Academic literature on the topic 'Non-stationary continuous time Bayesian networks'

Non-stationary continuous time Bayesian networks are introduced. They allow the parents set of each node to change over continuous time. Three settings are developed for learning non-stationary continuous time Bayesian networks from data: known transition times, known number of epochs and unknown number of epochs. A score function for each setting is derived and the corresponding learning algorithm is developed. A set of numerical experiments on synthetic data is used to compare the effectiveness of non-stationary continuous time Bayesian networks to that of non-stationary dynamic Bayesian networks. Furthermore, the performance achieved by non-stationary continuous time Bayesian networks is compared to that achieved by state-of-the-art algorithms on four real-world datasets, namely drosophila, saccharomyces cerevisiae, songbird and macroeconomics.

A key requirement facing organisms acting in uncertain dynamic environments is the real-time estimation and prediction of environmental states, based on which effective actions can be selected. While it is becoming evident that organisms employ exact or approximate Bayesian statistical calculations for these purposes, it is far less clear how these putative computations are implemented by neural networks in a strictly dynamic setting. In this work, we make use of rigorous mathematical results from the theory of continuous time point process filtering and show how optimal real-time state estimation and prediction may be implemented in a general setting using simple recurrent neural networks. The framework is applicable to many situations of common interest, including noisy observations, non-Poisson spike trains (incorporating adaptation), multisensory integration, and state prediction. The optimal network properties are shown to relate to the statistical structure of the environment, and the benefits of adaptation are studied and explicitly demonstrated. Finally, we recover several existing results as appropriate limits of our general setting.

Body-rocking is an undesired stereotypical motor movement performed by some individuals, and its detection is essential for self-awareness and habit change. We envision a pipeline that includes inertial wearable sensors and a real-time detection system for notifying the user so that they are aware of their body-rocking behavior. For this task, similarities of body rocking to other non-related repetitive activities may cause false detections which prevent continuous engagement, leading to alarm fatigue. We present a pipeline using Bayesian Neural Networks with uncertainty quantification for jointly reducing false positives and providing accurate detection. We show that increasing model capacity does not consistently yield higher performance by itself, while pairing it with the Bayesian approach does yield significant improvements. Disparities in uncertainty quantification are better quantified by calibrating them using deep neural networks. We show that the calibrated probabilities are effective quality indicators of reliable predictions. Altogether, we show that our approach provides additional insights on the role of Bayesian techniques in deep learning as well as aids in accurate body-rocking detection, improving our prior work on this subject.

This paper investigates the short-term wind farm generation forecast. It is observed from the real wind farm generation measurements that wind farm generation exhibits distinct features, such as the non-stationarity and the heterogeneous dynamics of ramp and non-ramp events across different classes of wind turbines. To account for the distinct features of wind farm generation, we propose a Drifting Streaming Peaks-over-Threshold (DSPOT)-enhanced self-evolving neural networks-based short-term wind farm generation forecast. Using DSPOT, the proposed method first classifies the wind farm generation data into ramp and non-ramp datasets, where time-varying dynamics are taken into account by utilizing dynamic ramp thresholds to separate the ramp and non-ramp events. We then train different neural networks based on each dataset to learn the different dynamics of wind farm generation by the NeuroEvolution of Augmenting Topologies (NEAT), which can obtain the best network topology and weighting parameters. As the efficacy of the neural networks relies on the quality of the training datasets (i.e., the classification accuracy of the ramp and non-ramp events), a Bayesian optimization-based approach is developed to optimize the parameters of DSPOT to enhance the quality of the training datasets and the corresponding performance of the neural networks. Based on the developed self-evolving neural networks, both distributional and point forecasts are developed. The experimental results show that compared with other forecast approaches, the proposed forecast approach can substantially improve the forecast accuracy, especially for ramp events. The experiment results indicate that the accuracy improvement in a 60 min horizon forecast in terms of the mean absolute error (MAE) is at least 33.6% for the whole year data and at least 37% for the ramp events. Moreover, the distributional forecast in terms of the continuous rank probability score (CRPS) is improved by at least 35.8% for the whole year data and at least 35.2% for the ramp events.

