201 results found
Kormushev P, Demiris Y, Caldwell DG, 2015, Encoderless Position Control of a Two-Link Robot Manipulator
Soh H, Demiris Y, 2015, Spatio-Temporal Learning With the Online Finite and Infinite Echo-State Gaussian Processes, IEEE Transactions on Neural Networks and Learning Systems, Vol: 26, Pages: 522-536, ISSN: 2162-237X
Successful biological systems adapt to change. In this paper, we are principally concerned with adaptive systems that operate in environments where data arrives sequentially and is multivariate in nature, for example, sensory streams in robotic systems. We contribute two reservoir inspired methods: 1) the online echostate Gaussian process (OESGP) and 2) its infinite variant, the online infinite echostate Gaussian process (OIESGP) Both algorithms are iterative fixed-budget methods that learn from noisy time series. In particular, the OESGP combines the echo-state network with Bayesian online learning for Gaussian processes. Extending this to infinite reservoirs yields the OIESGP, which uses a novel recursive kernel with automatic relevance determination that enables spatial and temporal feature weighting. When fused with stochastic natural gradient descent, the kernel hyperparameters are iteratively adapted to better model the target system. Furthermore, insights into the underlying system can be gleamed from inspection of the resulting hyperparameters. Experiments on noisy benchmark problems (one-step prediction and system identification) demonstrate that our methods yield high accuracies relative to state-of-the-art methods, and standard kernels with sliding windows, particularly on problems with irrelevant dimensions. In addition, we describe two case studies in robotic learning-by-demonstration involving the Nao humanoid robot and the Assistive Robot Transport for Youngsters (ARTY) smart wheelchair.
Ribes A, Cerquides J, Demiris Y, et al., 2015, Where is my keyboard? Model-based active adaptation of action-space in a humanoid robot, 15th IEEE-RAS International Conference on Humanoid Robots (Humanoids), Publisher: IEEE, Pages: 602-609, ISSN: 2164-0572
Soh H, Demiris Y, 2015, Learning Assistance by Demonstration: Smart Mobility With Shared Control and Paired Haptic Controllers, JOURNAL OF HUMAN-ROBOT INTERACTION, Vol: 4, Pages: 76-100, ISSN: 2163-0364
Wu Y, Su Y, Demiris Y, 2014, A morphable template framework for robot learning by demonstration: Integrating one-shot and incremental learning approaches, Robotics and Autonomous Systems, Vol: 62, Pages: 1517-1530
Robot learning by demonstration is key to bringing robots into daily social environments to interact with and learn from human and other agents. However, teaching a robot to acquire new knowledge is a tedious and repetitive process and often restrictive to a specific setup of the environment. We propose a template-based learning framework for robot learning by demonstration to address both generalisation and adaptability. This novel framework is based upon a one-shot learning model integrated with spectral clustering and an online learning model to learn and adapt actions in similar scenarios. A set of statistical experiments is used to benchmark the framework components and shows that this approach requires no extensive training for generalisation and can adapt to environmental changes flexibly. Two real-world applications of an iCub humanoid robot playing the tic-tac-toe game and soldering a circuit board are used to demonstrate the relative merits of the framework.
Su Y, Dong W, Wu Y, et al., 2014, Increasing the Accuracy and the Repeatability of Position Control for Micromanipulations Using Heteroscedastic Gaussian Processes, IEEE International Conference on Robotics and Automation (ICRA 2014), Pages: 4692-4698
Many recent studies describe micromanipulation systems by using complex Analytic Forward Models (AFM), but such models are difficult to build and incapable of describing unmodelable factors, such as manufacturing defects. In this work, we propose the Enhanced Analytic Forward Model (EAFM), an integrated model of the AFM and the Heteroscedastic Gaussian Processes (HGP). The EAFM can compensate the shortfalls of the AFM by training the HGP on the residual of the AFM. This also allows the HGP to learn the repeatability of the micromanipulation system. Based on the EAFM, we further contribute an optimal position controller for improving the accuracy and the repeatability. This optimal EAFM controller is implemented and tested on a three degree-of-freedom micromanipulator based micromanipulation system. Two sets of real-world experiments are carried out to verify our method. The results demonstrate that the controller using EAFM can statistically achieve higher accuracy and repeatability than solely using the AFM.
