With a view towards artificial cells, molecular communication systems, molecular multiagent systems and federated learning, we propose a novel reaction network scheme (termed the Baum-Welch (BW) ...reaction network) that learns parameters for hidden Markov models (HMMs). All variables including inputs and outputs are encoded by separate species. Each reaction in the scheme changes only one molecule of one species to one molecule of another. The reverse change is also accessible but via a different set of enzymes, in a design reminiscent of futile cycles in biochemical pathways. We show that every positive fixed point of the BW algorithm for HMMs is a fixed point of the reaction network scheme, and vice versa. Furthermore, we prove that the 'expectation' step and the 'maximization' step of the reaction network separately converge exponentially fast and compute the same values as the E-step and the M-step of the BW algorithm. We simulate example sequences, and show that our reaction network learns the same parameters for the HMM as the BW algorithm, and that the log-likelihood increases continuously along the trajectory of the reaction network.
Community detection and network reconstruction are two major concerns in network analysis. However, these two tasks are extremely challenging since most of the existing methods are not suitable for ...noisy and red time-evolving data, which are common in real world situations. To cope with this, we propose a novel method called the group-based binary time-evolving mixture (GBTM) model to detect communities and recover network structures jointly. This is the first to study address the challenges of community detection and network reconstruction in scenarios where data are dynamic and cannot be directly observed. In this work, the hidden Markov method is employed to capture the temporal evolution of node connections. In addition, we develop the grouped Baum-Welch algorithm for parameter estimation using a forward-backward procedure. Our GBTM model shows that conducting community detection and network reconstruction simultaneously can yield synergistic benefits. Furthermore, we introduce an innovative Bayesian information criterion (BIC) for determining the number of communities. The results of various simulations under different settings and two real-world networks show that the proposed GBTM model outperforms the existing community detection or network reconstruction methods and has great potential for solving time-evolving and noisy network problems.
The maximum likelihood problem for Hidden Markov Models is usually numerically solved by the Baum-Welch algorithm, which uses the Expectation-Maximization algorithm to find the estimates of the ...parameters. This algorithm has a recursion depth equal to the data sample size and cannot be computed in parallel, which limits the use of modern GPUs to speed up computation time. A new algorithm is proposed that provides the same estimates as the Baum-Welch algorithm, requiring about the same number of iterations, but is designed in such a way that it can be parallelized. As a consequence, it leads to a significant reduction in the computation time. This reduction is illustrated by means of numerical examples, where we consider simulated data as well as real datasets.
Nowadays, radio- or Internet-based communication is gaining popularity in various fields, e.g., in signal processing. As these are not reliable real-time communications, some of the data are lost ...during the transmission. There are several stochastic models allowing the analysis of this phenomenon. The spectral properties of these models result in specific distortion in the signals' spectra. As the spectrum of the signal can easily be calculated via the fast Fourier transform (FFT), FFT-based identification methods of the data loss can be developed. In this article, a new identification method is proposed for the simpler cases of the Gilbert-Elliott model class. The article summarizes the mathematical description of data loss and introduces the Gilbert-Elliott model family. The novelty of the article is the identification method that is based on the autocorrelation function of the Gilbert-Elliott model. The proposed method is compared with classical procedures based on the Baum-Welch algorithm and the novel ones based on global optimization. The theoretical results are supported by extensive simulations.
The development and applications of artificial intelligence (AI) have brought unprecedented opportunities to humans, but also brought many challenges and concerns such as unfairness, immorality, ...distrust, illegality, and discrimination. Responsible AI provides a new solution to effectively address these AI potential threats by integrating social/physical rules into AI systems. However, these rules are high-level regulations and ethical principles, which are difficult to be formalized. To this end, we attempt to use the data generated in various AI systems such as cyber-physical-social systems (CPSS) to discover and reflect these rules to provide more responsible services for humans. In this article, we first propose a data-driven responsible CPSS framework. Its core idea is to mine valuable rules through perception, fusion, processing, and analysis of CPSS data, and then use these rules to adaptively optimize CPSS. Based on this framework, three tensor-based couple hidden Markov models (T-CHMMs) are constructed to integrate three responsible features (i.e., timing, periodicity, and correlation) for mining potential and valuable rules. Then, the corresponding tensor-based Baum-Welch (TBW) algorithms are designed to solve their learning problems. Finally, the predictive accuracy and computational efficiency of the proposed models and algorithms are verified on three open datasets. The experimental results show that proposed methods have the best performances for various scenarios, which reflects that our methods are more promising and responsible than existing methods.
Hidden Markov models are widely used to model the probabilistic structures with latent variables. The main assumption of hidden Markov models is that; observation symbols are conditionally ...independent and identically distributed random variables. There exist some cases where this assumption may not be valid in practice. That is, an observation symbol that occurs in the current state may depend on the previous observation symbol that occurred in the previous state. In this study, a new type of hidden Markov model is introduced in which the current pair of hidden state-emitted observation symbol and the previous pair of those have a first-order Markov dependency. The proposed model is capable of capturing a possible first-order Markov dependency between the last and the previous steps of the system. In addition, it provides a better representation for the appropriate real-life problems where, if the observation symbols have conditional dependence. It is an alternative model to the classical hidden Markov model for revealing the Markov dependency between the current and the previous binary information of the system. An experimental study is conducted to show the performance of the proposed model compared to the classical hidden Markov model. Besides, two different case studies are conducted namely the occurrences of strong earthquakes and daily stock prices are modeled with both the classical hidden Markov model and the proposed model, and the results are compared.