Artificial intelligence methods and technologies are increasingly included in human's everyday life. Managing actors in the context of their activities, from the planning stage to the decision-making stage, are faced with the need to operate with big data, non-linear, exponentially growing, critically overloaded data scenarios. In these conditions, the need to introduce artificial intelligence technologies is due to the exhaustion of the intellectual and analytical capabilities of a person. The article discusses a variety of methods and approaches of artificial intelligence, examines the content of key algorithms, models and theories, their strengths and weaknesses in such important areas of the economy as planning and decision-making. The focus is on their classification. Due to the dependence of the planning process on environmental factors, both classical and non-classical planning environments are discussed. If the environment is fully observable, deterministic and static (external changes are ignored) and discrete in terms of time and action, then we are dealing with a classical planning environment. In the case of a partially observable or stochastic environment, we get a non-classical planning environment. The simplest and most intuitive approach to the planning process algorithms is a Total Order Planning. A scheduling algorithm with parallel execution of actions or without specifying the sequence of their execution is a Partial Order Planning algorithm. Recent research into the development of efficient algorithms has sparked interest in one of the earliest planning approaches – Prepositional Logic Planning. With the Critical Path Method, a schedule of activities is drawn up as part of a plan with zero critical travel time margin for each activity, taking into account the calculation of the time margin for each activity and sequence of activities. A forward-looking planning method for solving complex problems is a hierarchical decomposition based on a Hierarchical Task Networks. The influence of time and resource factors on planning procedures is separately highlighted. Approaches and methods used in a non-classical planning environment: compatible planning, conditional planning, continuous planning, multi-agent planning. Special attention is paid to the issues of constructing planning models in conditions of uncertainty based on the theoretical-probabilistic (stochastic) approaches. Bayesian networks are used to represent vagueness. The Relational Probability Model includes certain constraints on the presentation means, thereby guaranteeing a fully defined probability distributions. The main tasks of probabilistic representation in temporal models are: filtering, forecasting, smoothing, determining a probabilistic explanation. By combining these algorithms and additional enhancements, three large blocks of temporal models can be obtained: Hidden Markov Models, Kalman Filter, and Dynamic Bayesian Network. Decision theory allows the agent to determine the sequence of actions to be performed. A simpler formal system for solving decision-making problems is decision-making networks. The use of expert systems containing information about utility creates additional opportunities. Sequential multiple decision problems in an uncertain environment, such as Markov Decision Processes, are defined using transition models. When several agents interact simultaneously, game theory is used to describe the rational behavior of agents. As we can see, planning has recently become one of the most interesting and relevant directions in the field of artificial intelligence research. There is still a long way to go: it is necessary to develop a clear vision of the problem of choosing the appropriate specific methods depending on the type of task, perhaps by creating completely new methods and approaches.