Soh H, Demiris Y, 2014, Incrementally Learning Objects by Touch: Online Discriminative and Generative Models for Tactile-Based Recognition, IEEE Transactions on Haptics, Vol: 7, Pages: 512-525, ISSN: 1939-1412
Human beings not only possess the remarkable ability to distinguish objects through tactile feedback but are further able to improve upon recognition competence through experience. In this work, we explore tactile-based object recognition with learners capable of incremental learning. Using the sparse online infinite Echo-State Gaussian process (OIESGP), we propose and compare two novel discriminative and generative tactile learners that produce probability distributions over objects during object grasping/ palpation. To enable iterative improvement, our online methods incorporate training samples as they become available. We also describe incremental unsupervised learning mechanisms, based on novelty scores and extreme value theory, when teacher labels are not available. We present experimental results for both supervised and unsupervised learning tasks using the iCub humanoid, with tactile sensors on its five-fingered anthropomorphic hand, and 10 different object classes. Our classifiers perform comparably to state-of-the-art methods (C4.5 and SVM classifiers) and findings indicate that tactile signals are highly relevant for making accurate object classifications. We also show that accurate “early” classifications are possible using only 20-30 percent of the grasp sequence. For unsupervised learning, our methods generate high quality clusterings relative to the widely-used sequential k-means and self-organising map (SOM), and we present analyses into the differences between the approaches.
Ros R, Baroni I, Demiris Y, 2014, Adaptive human-robot interaction in sensorimotor task instruction: From human to robot dance tutors, Robotics and Autonomous Systems, Vol: 62, Pages: 707-720, ISSN: 1872-793X
We explore the potential for humanoid robots to interact with children in a dance activity. In this context, the robot plays the role of an instructor to guide the child through several dance moves to learn a dance phrase. We participated in 30 dance sessions in schools to study human–human interaction between children and a human dance teacher, and to identify the applied methodologies. Based on the strategies observed, both social and task-dependent, we implemented a robotic system capable of autonomously instructing dance sequences to children while displaying basic social cues to engage the child in the task. Experiments were performed in a hospital with the Nao robot interacting with 12 children through multiple encounters, when possible (18 sessions, 236 min). Observational analysis through video recordings and survey evaluations were used to assess the quality of interaction. Moreover, we introduce an involvement measure based on the aggregation of observed behavioral cues to assess the level of interest in the interaction through time. The analysis revealed high levels of involvement, while highlighting the need for further research into social engagement and adaptation with robots over repeated sessions.
Ros R, Coninx A, Demiris Y, et al., 2014, Behavioral Accommodation towards a Dance Robot Tutor, International Conference on Human-Robot Interaction, Publisher: ACM/IEEE, Pages: 278-279
We report first results on children adaptive behavior towards a dance tutoring robot. We can observe that children behavior rapidly evolves through few sessions in order to accommodate with the robotic tutor rhythm and instructions.
Demiris Y, Aziz-Zadeh L, Bonaiuto J, 2014, Information Processing in the Mirror Neuron System in Primates and Machines, Neuroinformatics, Vol: 12, Pages: 63-91, ISSN: 1539-2791
The mirror neuron system in primates matches observations of actions with the motor representations used for their execution, and is a topic of intense research and debate in biological and computational disciplines. In robotics, models of this system have been used for enabling robots to imitate and learn how to perform tasks from human demonstrations. Yet, existing computational and robotic models of these systems are found in multiple levels of description, and although some models offer plausible explanations and testable predictions, the difference in the granularity of the experimental setups, methodologies, computational structures and selected modeled data make principled meta-analyses, common in other fields, difficult. In this paper, we adopt an interdisciplinary approach, using the BODB integrated environment in order to bring together several different but complementary computational models, by functionally decomposing them into brain operating principles (BOPs) which each capture a limited subset of the model’s functionality. We then explore links from these BOPs to neuroimaging and neurophysiological data in order to pinpoint complementary and conflicting explanations and compare predictions against selected sets of neurobiological data. The results of this comparison are used to interpret mirror system neuroimaging results in terms of neural network activity, evaluate the biological plausibility of mirror system models, and suggest new experiments that can shed light on the neural basis of mirror systems.
