Patient-Specific Modeling and Model Predictive Control Approach to Personalized Optimal Anemia Management.

In the condition of anemia, kidneys produce less erythropoietin hormone to stimulate the bone marrow to make red blood cells (RBC) leading to a reduced hemoglobin (Hgb) level, also known as chronic kidney disease (CKD). External recombinant human erythropoietin (EPO) is administrated to maintain a healthy level of Hgb, i.e., 10 - 12 g/dl. The semi-blind robust model identification method is used to obtain a personalized patient model using minimum dose-response data points. The identified patient models are used as predictive models in the model predictive control (MPC) framework. The simulation results of MPC for different CKD patients are compared with those obtained from the existing clinical method, known as anemia management protocol (AMP), used in hospitals. The in-silico results show that MPC outperforms AMP to maintain healthy levels of Hgb without over-or-under- shoots. This offers a considerable performance improvement compared to AMP which is unable to stabilize EPO dosage and shows oscillations in Hgb levels throughout the treatment.Clinical Relevance-This research work provides a framework to help clinicians in decision-making for personalized EPO dose guidance using MPC with semi-blind robust model identification using minimum clinical patient dose-response data.

Convergence Analysis of Online Gradient Method for High-Order Neural Networks and Their Sparse Optimization.

In this article, we investigate the boundedness and convergence of the online gradient method with the smoothing group L1/2 regularization for the sigma-pi-sigma neural network (SPSNN). This enhances the sparseness of the network and improves its generalization ability. For the original group L1/2 regularization, the error function is nonconvex and nonsmooth, which can cause oscillation of the error function. To ameliorate this drawback, we propose a simple and effective smoothing technique, which can effectively eliminate the deficiency of the original group L1/2 regularization. The group L1/2 regularization effectively optimizes the network structure from two aspects redundant hidden nodes tending to zero and redundant weights of surviving hidden nodes in the network tending to zero. This article shows the strong and weak convergence results for the proposed method and proves the boundedness of weights. Experiment results clearly demonstrate the capability of the proposed method and the effectiveness of redundancy control. The simulation results are observed to support the theoretical results.

Control-Relevant Adaptive Personalized Modeling From Limited Clinical Data for Precise Warfarin Management.

Warfarin is a challenging drug to administer due to the narrow therapeutic index of the International Normalized Ratio (INR), the inter- and intra-variability of patients, limited clinical data, genetics, and the effects of other medications. Goal: To predict the optimal warfarin dosage in the presence of the aforementioned challenges, we present an adaptive individualized modeling framework based on model (In)validation and semi-blind robust system identification. The model (In)validation technique adapts the identified individualized patient model according to the change in the patient's status to ensure the model's suitability for prediction and controller design. Results: To implement the proposed adaptive modeling framework, the clinical data of warfarin-INR of forty-four patients has been collected at the Robley Rex Veterans Administration Medical Center, Louisville. The proposed algorithm is compared with recursive ARX and ARMAX model identification methods. The results of identified models using one-step-ahead prediction and minimum mean squared analysis (MMSE) show that the proposed framework effectively predicts the warfarin dosage to keep the INR values within the desired range and adapt the individualized patient model to exhibit the true status of the patient throughout treatment. Conclusion: This paper proposes an adaptive personalized patient modeling framework from limited patientspecific clinical data. It is shown by rigorous simulations that the proposed framework can accurately predict a patient's doseresponse characteristics and it can alert the clinician whenever identified models are no longer suitable for prediction and adapt the model to the current status of the patient to reduce the prediction error.

Analysis of Equilibria for a Class of Recurrent Neural Networks With Two Subnetworks.

This article is concerned with the problem of the number and dynamical properties of equilibria for a class of connected recurrent networks with two switching subnetworks. In this network model, parameters serve as switches that allow two subnetworks to be turned ON or OFF among different dynamic states. The two subnetworks are described by a nonlinear coupled equation with a complicated relation among network parameters. Thus, the number and dynamical properties of equilibria have been very hard to investigate. By using Sturm's theorem, together with the geometrical properties of the network equation, we give a complete analysis of equilibria, including the existence, number, and dynamical properties. Necessary and sufficient conditions for the existence and exact number of equilibria are established. Moreover, the dynamical property of each equilibrium point is discussed without prior assumption of their locations. Finally, simulation examples are given to illustrate the theoretical results in this article.