B-cell receptor (BCR) signalling is central for the pathomechanism of chronic lymphocytic leukemia (CLL). Novel inhibitors of BCR signalling have recently substantially improved treatment of CLL, and a better characterization of the molecular circuitry of leukemic BCR signalling will allow a more refined targeting of this Achilles heel. In order to model malignant and non-malignant BCR signalling, we quantified after stimulation 5 components of BCR signaling (ZAP70/SYK, BTK, PLCy2, AKT, ERK1/2) in single cells from primary human leukemic and non-malignant tissue via phospho-specific flow cytometry over 6 time points. We stimulated cells from 11 patients and non-malignant CD19 negative enriched B-cells from 5 healthy donors by crosslinking the BCR with anti-IgM and/or anti-CD19 and synchronous inhibition of phosphatases with H2O2. As expected, we found more phosphorylation of all BCR signalling components after stimulation in malignant vs non-malignant cells and in IGHV non-mutated CLL cells compared to IGHV mutated CLL cells. Intriguingly, inhibition of phosphatases with H2O2 led to higher phosphorylation of BCR components in CLL cells with mutated IGHV genes compared to CLL cells with non-mutated IGHV genes, suggesting a stronger dampening of signalling activity in mutated IGHV CLL by phosphatases. In order to characterize the signalling circuitry, we modelled the connectivity of the cascade components by correlating signal intensities across single cells of the cell populations of single samples (Figure 1). Surprisingly, upon stimulation no substantial differences in network topology were observed between malignant and non-malignant cells. To additionally test for changes in network topology, we challenged the BCR signaling cascade with inhibitors for BTK (ibrutinib), PI3K (idelalisib). Ibrutinib and idelalisib acted complementary, but not synergistic, and were similarly effective in IGHV mutated and non-mutated CLL. Effects of idelalisib were the same on malignant and non-malignant cells, whereas ibrutinib was mostly active on CLL cells, not on non-malignant B-cells. Upon stimulation with combinations of IgM and CD19 crosslinking augmented with H2O2, phosphorylation of PLCy2 could not be significantly inhibited by idelalisib or ibrutinib on a timescale of 28mins. We therefore aimed to identify central activating nodes of the BCR signalling cascade using targeted inhibitors. In fact, we found that inhibition of LYN with dasatinib and inhibition of SYK with entospletinib could substantially reduce phosphorylation of PLCy2, BTK and ERK but not AKT after all combinations of BCR stimulation. This suggests additional signalling cascades modulating AKT and a strong impact of SYK/LYN activity on the regulation of PLCy2. In summary, our findings underline the importance of single cell analysis of the dynamic circuitry of B-cell receptor signalling to understand development of resistance mechanisms and potential vulnerabilities. Figure 1: Workflow scheme of the Bayesian network learning and averaging approach. After discretizing the continuous single cell data, an optimal network is derived from each of R bootstrap samples. The Bayesian network learning strategy uses the BDe scoring function and a greedy hill-climbing algorithm to find the network model that represents the resampled data best. An average arc strength for each connection between nodes is derived from the number of occurrences of the respective connection in the set of R best scoring networks. Further averaging among networks derived from different data sets was applied for identifying conditional, temporal, and group-specific differences. Figure 1 Disclosures Döhner: Novartis: Consultancy, Honoraria, Research Funding; Astex: Consultancy, Honoraria; Bristol Myers Swuibb: Research Funding; Amgen: Consultancy, Honoraria, Research Funding; Arog: Research Funding; Seattle Genetics: Consultancy, Honoraria; Astellas: Consultancy, Honoraria; Roche: Consultancy, Honoraria; Janssen: Consultancy, Honoraria; Agios: Consultancy, Honoraria; Pfizer: Research Funding; Celgene Corporation: Consultancy, Honoraria, Research Funding; Jazz: Consultancy, Honoraria, Research Funding; AbbVie: Consultancy, Honoraria. Stilgenbauer:GSK: Consultancy, Honoraria, Research Funding, Speakers Bureau; Janssen: Consultancy, Honoraria, Research Funding, Speakers Bureau; Pharmacyclics: Other: Travel support; Amgen: Consultancy, Honoraria, Research Funding, Speakers Bureau; Novartis: Consultancy, Honoraria, Research Funding, Speakers Bureau; Gilead: Consultancy, Honoraria, Research Funding, Speakers Bureau; AstraZeneca: Consultancy, Honoraria, Research Funding, Speakers Bureau; Celgene: Consultancy, Honoraria, Research Funding, Speakers Bureau; Hoffmann La-Roche: Consultancy, Honoraria, Research Funding, Speakers Bureau; AbbVie: Consultancy, Honoraria, Research Funding, Speakers Bureau.

Most environments change over time. Being able to adapt to such non-stationary environments is vital for real-world applications of many machine learning algorithms. In this work, we propose CORAL, a computationally efficient regression algorithm capable of adapting to a non-stationary target. CORAL is based on Bayesian linear regression with a sliding window and offline/online meta-learning. The sliding window makes our model focus on the recently received data and ignores older observations. The meta-learning approach allows us to learn the prior distribution of the model parameters. It speeds up the model adaptation, complements the sliding window’s drawback, and enhances the performance. We evaluate CORAL on two tasks: a toy problem and a more complex blood glucose level prediction task. Our approach improves the prediction accuracy for the non-stationary target significantly while also performing well for the stationary target. We show that the two components of our method work in a complementary fashion to achieve this.