Lee K, Su Y, Kim T-K, et al., 2013, A syntactic approach to robot imitation learning using probabilistic activity grammars, Robotics and Autonomous Systems, Vol: 61, Pages: 1323-1334, ISSN: 0921-8890
This paper describes a syntactic approach to imitation learning that captures important task structures in the form of probabilistic activity grammars from a reasonably small number of samples under noisy conditions. We show that these learned grammars can be recursively applied to help recognize unforeseen, more complicated tasks that share underlying structures. The grammars enforce an observation to be consistent with the previously observed behaviors which can correct unexpected, out-of-context actions due to errors of the observer and/or demonstrator. To achieve this goal, our method (1) actively searches for frequently occurring action symbols that are subsets of input samples to uncover the hierarchical structure of the demonstration, and (2) considers the uncertainties of input symbols due to imperfect low-level detectors.We evaluate the proposed method using both synthetic data and two sets of real-world humanoid robot experiments. In our Towers of Hanoi experiment, the robot learns the important constraints of the puzzle after observing demonstrators solving it. In our Dance Imitation experiment, the robot learns 3 types of dances from human demonstrations. The results suggest that under reasonable amount of noise, our method is capable of capturing the reusable task structures and generalizing them to cope with recursions.
Korkinof D, Demiris Y, 2013, Online Quantum Mixture Regression for Trajectory Learning by Demonstration, International Conference on Intelligent Systems and Robots (IROS), Publisher: IEEE, Pages: 3222-3229, ISSN: 2153-0858
In this work, we present the online Quantum Mixture Model (oQMM), which combines the merits of quantum mechanics and stochastic optimization. More specifically it allows for quantum effects on the mixture states, which in turn become a superposition of conventional mixture states. We propose an efficient stochastic online learning algorithm based on the online Expectation Maximization (EM), as well as a generation and decay scheme for model components. Our method is suitable for complex robotic applications, where data is abundant or where we wish to iteratively refine our model and conduct predictions during the course of learning. With a synthetic example, we show that the algorithm can achieve higher numerical stability. We also empirically demonstrate the efficacy of our method in well-known regression benchmark datasets. Under a trajectory Learning by Demonstration setting we employ a multi-shot learning application in joint angle space, where we observe higher quality of learning and reproduction. We compare against popular and well-established methods, widely adopted across the robotics community.
Soh H, Demiris Y, 2013, When and how to help: An iterative probabilistic model for learning assistance by demonstration, International Conference on Intelligent Robots and Systems (IROS), Publisher: IEEE, Pages: 3230-3236, ISSN: 2153-0858
Crafting a proper assistance policy is a difficult endeavour but essential for the development of robotic assistants. Indeed, assistance is a complex issue that depends not only on the task-at-hand, but also on the state of the user, environment and competing objectives. As a way forward, this paper proposes learning the task of assistance through observation; an approach we term Learning Assistance by Demonstration (LAD). Our methodology is a subclass of Learning-by-Demonstration (LbD), yet directly addresses difficult issues associated with proper assistance such as when and how to appropriately assist. To learn assistive policies, we develop a probabilistic model that explicitly captures these elements and provide efficient, online, training methods. Experimental results on smart mobility assistance — using both simulation and a real-world smart wheelchair platform — demonstrate the effectiveness of our approach; the LAD model quickly learns when to assist (achieving an AUC score of 0.95 after only one demonstration) and improves with additional examples. Results show that this translates into better task-performance; our LAD-enabled smart wheelchair improved participant driving performance (measured in lap seconds) by 20.6s (a speedup of 137%), after a single teacher demonstration.
