, we apply the proposed design to the visual inertial navigation problem.
Neural density estimators have proven remarkably powerful in performing efficient simulation-based Bayesian inference in various research domains. In particular, the BayesFlow framework uses a two-step approach to enable amortized parameter estimation in settings where the likelihood function is implicitly defined by a simulation program. But how faithful is such inference when simulations are poor representations of reality? In this paper, we conceptualize the types of model misspecification arising in simulation-based inference and systematically investigate the performance of the BayesFlow framework under these misspecifications. We propose an augmented optimization objective which imposes a probabilistic structure on the latent data space and utilize maximum mean discrepancy (MMD) to detect potentially catastrophic misspecifications during inference undermining the validity of the obtained results. We verify our detection criterion on a number of artificial and realistic misspecifications, ranging from toy conjugate models to complex models of decision making and disease outbreak dynamics applied to real data. Further, we show that posterior inference errors increase as a function of the distance between the true data-generating distribution and the typical set of simulations in the latent summary space. Thus, we demonstrate the dual utility of MMD as a method for detecting model misspecification and as a proxy for verifying the faithfulness of amortized Bayesian inference.
Principal component analysis (PCA) is a popular dimension reduction technique for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for matrix data, which can substantially reduce the number of parameters in PCA while yield satisfactory performance. However, FPCA is based on the Gaussian assumption and thereby susceptible to outliers. Although the multivariate $t$ distribution as a robust modeling tool for vector data has a very long history, its application to matrix data is very limited. The main reason is that the dimension of the vectorized matrix data is often very high and the higher the dimension, the lower the breakdown point that measures the robustness. To solve the robustness problem suffered by FPCA and make it applicable to matrix data, in this paper we propose a robust extension of FPCA (RFPCA), which is built upon a $t$-type distribution called matrix-variate $t$ distribution. Like the multivariate $t$ distribution, the matrix-variate $t$ distribution can adaptively down-weight outliers and yield robust estimates. We develop a fast EM-type algorithm for parameter estimation. Experiments on synthetic and real-world datasets reveal that RFPCA is compared favorably with several related methods and RFPCA is a simple but powerful tool for matrix-valued outlier detection.
Stochastic volatility models have existed in Option pricing theory ever since the crash of 1987 which violated the Black-Scholes model assumption of constant volatility. Heston model is one such stochastic volatility model that is widely used for volatility estimation and option pricing. In this paper, we design a novel method to estimate parameters of Heston model under state-space representation using Bayesian filtering theory and Posterior Cramer-Rao Lower Bound (PCRLB), integrating it with Normal Maximum Likelihood Estimation (NMLE) proposed in [1]. Several Bayesian filters like Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particle Filter (PF) are used for latent state and parameter estimation. We employ a switching strategy proposed in [2] for adaptive state estimation of the non-linear, discrete-time state-space model (SSM) like Heston model. We use a particle filter approximated PCRLB [3] based performance measure to judge the best filter at each time step. We test our proposed framework on pricing data from S&P 500 and NSE Index, estimating the underlying volatility and parameters from the index. Our proposed method is compared with the VIX measure and historical volatility for both the indexes. The results indicate an effective framework for estimating volatility adaptively with changing market dynamics.