<abstract><p>Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor stochastic, discrete population, continuous time models. The stationary distributions provide snapshots of the model behavior at the stationary regime, and as such finding their expression in terms of the model parameters is of great interest. The aim of the present paper is to describe when the stationary distributions of the original model, whose state space is potentially infinite, coincide exactly with the stationary distributions of the process truncated to finite subsets of states, up to a normalizing constant. The finite subsets of states we identify are called <italic>copies</italic> and are inspired by the modular topology of reaction network models. With such a choice we prove a novel graphical characterization of the concept of complex balancing for stochastic models of reaction networks. The results of the paper hold for the commonly used mass-action kinetics but are not restricted to it, and are in fact stated for more general setting.</p></abstract>

The article describes an approach to modelling and forecasting non-linear non-stationary time series for various purposes using Bayesian structural time series. The concepts of non-linearity and non-stationarity, as well as methods for processing non-linearity’sand non-stationarity in the construction of forecasting models are considered. The features of the Bayesian approach in the processing of nonlinearities and nonstationaryare presented. An approach to the construction of probabilistic-statistical models based on Bayesian structural models of time series has been studied. Parametric and non-parametric methods for forecasting non-linear and non-stationary time series are considered. Parametric methods include methods: classical autoregressive models, neural networks, models of support vector machines, hidden Markov models. Non-parametric methods include methods: state-space models, functional decomposition models, Bayesian non-parametric models. One of the types of non-parametric models isBayesian structural time series. The main features of constructing structural time series are considered. Models of structural time series are presented. The process of learning the Bayesianstructural model of time series is described. Training is performed in four stages: setting the structure of the model and a priori probabilities; applying a Kalman filter to update state estimates based on observed data;application of the “spike-and-slab”method to select variables in a structural model; Bayesian averaging to combine the results to make a prediction. An algorithm for constructing a Bayesian structural time seriesmodel is presented. Various components of the BSTS model are considered andanalysed, with the help of which the structures of alternative predictive models are formed. As an example of the application of Bayesian structural time series, the problem of predicting Amazon stock prices is considered. The base dataset is amzn_share. After loading, the structure and data types were analysed, and missing values were processed. The data are characterized by irregular registration of observations, which leads to a large number of missing values and “masking” possible seasonal fluctuations. This makes the task of forecasting rather difficult. To restore gaps in the amzn_sharetime series, the linear interpolation method was used. Using a set of statistical tests (ADF, KPSS, PP), the series was tested for stationarity. The data set is divided into two parts: training and testing. The fitting of structural models of time series was performed using the Kalman filterand the Monte Carlo method according to the Markov chain scheme. To estimate and simultaneously regularize the regression coefficients, the spike-and-slab method was applied. The quality of predictive models was assessed.

We introduce a batch service discipline, called assemble-transfer batch service, for continuous-time open queueing networks with batch movements. Under this service discipline a requested number of customers is simultaneously served at a node, and transferred to another node as, possibly, a batch of different size, if there are sufficient customers there; the node is emptied otherwise. We assume a Markovian setting for the arrival process, service times and routing, where batch sizes are generally distributed.Under the assumption that extra batches arrive while nodes are empty, and under a stability condition, it is shown that the stationary distribution of the queue length has a geometric product form over the nodes if and only if certain conditions are satisfied for the extra arrivals. This gives a new class of queueing networks which have tractable stationary distributions, and simultaneously shows that the product form provides a stochastic upper bound for the stationary distribution of the corresponding queueing network without the extra arrivals.