Korkinof D, Demiris Y, 2013, Online Quantum Mixture Regression for Trajectory Learning by Demonstration, IROS 2013, Publisher: IEEE, Pages: 3222-3229
In this work, we present the online Quantum Mixture Model (oQMM), which combines the merits of quan- tum mechanics and stochastic optimization. More specifically it allows for quantum effects on the mixture states, which in turn become a superposition of conventional mixture states. We propose an efficient stochastic online learning algorithm based on the online Expectation Maximization (EM), as well as a generation and decay scheme for model components. Our method is suitable for complex robotic applications, where data is abundant or where we wish to iteratively refine our model and conduct predictions during the course of learning. With a synthetic example, we show that the algorithm can achieve higher numerical stability. We also empirically demonstrate the efficacy of our method in well-known regression benchmark datasets. Under a trajectory Learning by Demonstration setting we employ a multi-shot learning application in joint angle space, where we observe higher quality of learning and reproduction. We compare against popular and well-established methods, widely adopted across the robotics community.
Ros R, Demiris Y, 2013, Creative Dance: An Approach for Social Interaction between Robots and Children, 4th International Workshop on Human Behavior Understanding (HBU), Publisher: Springer, Pages: 40-51, ISSN: 0302-9743
In this paper we discuss the potential of using a dance robot tutor with children in the context of creative dance to study child-robot interaction through several encounters. We have taken part of dance sessions in order to extract strategies and models to inspire and justify the design of a robot dance tutor. Moreover, we present implementation details and preliminary results on a pilot study to extract initial feedback to further improve and test our system with a broader children population.
Ognibene D, Chinellato E, Sarabia M, et al., 2013, Contextual action recognition and target localization with an active allocation of attention on a humanoid robot, Bioinspiration & Biomimetics, Vol: 8
Exploratory gaze movements are fundamental for gathering the most relevant information regarding the partner during social interactions. Inspired by the cognitive mechanisms underlying human social behaviour, we have designed and implemented a system for a dynamic attention allocation which is able to actively control gaze movements during a visual action recognition task exploiting its own action execution predictions. Our humanoid robot is able, during the observation of a partner's reaching movement, to contextually estimate the goal position of the partner's hand and the location in space of the candidate targets. This is done while actively gazing around the environment, with the purpose of optimizing the gathering of information relevant for the task. Experimental results on a simulated environment show that active gaze control, based on the internal simulation of actions, provides a relevant advantage with respect to other action perception approaches, both in terms of estimation precision and of time required to recognize an action. Moreover, our model reproduces and extends some experimental results on human attention during an action perception.
Ognibene D, Demiris Y, 2013, Towards Active Event Recognition, International Joint Conference on Artificial Intelligence (IJCAI), Publisher: AIII Press, Pages: 2495-2501
Directing robot attention to recognise activities and to anticipate events like goal-directed actions is a crucial skill for human-robot interaction. Unfortunately, issues like intrinsic time constraints, the spatially distributed nature of the entailed information sources, and the existence of a multitude of unobservable states affecting the system, like latent intentions, have long rendered achievement of such skills a rather elusive goal. The problem tests the limits of current attention control systems. It requires an integrated solution for tracking, exploration and recognition, which traditionally have been seen as separate problems in active vision.We propose a probabilistic generative framework based on a mixture of Kalman filters and information gain maximisation that uses predictions in both recognition and attention-control. This framework can efficiently use the observations of one element in a dynamic environment to provide information on other elements, and consequently enables guided exploration.Interestingly, the sensors-control policy, directly derived from first principles, represents the intuitive trade-off between finding the most discriminative clues and maintaining overall awareness.Experiments on a simulated humanoid robot observing a human executing goal-oriented actions demonstrated improvement on recognition time and precision over baseline systems.
Chatzis S, Demiris Y, 2013, The Infinite-Order Conditional Random Field Model for Sequential Data Modeling, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol: 6, Pages: 1523-1534, ISSN: 0162-8828
Sequential data labeling is a fundamental task in machine learning applications, with speech and natural language processing, activity recognition in video sequences, and biomedical data analysis being characteristic examples, to name just a few. The conditional random field (CRF), a log-linear model representing the conditional distribution of the observation labels, is one of the most successful approaches for sequential data labeling and classification, and has lately received significant attention in machine learning as it achieves superb prediction performance in a variety of scenarios. Nevertheless, existing CRF formulations can capture only one- or few-timestep interactions and neglect higher order dependences, which are potentially useful in many real-life sequential data modeling applications. To resolve these issues, in this paper we introduce a novel CRF formulation, based on the postulation of an energy function which entails infinitely long time-dependences between the modeled data. Building blocks of our novel approach are: 1) the sequence memoizer (SM), a recently proposed nonparametric Bayesian approach for modeling label sequences with infinitely long time dependences, and 2) a mean-field-like approximation of the model marginal likelihood, which allows for the derivation of computationally efficient inference algorithms for our model. The efficacy of the so-obtained infinite-order CRF model is experimentally demonstrated.