Adaptive Individualized Drug-Dose Response Modeling from a Limited Clinical Data: Case of Warfarin Management.

Administration of drugs requires sophisticated methods to determine the drug quantity for optimal results, and it has been a challenging task for the number of diseases. To solve these challenges, in this paper, we present the semi-blind robust model identification technique to find individualized patient models using the minimum number of clinically acquired patient-specific data to determine optimal drug dosage. To ensure the usability of these models for dosage predictability and controller design, the model (In)validation technique is also investigated. As a case study, the patients treated with warfarin are studied to demonstrate the semi-blind robust identification and model (In)validation techniques. The performance of models is assessed by calculating minimum means squared error (MMSE).Clinical Relevance- This work establishes a general framework for adaptive individualized drug-dose response models from a limited number of clinical patient-specific data. This work will help clinicians in decision-making for improved drug dosing, patient care, and limiting patient exposure to agents with a narrow therapeutic range.

Precise Warfarin Management through Personalized Modeling and Control with Limited Clinical Data.

Warfarin belongs to a medication class called anticoagulants or blood thinners. It is used for the treatment to prevent blood clots from forming or growing larger. Patients with venous thrombosis, pulmonary embolism, or who have suffered a heart attack, have an irregular heartbeat, or prosthetic heart valves are prescribed with warfarin. It is challenging to find optimal doses due to inter-patient and intra-patient variabilities and narrow therapeutic index. This work presents an individualized warfarin dosing method by utilizing the individual patient model generated using limited clinical data of the patients with chronic conditions under warfarin anticoagulation treatment. Then, the individual precise warfarin dosing is formalized as an optimal control problem, which is solved using the DORBF control approach. The efficiency of the proposed approach is compared with results obtained from practiced clinical protocol.

Redundant feature pruning for accelerated inference in deep neural networks.

This paper presents an efficient technique to reduce the inference cost of deep and/or wide convolutional neural network models by pruning redundant features (or filters). Previous studies have shown that over-sized deep neural network models tend to produce a lot of redundant features that are either shifted version of one another or are very similar and show little or no variations, thus resulting in filtering redundancy. We propose to prune these redundant features along with their related feature maps according to their relative cosine distances in the feature space, thus leading to smaller networks with reduced post-training inference computational costs and competitive performance. We empirically show on select models (VGG-16, ResNet-56, ResNet-110, and ResNet-34) and dataset (MNIST Handwritten digits, CIFAR-10, and ImageNet) that inference costs (in FLOPS) can be significantly reduced while overall performance is still competitive with the state-of-the-art.

Regularizing Deep Neural Networks by Enhancing Diversity in Feature Extraction.

This paper proposes a new and efficient technique to regularize the neural network in the context of deep learning using correlations among features. Previous studies have shown that oversized deep neural network models tend to produce a lot of redundant features that are either the shifted version of one another or are very similar and show little or no variations, thus resulting in redundant filtering. We propose a way to address this problem and show that such redundancy can be avoided using regularization and adaptive feature dropout mechanism. We show that regularizing both negative and positive correlated features according to their differentiation and based on their relative cosine distances yields network extracting dissimilar features with less overfitting and better generalization. This concept is illustrated with deep multilayer perceptron, convolutional neural network, sparse autoencoder, gated recurrent unit, and long short-term memory on MNIST digits recognition, CIFAR-10, ImageNet, and Stanford Natural Language Inference data sets.

The convergence analysis of SpikeProp algorithm with smoothing L1∕2 regularization.

Unlike the first and the second generation artificial neural networks, spiking neural networks (SNNs) model the human brain by incorporating not only synaptic state but also a temporal component into their operating model. However, their intrinsic properties require expensive computation during training. This paper presents a novel algorithm to SpikeProp for SNN by introducing smoothing L1∕2 regularization term into the error function. This algorithm makes the network structure sparse, with some smaller weights that can be eventually removed. Meanwhile, the convergence of this algorithm is proved under some reasonable conditions. The proposed algorithms have been tested for the convergence speed, the convergence rate and the generalization on the classical XOR-problem, Iris problem and Wisconsin Breast Cancer classification.