L'analisi dell'enorme quantità di dati finanziari, messi a disposizione dai mercati elettronici, richiede lo sviluppo di nuovi modelli e tecniche per estrarre efficacemente la conoscenza da utilizzare in un processo decisionale informato. Lo scopo della tesi concerne l'introduzione di modelli grafici probabilistici utilizzati per il ragionamento e l'attività decisionale in tale contesto. Nella prima parte della tesi viene presentato un framework che utilizza le reti Bayesiane per effettuare l'analisi e l'ottimizzazione di portafoglio in maniera olistica. In particolare, esso sfrutta, da un lato, la capacità delle reti Bayesiane di rappresentare distribuzioni di probabilità in modo compatto ed efficiente per modellare il portafoglio e, dall'altro, la loro capacità di fare inferenza per ottimizzare il portafoglio secondo diversi scenari economici. In molti casi, si ha la necessità di ragionare in merito a scenari di mercato nel tempo, ossia si vuole rispondere a domande che coinvolgono distribuzioni di probabilità che evolvono nel tempo. Le reti Bayesiane a tempo continuo possono essere utilizzate in questo contesto. Nella seconda parte della tesi viene mostrato il loro utilizzo per affrontare problemi finanziari reali e vengono descritte due importanti estensioni. La prima estensione riguarda il problema di classificazione, in particolare vengono introdotti un algoritmo per apprendere tali classificatori da Big Data e il loro utilizzo nel contesto di previsione dei cambi valutari ad alta frequenza. La seconda estensione concerne l'apprendimento delle reti Bayesiane a tempo continuo in domini non stazionari, in cui vengono modellate esplicitamente le dipendenze statistiche presenti nelle serie temporali multivariate consentendo loro di cambiare nel corso del tempo. Nella terza parte della tesi viene descritto l'uso delle reti Bayesiane a tempo continuo nell'ambito dei processi decisionali di Markov, i quali consentono di modellare processi decisionali sequenziali in condizioni di incertezza. In particolare, viene introdotto un metodo per il controllo di sistemi dinamici a tempo continuo che sfrutta le proprietà additive e contestuali per scalare efficacemente su grandi spazi degli stati. Infine, vengono mostrate le prestazioni di tale metodo in un contesto significativo di trading.
The analysis of the huge amount of financial data, made available by electronic markets, calls for new models and techniques to effectively extract knowledge to be exploited in an informed decision-making process. The aim of this thesis is to introduce probabilistic graphical models that can be used to reason and to perform actions in such a context. In the first part of this thesis, we present a framework which exploits Bayesian networks to perform portfolio analysis and optimization in a holistic way. It leverages on the compact and efficient representation of high dimensional probability distributions offered by Bayesian networks and their ability to perform evidential reasoning in order to optimize the portfolio according to different economic scenarios. In many cases, we would like to reason about the market change, i.e. we would like to express queries as probability distributions over time. Continuous time Bayesian networks can be used to address this issue. In the second part of the thesis, we show how it is possible to use this model to tackle real financial problems and we describe two notable extensions. The first one concerns classification, where we introduce an algorithm for learning these classifiers from Big Data, and we describe their straightforward application to the foreign exchange prediction problem in the high frequency domain. The second one is related to non-stationary domains, where we explicitly model the presence of statistical dependencies in multivariate time-series while allowing them to change over time. In the third part of the thesis, we describe the use of continuous time Bayesian networks within the Markov decision process framework, which provides a model for sequential decision-making under uncertainty. We introduce a method to control continuous time dynamic systems, based on this framework, that relies on additive and context-specific features to scale up to large state spaces. Finally, we show the performances of our method in a simplified, but meaningful trading domain.