Petit M, Lallée S, Boucher J-D, et al., 2013, The Coordinating Role of Language in Real-Time Multi-Modal Learning of Cooperative Tasks, IEEE Transactions on Autonomous Mental Development, Vol: 5, Pages: 3-17, ISSN: 1943-0604
One of the defining characteristics of human cognition is our outstanding capacity to cooperate. A central requirement for cooperation is the ability to establish a “shared plan”-which defines the interlaced actions of the two cooperating agents-in real time, and even to negotiate this shared plan during its execution. In the current research we identify the requirements for cooperation, extending our earlier work in this area. These requirements include the ability to negotiate a shared plan using spoken language, to learn new component actions within that plan, based on visual observation and kinesthetic demonstration, and finally to coordinate all of these functions in real time. We present a cognitive system that implements these requirements, and demonstrate the system's ability to allow a Nao humanoid robot to learn a nontrivial cooperative task in real-time. We further provide a concrete demonstration of how the real-time learning capability can be easily deployed on a different platform, in this case the iCub humanoid. The results are considered in the context of how the development of language in the human infant provides a powerful lever in the development of cooperative plans from lower-level sensorimotor capabilities.
Belpaeme T, Baxter PE, Read R, et al., 2013, Multimodal Child-Robot Interaction: Building Social Bonds, Journal of Human-Robot Interaction, Vol: 1, Pages: 33-53
For robots to interact effectively with human users they must be capable of coordinated, timely behavior in response to social context. The Adaptive Strategies for Sustainable Long-Term Social Interaction (ALIZ-E) project focuses on the design of long-term, adaptive social interaction between robots and child users in real-world settings. In this paper, we report on the iterative approach taken to scientific and technical developments toward this goal: advancing individual technical competen- cies and integrating them to form an autonomous robotic system for evaluation “in the wild.” The first evaluation iterations have shown the potential of this methodology in terms of adaptation of the robot to the interactant and the resulting influences on engagement. This sets the foundation for an ongoing research program that seeks to develop technologies for social robot companions.
Su Y, Wu Y, Soh H, et al., 2013, Enhanced Kinematic Model for Dexterous Manipulation with an Underactuated Hand, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Publisher: IEEE, Pages: 2493-2499, ISSN: 2153-0858
Ognibene D, Demiris Y, 2013, Towards active event recognition
Chinellato E, Ognibene D, Sartori L, et al., 2013, Time to Change: Deciding When to Switch Action Plans during a Social Interaction, Publisher: Springer Berlin Heidelberg, Pages: 47-58
Sarabia M, Demiris Y, 2013, A Humanoid Robot Companion for Wheelchair Users, International Conference on Social Robotics (ICSR), Publisher: Springer, Pages: 432-441
In this paper we integrate a humanoid robot with a powered wheelchair with the aim of lowering the cognitive requirements needed for powered mobility. We propose two roles for this companion: pointing out obstacles and giving directions. We show that children enjoyed driving with the humanoid companion by their side during a field-trial in an uncontrolled environment. Moreover, we present the results of a driving experiment for adults where the companion acted as a driving aid and conclude that participants preferred the humanoid companion to a simulated companion. Our results suggest that people will welcome a humanoid companion for their wheelchairs.
