A flat Dirichlet process switching model for Bayesian estimation of hybrid systems

AbstractHybrid systems are often used to describe many complex dynamic phenomena by combining multiple modes of dynamics into whole systems. In this paper, we present a flat Dirichlet process switching (FDPS) model that defines a prior on mode switching dynamics of hybrid systems. Compared with the classical Markovian jump system (MJS) models, the FDPS model is nonparametric and can be applied to the hybrid systems with an unbounded number of potential modes. On the other hand, the probability structure of the new model is simpler and more flexible than the recently proposed hierarchical Dirichlet process (HDP) based MJS. Furthermore, we develop a Markov chain Monte Carlo (MCMC) method for estimating the states of hybrid systems with FDPS prior. And the numerical simulations of a hybrid system in different conditions are employed to show the effectiveness of the proposed approach

Modulation Classification for MIMO-OFDM Signals via Approximate Bayesian Inference

The problem of modulation classification for a multiple-antenna (MIMO) system employing orthogonal frequency division multiplexing (OFDM) is investigated under the assumption of unknown frequency-selective fading channels and signal-to-noise ratio (SNR). The classification problem is formulated as a Bayesian inference task, and solutions are proposed based on Gibbs sampling and mean field variational inference. The proposed methods rely on a selection of the prior distributions that adopts a latent Dirichlet model for the modulation type and on the Bayesian network formalism. The Gibbs sampling method converges to the optimal Bayesian solution and, using numerical results, its accuracy is seen to improve for small sample sizes when switching to the mean field variational inference technique after a number of iterations. The speed of convergence is shown to improve via annealing and random restarts. While most of the literature on modulation classification assume that the channels are flat fading, that the number of receive antennas is no less than that of transmit antennas, and that a large number of observed data symbols are available, the proposed methods perform well under more general conditions. Finally, the proposed Bayesian methods are demonstrated to improve over existing non-Bayesian approaches based on independent component analysis and on prior Bayesian methods based on the `superconstellation' method.Comment: To be appear in IEEE Trans. Veh. Technolog

Learning and Designing Stochastic Processes from Logical Constraints

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics must be known exactly. As this is seldom the case, many methods have been devised over the last decade to infer (learn) such parameters from observations of the state of the system. In this paper, we depart from this approach by assuming that our observations are {\it qualitative} properties encoded as satisfaction of linear temporal logic formulae, as opposed to quantitative observations of the state of the system. An important feature of this approach is that it unifies naturally the system identification and the system design problems, where the properties, instead of observations, represent requirements to be satisfied. We develop a principled statistical estimation procedure based on maximising the likelihood of the system's parameters, using recent ideas from statistical machine learning. We demonstrate the efficacy and broad applicability of our method on a range of simple but non-trivial examples, including rumour spreading in social networks and hybrid models of gene regulation

The brain as a generative model: information-theoretic surprise in learning and action

Our environment is rich with statistical regularities, such as a sudden cold gust of wind indicating a potential change in weather. A combination of theoretical work and empirical evidence suggests that humans embed this information in an internal representation of the world. This generative model is used to perform probabilistic inference, which may be approximated through surprise minimization. This process rests on current beliefs enabling predictions, with expectation violation amounting to surprise. Through repeated interaction with the world, beliefs become more accurate and grow more certain over time. Perception and learning may be accounted for by minimizing surprise of current observations, while action is proposed to minimize expected surprise of future events. This framework thus shows promise as a common formulation for different brain functions. The work presented here adopts information-theoretic quantities of surprise to investigate both perceptual learning and action. We recorded electroencephalography (EEG) of participants in a somatosensory roving-stimulus paradigm and performed trial-by-trial modeling of cortical dynamics. Bayesian model selection suggests early processing in somatosensory cortices to encode confidence-corrected surprise and subsequently Bayesian surprise. This suggests the somatosensory system to signal surprise of observations and update a probabilistic model learning transition probabilities. We also extended this framework to include audition and vision in a multi-modal roving-stimulus study. Next, we studied action by investigating a sensitivity to expected Bayesian surprise. Interestingly, this quantity is also known as information gain and arises as an incentive to reduce uncertainty in the active inference framework, which can correspond to surprise minimization. In comparing active inference to a classical reinforcement learning model on the two-step decision-making task, we provided initial evidence for active inference to better account for human model-based behaviour. This appeared to relate to participants’ sensitivity to expected Bayesian surprise and contributed to explaining exploration behaviour not accounted for by the reinforcement learning model. Overall, our findings provide evidence for information-theoretic surprise as a model for perceptual learning signals while also guiding human action.Unsere Umwelt ist reich an statistischen Regelmäßigkeiten, wie z. B. ein plötzlicher kalter Windstoß, der einen möglichen Wetterumschwung ankündigt. Eine Kombination aus theoretischen Arbeiten und empirischen Erkenntnissen legt nahe, dass der Mensch diese Informationen in eine interne Darstellung der Welt einbettet. Dieses generative Modell wird verwendet, um probabilistische Inferenz durchzuführen, die durch Minimierung von Überraschungen angenähert werden kann. Der Prozess beruht auf aktuellen Annahmen, die Vorhersagen ermöglichen, wobei eine Verletzung der Erwartungen einer Überraschung gleichkommt. Durch wiederholte Interaktion mit der Welt nehmen die Annahmen mit der Zeit an Genauigkeit und Gewissheit zu. Es wird angenommen, dass Wahrnehmung und Lernen durch die Minimierung von Überraschungen bei aktuellen Beobachtungen erklärt werden können, während Handlung erwartete Überraschungen für zukünftige Beobachtungen minimiert. Dieser Rahmen ist daher als gemeinsame Bezeichnung für verschiedene Gehirnfunktionen vielversprechend. In der hier vorgestellten Arbeit werden informationstheoretische Größen der Überraschung verwendet, um sowohl Wahrnehmungslernen als auch Handeln zu untersuchen. Wir haben die Elektroenzephalographie (EEG) von Teilnehmern in einem somatosensorischen Paradigma aufgezeichnet und eine trial-by-trial Modellierung der kortikalen Dynamik durchgeführt. Die Bayes'sche Modellauswahl deutet darauf hin, dass frühe Verarbeitung in den somatosensorischen Kortizes confidence corrected surprise und Bayesian surprise kodiert. Dies legt nahe, dass das somatosensorische System die Überraschung über Beobachtungen signalisiert und ein probabilistisches Modell aktualisiert, welches wiederum Wahrscheinlichkeiten in Bezug auf Übergänge zwischen Reizen lernt. In einer weiteren multimodalen Roving-Stimulus-Studie haben wir diesen Rahmen auch auf die auditorische und visuelle Modalität ausgeweitet. Als Nächstes untersuchten wir Handlungen, indem wir die Empfindlichkeit gegenüber der erwarteten Bayesian surprise betrachteten. Interessanterweise ist diese informationstheoretische Größe auch als Informationsgewinn bekannt und stellt, im Rahmen von active inference, einen Anreiz dar, Unsicherheit zu reduzieren. Dies wiederum kann einer Minimierung der Überraschung entsprechen. Durch den Vergleich von active inference mit einem klassischen Modell des Verstärkungslernens (reinforcement learning) bei der zweistufigen Entscheidungsaufgabe konnten wir erste Belege dafür liefern, dass active inference menschliches modellbasiertes Verhalten besser abbildet. Dies scheint mit der Sensibilität der Teilnehmer gegenüber der erwarteten Bayesian surprise zusammenzuhängen und trägt zur Erklärung des Explorationsverhaltens bei, das jedoch nicht vom reinforcement learning-Modell erklärt werden kann. Insgesamt liefern unsere Ergebnisse Hinweise für Formulierungen der informationstheoretischen Überraschung als Modell für Signale wahrnehmungsbasierten Lernens, die auch menschliches Handeln steuern