•A binary-dependent HMM which uses more information from the past is proposed.•The distribution of the current information depends on the previous information.•Baum–Welch and Viterbi algorithms are modified based on the assumptions.•The dependence between the current and the previous information can be revealed.•Two case studies are presented to support the justification of the model.
Hidden Markov Models (HMM) are used in a wide range of artifificial intelligence applications including speech recognition, computer vision, computational biology and fifinance. Estimating an HMM ...parameters is often addressed via the Baum-Welch algorithm (BWA), but this algorithm tends to convergence to local optimum of the model parameters. Therefore, optimizing HMM parameters remains a crucial and challenging work. In this paper, a Variable Neighborhood Search (VNS) combined with Baum-Welch algorithm (VNS-BWA) is proposed. The idea is to use VNS to escape from local minima, enable greater exploration of the search space, and enhance the learning capability of HMMs models. The proposed algorithm has entire advantage of combination of the search mechanism in VNS algorithm for training with no gradient information, and the BWA algorithm that utilizes this kind of knowledge. The performance of the proposed method is validated on a real dataset. The results show that the VNS-BWA has better performance fifinding the optimal parameters of HMM models, enhancing its learning capability and classifification performance.
We develop and implement a method for maximum likelihood estimation of a regime-switching stochastic volatility model. Our model uses a continuous time stochastic process for the stock dynamics with ...the instantaneous variance driven by a Cox-Ingersoll-Ross process and each parameter modulated by a hidden Markov chain. We propose an extension of the EM algorithm through the Baum-Welch implementation to estimate our model and filter the hidden state of the Markov chain while using the VIX index to invert the latent volatility state. Using Monte Carlo simulations, we test the convergence of our algorithm and compare it with an approximate likelihood procedure where the volatility state is replaced by the VIX index. We found that our method is more accurate than the approximate procedure. Then, we apply Fourier methods to derive a semi-analytical expression of S&P500 and VIX option prices, which we calibrate to market data. We show that the model is sufficiently rich to encapsulate important features of the joint dynamics of the stock and the volatility and to consistently fit option market prices.
We focus on the detection of sporadic low-power acoustic/seismic signals of unknown structure and statistics, such as the detection of sound produced by marine mammals, low-power underground signals, ...or the discovery of events such as volcano eruptions. In these cases, since the ambient noise may be fast time varying and may include many noise transients, threshold-based detection may lead to a significant false alarm rate. Instead, we propose a detection scheme that avoids the use of a decision threshold. Our method is based on clustering the samples of the observed buffer according to a binary hidden Markov model to discriminate between "noise" and "signal" states. Our detector is a modification of the Baum-Welch algorithm that takes into account the expected continuity of the desired signal and obtains a robust detection using the complex but flexible general Gaussian mixture model. The result is a combination of a constrained expectation-maximization algorithm with the Viterbi algorithm. We evaluate the performance of our scheme in numerical simulations, in a seimic test, and in an ocean experiment. The results are close to the hybrid Cramér-Rao lower bound and show that, at the cost of some additional complexity, our proposed algorithm outperforms common benchmark methods in terms of detection and false alarm rates, and also achieves a better accuracy of the time of detection. To allow reproducibility of the results, we publish our code.
Brain signals are nonlinear and nonstationary time series, which provide information about spatiotemporal patterns of electrical activity in the brain. CHMMs are suitable tools for modeling ...multi-channel time-series dependent on both time and space, but state-space parameters grow exponentially with the number of channels. To cope with this limitation, we consider the influence model as the interaction of hidden Markov chains called Latent Structure Influence Models (LSIMs). LSIMs are capable of detecting nonlinearity and nonstationarity, making them well suited for multi-channel brain signals. We apply LSIMs to capture the spatial and temporal dynamics in multi-channel EEG/ECoG signals. The current manuscript extends the scope of the re-estimation algorithm from HMMs to LSIMs. We prove that the re-estimation algorithm of LSIMs will converge to stationary points corresponding to Kullback-Leibler divergence. We prove convergence by developing a new auxiliary function using the influence model and a mixture of strictly log-concave or elliptically symmetric densities. The theories that support this proof are derived from previous studies by Baum, Liporace, Dempster, and Juang. We then develop a closed-form expression for re-estimation formulas using tractable marginal forward-backward parameters defined in our previous study. Simulated datasets and EEG/ECoG recordings confirm the practical convergence of the derived re-estimation formulas. We also study the use of LSIMs for modeling and classification on simulated and real EEG/ECoG datasets. Based on AIC and BIC, LSIMs perform better than HMMs and CHMMs in modeling embedded Lorenz systems and ECoG recordings. LSIMs are more reliable and better classifiers than HMMs, SVMs and CHMMs in 2-class simulated CHMMs. EEG biometric verification results indicate that the LSIM-based method improves the area under curve (AUC) values by about 6.8% and decreases the standard deviation of AUC values from 5.4% to 3.3% compared to the existing HMM-based method for all conditions on the BED dataset.
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