Deep Learning of Constrained Autoencoders for Enhanced Understanding of Data.

Unsupervised feature extractors are known to perform an efficient and discriminative representation of data. Insight into the mappings they perform and human ability to understand them, however, remain very limited. This is especially prominent when multilayer deep learning architectures are used. This paper demonstrates how to remove these bottlenecks within the architecture of non-negativity constrained autoencoder. It is shown that using both L1 and L2 regularizations that induce non-negativity of weights, most of the weights in the network become constrained to be non-negative, thereby resulting into a more understandable structure with minute deterioration in classification accuracy. Also, this proposed approach extracts features that are more sparse and produces additional output layer sparsification. The method is analyzed for accuracy and feature interpretation on the MNIST data, the NORB normalized uniform object data, and the Reuters text categorization data set.

A Novel Pruning Algorithm for Smoothing Feedforward Neural Networks Based on Group Lasso Method.

In this paper, we propose four new variants of the backpropagation algorithm to improve the generalization ability for feedforward neural networks. The basic idea of these methods stems from the Group Lasso concept which deals with the variable selection problem at the group level. There are two main drawbacks when the Group Lasso penalty has been directly employed during network training. They are numerical oscillations and theoretical challenges in computing the gradients at the origin. To overcome these obstacles, smoothing functions have then been introduced by approximating the Group Lasso penalty. Numerical experiments for classification and regression problems demonstrate that the proposed algorithms perform better than the other three classical penalization methods, Weight Decay, Weight Elimination, and Approximate Smoother, on both generalization and pruning efficiency. In addition, detailed simulations based on a specific data set have been performed to compare with some other common pruning strategies, which verify the advantages of the proposed algorithm. The pruning abilities of the proposed strategy have been investigated in detail for a relatively large data set, MNIST, in terms of various smoothing approximation cases.

Individualized drug dosing using RBF-Galerkin method: Case of anemia management in chronic kidney disease.

BACKGROUND AND OBJECTIVE: Anemia is a common comorbidity in patients with chronic kidney disease (CKD) and is frequently associated with decreased physical component of quality of life, as well as adverse cardiovascular events. Current treatment methods for renal anemia are mostly population-based approaches treating individual patients with a one-size-fits-all model. However, FDA recommendations stipulate individualized anemia treatment with precise control of the hemoglobin concentration and minimal drug utilization. In accordance with these recommendations, this work presents an individualized drug dosing approach to anemia management by leveraging the theory of optimal control. METHODS: A Multiple Receding Horizon Control (MRHC) approach based on the RBF-Galerkin optimization method is proposed for individualized anemia management in CKD patients. Recently developed by the authors, the RBF-Galerkin method uses the radial basis function approximation along with the Galerkin error projection to solve constrained optimal control problems numerically. The proposed approach is applied to generate optimal dosing recommendations for individual patients. RESULTS: Performance of the proposed approach (MRHC) is compared in silico to that of a population-based anemia management protocol and an individualized multiple model predictive control method for two case scenarios: hemoglobin measurement with and without observational errors. In silico comparison indicates that hemoglobin concentration with MRHC method has less variation among the methods, especially in presence of measurement errors. In addition, the average achieved hemoglobin level from the MRHC is significantly closer to the target hemoglobin than that of the other two methods, according to the analysis of variance (ANOVA) statistical test. Furthermore, drug dosages recommended by the MRHC are more stable and accurate and reach the steady-state value notably faster than those generated by the other two methods. CONCLUSIONS: The proposed method is highly efficient for the control of hemoglobin level, yet provides accurate dosage adjustments in the treatment of CKD anemia.

Nonredundant sparse feature extraction using autoencoders with receptive fields clustering.