Short Term Probabilistic Load Forecasting at Local Level in Distribution Networks

Along with the growing inclusion of smart technologies into the electrical power grids, benefits, which can be originated form advanced metering infrastructure (AMI), have grabbed noticeable attention from distribution utilities. Since the number of meters are severely ample in practical systems, the utilities now is able to create virtual meter data by aggregating loads for distribution substations, feeders, transformers, or regions with the help of geographic information system. Such an important change brought by smart meter rollout is considered as the main factor which motivates this thesis to delve more into the load pattern modeling and forecasting at local level and find approaches which can yield to the enhanced applications in distribution networks. However, low aggregation level leads to high volatile load characteristic. In this regard, this thesis proposes a comprehensive methodology for uncertainty modeling and short-term probabilistic load forecasting (STPLF) in distribution networks. Existing methods related to uncertainty modeling and forecasting are rarely applied to local level loads and they suffer from over- or under-fitting of data when there is a misfit between the complexity of the model and the amount of data available. These models are limited to specific situations due to the great diversity of loads in distribution networks and need to be tuned every time when the load aggregation level changes. They also need a relatively large data set to support the recovery of the predictive densities. Our proposed method addresses this issue and is based on Bayesian nonparametric model which has unbounded complexity and allow the complexity to automatically grow and be inferred from the observed data. The uncertainty underlying load patterns can be endowed with any type of prior distribution and is given in a nonparametric form, i.e. a mixture model with countably infinite number of mixtures, inferred from the posterior using the Gibbs Sampling, which is a Markov Chain Monte Carlo (MCMC) technique. All effective samples from the sampling procedure along with the exogenous variables are fed to an ensemble learning machine. The final result of the probabilistic load forecasting (PLF) is averaged on the outputs of all learning models, thus reducing the model variance and enhancing the model consistency. The proposed method is tested on both a public data set and a local data set from the Saskatoon Light &Power AMI Meter Replacement Program which offers electricity consumption at a granularity of 30 minutes of more than 65,000 electricity customers including industrial, commercial and residential sectors in the city of Saskatoon, Canada

J Am Stat Assoc

The National Birth Defects Prevention Study (NBDPS) is a case-control study of birth defects conducted across 10 U.S. states. Researchers are interested in characterizing the etiologic role of maternal diet, collected using a food frequency questionnaire. Because diet is multi-dimensional, dimension reduction methods such as cluster analysis are often used to summarize dietary patterns. In a large, heterogeneous population, traditional clustering methods, such as latent class analysis, used to estimate dietary patterns can produce a large number of clusters due to a variety of factors, including study size and regional diversity. These factors result in a loss of interpretability of patterns that may differ due to minor consumption changes. Based on adaptation of the local partition process, we propose a new method, Robust Profile Clustering, to handle these data complexities. Here, participants may be clustered at two levels: (1) globally, where women are assigned to an overall population-level cluster via an overfitted finite mixture model, and (2) locally, where regional variations in diet are accommodated via a beta-Bernoulli process dependent on subpopulation differences. We use our method to analyze the NBDPS data, deriving pre-pregnancy dietary patterns for women in the NBDPS while accounting for regional variability.U01 DD001036/DD/NCBDD CDC HHS/United StatesP2C HD050924/HD/NICHD NIH HHS/United StatesT32 ES007018/ES/NIEHS NIH HHS/United StatesR01 ES027498/ES/NIEHS NIH HHS/United StatesR01 ES020619/ES/NIEHS NIH HHS/United StatesU01 DD001231/DD/NCBDD CDC HHS/United States2021-01-01T00:00:00Z32952235PMC75004908874vault:3598