A basic task of machine learning and data mining is to automatically uncover <b>patterns</b> that reflect regularities in a data set. When dealing with a large database, especially when domain knowledge is not available or very weak, this can be a challenging task. The purpose of <b>pattern discovery</b> is to find non-random relations among events from data sets. For example, the “exclusive OR” (XOR) problem concerns 3 binary variables, A, B and C=A<img src="http://resources.igi-global.com/Marketing/Preface_Figures/x_symbol.png">B, i.e. C is true when either A or B, but not both, is true. Suppose not knowing that it is the XOR problem, we would like to check whether or not the occurrence of the compound event [A=T, B=T, C=F] is just a random happening. If we could estimate its frequency of occurrences under the random assumption, then we know that it is not random if the observed frequency deviates significantly from that assumption. We refer to such a compound event as an event association pattern, or simply a <b>pattern</b>, if its frequency of occurrences significantly deviates from the default random assumption in the statistical sense. For instance, suppose that an XOR database contains 1000 samples and each primary event (e.g. [A=T]) occurs 500 times. The expected frequency of occurrences of the compound event [A=T, B=T, C=F] under the independence assumption is 0.5×0.5×0.5×1000 = 125. Suppose that its observed frequency is 250, we would like to see whether or not the difference between the observed and expected frequencies (i.e. 250 – 125) is significant enough to indicate that the compound event is not a random happening.<div><br></div><div>In statistics, to test the correlation between random variables, <b>contingency table</b> with chi-squared statistic (Mills, 1955) is widely used. Instead of investigating variable correlations, pattern discovery shifts the traditional correlation analysis in statistics at the variable level to association analysis at the event level, offering an effective method to detect statistical association among events.</div><div><br></div><div>In the early 90’s, this approach was established for second order event associations (Chan &amp; Wong, 1990). A higher order <b>pattern discovery</b> algorithm was devised in the mid 90’s for discrete-valued data sets (Wong &amp; Yang, 1997). In our methods, patterns inherent in data are defined as statistically significant associations of two or more primary events of different attributes if they pass a statistical test for deviation significance based on <b>residual analysis</b>. The discovered high order patterns can then be used for classification (Wang &amp; Wong, 2003). With continuous data, events are defined as Borel sets and the pattern discovery process is formulated as an optimization problem which recursively partitions the sample space for the best set of significant events (patterns) in the form of high dimension intervals from which probability density can be estimated by Gaussian kernel fit (Chau &amp; Wong, 1999). Classification can then be achieved using Bayesian classifiers. For data with a mixture of discrete and continuous data (Wong &amp; Yang, 2003), the latter is categorized based on a global optimization discretization algorithm (Liu, Wong &amp; Yang, 2004). As demonstrated in numerous real-world and commercial applications (Yang, 2002), pattern discovery is an ideal tool to uncover subtle and useful patterns in a database. </div><div><br></div><div>In pattern discovery, three open problems are addressed. The first concerns learning where noise and uncertainty are present. In our method, noise is taken as inconsistent samples against statistically significant patterns. Missing attribute values are also considered as noise. Using a standard statistical <b>hypothesis testing</b> to confirm statistical patterns from the candidates, this method is a less ad hoc approach to discover patterns than most of its contemporaries. The second problem concerns the detection of polythetic patterns without relying on exhaustive search. Efficient systems for detecting monothetic patterns between two attributes exist (e.g. Chan &amp; Wong, 1990). However, for detecting polythetic patterns, an exhaustive search is required (Han, 2001). In many problem domains, polythetic assessments of feature combinations (or higher order relationship detection) are imperative for robust learning. Our method resolves this problem by directly constructing polythetic concepts while screening out non-informative pattern candidates, using statisticsbased heuristics in the discovery process. The third problem concerns the representation of the detected patterns. Traditionally, if-then rules and graphs, including networks and trees, are the most popular ones. However, they have shortcomings when dealing with multilevel and multiple order patterns due to the non-exhaustive and unpredictable hierarchical nature of the inherent patterns. We adopt <b>attributed hypergraph</b> (AHG) (Wang &amp; Wong, 1996) as the representation of the detected patterns. It is a data structure general enough to encode information at many levels of abstraction, yet simple enough to quantify the information content of its organized structure. It is able to encode both the qualitative and the quantitative characteristics and relations inherent in the data set.<br></div>

Non-stationary continuous time Bayesian networks are introduced. They allow the parents set of each node in a continuous time Bayesian network to change over time. Structural learning of nonstationary continuous time Bayesian networks is developed under different knowledge settings. A macroeconomic dataset is used to assess the effectiveness of learning non-stationary continuous time Bayesian networks from real-world data.

Abstract Precise time series prediction serves as an important role in constructing a Digital Twin (DT). The various internal and external interferences result in highly non-linear and stochastic time series data sampled from real situations. Although artificial Neural Networks (ANNs) are often used to forecast time series for their strong self-learning and nonlinear fitting capabilities, it is a challenging and time-consuming task to obtain the optimal ANN architecture. This paper proposes a hybrid time series prediction model based on ensemble empirical mode decomposition (EEMD), long short-term memory (LSTM) neural networks, and Bayesian optimization (BO). To improve the predictability of stochastic and nonstationary time series, the EEMD method is implemented to decompose the original time series into several components, each of which is composed of single-frequency and stationary signal, and a residual signal. The decomposed signals are used to train the BO-LSTM neural networks, in which the hyper-parameters of the LSTM neural networks are fine-tuned by the BO algorithm. The following time series data are predicted by summating all the predictions of the decomposed signals based on the trained neural networks. To evaluate the performance of the proposed hybrid method (EEMD-BO-LSTM), this paper conducts a case study of wind speed time series prediction and has a comprehensive comparison between the proposed method and other approaches including the persistence model, ARIMA, LSTM neural networks, B0-LSTM neural networks, and EEMD-LSTM neural networks. Results show an improved prediction accuracy using the EEMD-BO-LSTM method by multiple accuracy metrics.