This paper proposes new techniques for data representation in the context of deep learning using agglomerative clustering. Existing autoencoder-based data representation techniques tend to produce a number of encoding and decoding receptive fields of layered autoencoders that are duplicative, thereby leading to extraction of similar features, thus resulting in filtering redundancy. We propose a way to address this problem and show that such redundancy can be eliminated. This yields smaller networks and produces unique receptive fields that extract distinct features. It is also shown that autoencoders with nonnegativity constraints on weights are capable of extracting fewer redundant features than conventional sparse autoencoders. The concept is illustrated using conventional sparse autoencoder and nonnegativity-constrained autoencoders with MNIST digits recognition, NORB normalized-uniform object data and Yale face dataset.

Boundedness and convergence analysis of weight elimination for cyclic training of neural networks.

Weight elimination offers a simple and efficient improvement of training algorithm of feedforward neural networks. It is a general regularization technique in terms of the flexible scaling parameters. Actually, the weight elimination technique also contains the weight decay regularization for a large scaling parameter. Many applications of this technique and its improvements have been reported. However, there is little research concentrated on its convergence behavior. In this paper, we theoretically analyze the weight elimination for cyclic learning method and determine the conditions for the uniform boundedness of weight sequence, and weak and strong convergence. Based on the assumed network parameters, the optimal choice for the scaling parameter can also be determined. Moreover, two illustrative simulations have been done to support the theoretical explorations as well.

Convergence of batch gradient learning with smoothing regularization and adaptive momentum for neural networks.

This paper presents new theoretical results on the backpropagation algorithm with smoothing [Formula: see text] regularization and adaptive momentum for feedforward neural networks with a single hidden layer, i.e., we show that the gradient of error function goes to zero and the weight sequence goes to a fixed point as n (n is iteration steps) tends to infinity, respectively. Also, our results are more general since we do not require the error function to be quadratic or uniformly convex, and neuronal activation functions are relaxed. Moreover, compared with existed algorithms, our novel algorithm can get more sparse network structure, namely it forces weights to become smaller during the training and can eventually removed after the training, which means that it can simply the network structure and lower operation time. Finally, two numerical experiments are presented to show the characteristics of the main results in detail.

Deep Learning of Part-Based Representation of Data Using Sparse Autoencoders With Nonnegativity Constraints.

We demonstrate a new deep learning autoencoder network, trained by a nonnegativity constraint algorithm (nonnegativity-constrained autoencoder), that learns features that show part-based representation of data. The learning algorithm is based on constraining negative weights. The performance of the algorithm is assessed based on decomposing data into parts and its prediction performance is tested on three standard image data sets and one text data set. The results indicate that the nonnegativity constraint forces the autoencoder to learn features that amount to a part-based representation of data, while improving sparsity and reconstruction quality in comparison with the traditional sparse autoencoder and nonnegative matrix factorization. It is also shown that this newly acquired representation improves the prediction performance of a deep neural network.

Infant Brain Extraction in T1-Weighted MR Images Using BET and Refinement Using LCDG and MGRF Models.

In this paper, we propose a novel framework for the automated extraction of the brain from T1-weighted MR images. The proposed approach is primarily based on the integration of a stochastic model [a two-level Markov-Gibbs random field (MGRF)] that serves to learn the visual appearance of the brain texture, and a geometric model (the brain isosurfaces) that preserves the brain geometry during the extraction process. The proposed framework consists of three main steps: 1) Following bias correction of the brain, a new three-dimensional (3-D) MGRF having a 26-pairwise interaction model is applied to enhance the homogeneity of MR images and preserve the 3-D edges between different brain tissues. 2) The nonbrain tissue found in the MR images is initially removed using the brain extraction tool (BET), and then the brain is parceled to nested isosurfaces using a fast marching level set method. 3) Finally, a classification step is applied in order to accurately remove the remaining parts of the skull without distorting the brain geometry. The classification of each voxel found on the isosurfaces is made based on the first- and second-order visual appearance features. The first-order visual appearance is estimated using a linear combination of discrete Gaussians (LCDG) to model the intensity distribution of the brain signals. The second-order visual appearance is constructed using an MGRF model with analytically estimated parameters. The fusion of the LCDG and MGRF, along with their analytical estimation, allows the approach to be fast and accurate for use in clinical applications. The proposed approach was tested on in vivo data using 300 infant 3-D MR brain scans, which were qualitatively validated by an MR expert. In addition, it was quantitatively validated using 30 datasets based on three metrics: the Dice coefficient, the 95% modified Hausdorff distance, and absolute brain volume difference. Results showed the capability of the proposed approach, outperforming four widely used BETs: BET, BET2, brain surface extractor, and infant brain extraction and analysis toolbox. Experiments conducted also proved that the proposed framework can be generalized to adult brain extraction as well.

3-D Lung Segmentation by Incremental Constrained Nonnegative Matrix Factorization.

Accurate lung segmentation from large-size 3-D chest-computed tomography images is crucial for computer-assisted cancer diagnostics. To efficiently segment a 3-D lung, we extract voxel-wise features of spatial image contexts by unsupervised learning with a proposed incremental constrained nonnegative matrix factorization (ICNMF). The method applies smoothness constraints to learn the features, which are more robust to lung tissue inhomogeneities, and thus, help to better segment internal lung pathologies than the known state-of-the-art techniques. Compared to the latter, the ICNMF depends less on the domain expert knowledge and is more easily tuned due to only a few control parameters. Also, the proposed slice-wise incremental learning with due regard for interslice signal dependencies decreases the computational complexity of the NMF-based segmentation and is scalable to very large 3-D lung images. The method is quantitatively validated on simulated realistic lung phantoms that mimic different lung pathologies (seven datasets), in vivo datasets for 17 subjects, and 55 datasets from the Lobe and Lung Analysis 2011 (LOLA11) study. For the in vivo data, the accuracy of our segmentation w.r.t. the ground truth is 0.96 by the Dice similarity coefficient, 9.0 mm by the modified Hausdorff distance, and 0.87% by the absolute lung volume difference, which is significantly better than for the NMF-based segmentation. In spite of not being designed for lungs with severe pathologies and of no agreement between radiologists on the ground truth in such cases, the ICNMF with its total accuracy of 0.965 was ranked fifth among all others in the LOLA11. After excluding the nine too pathological cases from the LOLA11 dataset, the ICNMF accuracy increased to 0.986.

Self-organizing neural networks integrating domain knowledge and reinforcement learning.

The use of domain knowledge in learning systems is expected to improve learning efficiency and reduce model complexity. However, due to the incompatibility with knowledge structure of the learning systems and real-time exploratory nature of reinforcement learning (RL), domain knowledge cannot be inserted directly. In this paper, we show how self-organizing neural networks designed for online and incremental adaptation can integrate domain knowledge and RL. Specifically, symbol-based domain knowledge is translated into numeric patterns before inserting into the self-organizing neural networks. To ensure effective use of domain knowledge, we present an analysis of how the inserted knowledge is used by the self-organizing neural networks during RL. To this end, we propose a vigilance adaptation and greedy exploitation strategy to maximize exploitation of the inserted domain knowledge while retaining the plasticity of learning and using new knowledge. Our experimental results based on the pursuit-evasion and minefield navigation problem domains show that such self-organizing neural network can make effective use of domain knowledge to improve learning efficiency and reduce model complexity.

Individualized model discovery: the case of anemia patients.

The universal sequel to chronic kidney condition (CKD) is anemia. Patients of anemia have kidneys that are incapable of performing certain basic functions such as sensing of oxygen levels to secrete erythropoietin when red blood cell counts are low. Under such conditions, external administration of human recombinant erythropoietin (EPO) is administered as alternative to improve conditions of CKD patients by increasing their hemoglobin (Hb) levels to a given therapeutic range. Presently, EPO dosing strategies extensively depend on packet inserts and on "average" responses to the medication from previous patients. Clearly dosage strategies based on these approaches are, at best, nonoptimal to EPO medication and potentially dangerous to patients that do not adhere to the notion of expected "average" response. In this work, a technique called semi-blind robust identification is provided to uniquely identify models of the individual patients of anemia based on their actual Hb responses and EPO administration. Using the a priori information and the measured input-output data of the individual patients, the procedure identifies a unique model consisting of a nominal model and the associated model uncertainty for the patients. By incorporating the effects of unknown system initial conditions, considerably small measurement samples can be used in the modeling process.