Sarabia M, Le Mau T, Soh H, et al., 2013, iCharibot : Design and Field Trials of a Fundraising Robot, International Conference on Social Robotics (ICSR 2013), Publisher: Springer, Pages: 412-421
In this work, we address the problem of increasing charitable donations through a novel, engaging fundraising robot: the Imperial Charity Robot (iCharibot). To better understand how to engage passers-by, we conducted a field trial in outdoor locations at a busy area in London, spread across 9 sessions of 40 minutes each. During our experiments, iCharibot attracted 679 people and engaged with 386 individuals. Our results show that interactivity led to longer user engagement with the robot. Our data further suggests both saliency and interactivity led to an increase in the total donation amount. These findings should prove useful for future design of robotic fundraisers in particular and for social robots in general.
Ognibene D, Wu Y, Lee K, et al., 2013, Hierarchies for embodied action perception, Computational and Robotic Models of the Hierarchical Organization of Behavior, Editors: Baldassarre, Mirolli, Publisher: Springer, Pages: 81-98
During social interactions, humans are capable of initiating and responding to rich and complex social actions despite having incomplete world knowledge, and physical, perceptual and computational constraints. This capability relies on action perception mechanisms that exploit regularities in observed goal-oriented behaviours to generate robust predictions and reduce the workload of sensing systems. To achieve this essential capability, we argue that the following three factors are fundamental. First, human knowledge is frequently hierarchically structured, both in the perceptual and execution domains. Second, human perception is an active process driven by current task requirements and context; this is particularly important when the perceptual input is complex (e.g. human motion) and the agent has to operate under embodiment constraints. Third, learning is at the heart of action perception mechanisms, underlying the agent’s ability to add new behaviours to its repertoire. Based on these factors, we review multiple instantiations of a hierarchically-organised biologically-inspired framework for embodied action perception, demonstrating its flexibility in addressing the rich computational contexts of action perception and learning in robotic platforms.
Su Y, Wu Y, Lee K, et al., 2012, Robust Grasping for an Under-actuated Anthropomorphic Handunder Object Position Uncertainty, Osaka, Japan, International Conference on Humanoid Robots (Humanoids), Publisher: IEEE, Pages: 719-725
This paper presents a grasp execution strategy for grasping an object with one trial when there is uncertainty in the object position. This strategy is based on three grasping components: 1) robust grasp trajectory planning which can cope with reasonable amount of initial object position error, 2) sensor-based grasp adaptation, and 3) compliant characteristics of the under actuated mechanism. This strategy is implemented and tested on the iCub humanoid robot. Two experiments and a demo of the iCub robot playing the Towers of Hanoi game are carried out to verify our system. The results demonstrate that the iCub using this approach can successfully grasp objects under certain position error with its under-actuated anthropomorphic hand.
Chatzis SP, Demiris Y, 2012, Nonparametric mixtures of Gaussian processes with power-law behavior, IEEE Transactions on Neural Networks, Vol: 23, Pages: 1862-1871, ISSN: 2162-237X
Gaussian processes (GPs) constitute one of the most important Bayesian machine learning approaches, based on a particularly effective method for placing a prior distribution overthe space of regression functions. Several researchers have considered postulating mixtures of Gaussian processes as a means ofdealing with non-stationary covariance functions, discontinuities, multi-modality, and overlapping output signals. In existing works, mixtures of Gaussian processes are based on the introduction of a gating function defined over the space of model input variables. This way, each postulated mixture component Gaussian process is effectively restricted in a limited subset of the input space. In this work, we follow a different approach: We consider a fully generative nonparametric Bayesian model with power-law behavior, generating Gaussian processes over the whole input space of the learned task. We provide an efficient algorithm for model inference, based on the variational Bayesian framework, and exhibit its efficacy using benchmark and real-world datasets.
Lee K, Kim TK, Demiris Y, 2012, Learning Action Symbols for Hierarchical Grammar Induction, Tsukuba, Japan, International Conference on Pattern Recognition (ICPR), Publisher: IEEE, Pages: 3778-3782
We present an unsupervised method of learning action symbols from video data, which self-tunes the number of symbols to effectively build hierarchical activity grammars. A video stream is given as a sequence of unlabeled segments. Similar segments are incrementally grouped to form a hierarchical tree structure. The tree is cut into clusters where each cluster is used to train an action symbol. Our goal is to find a good set of clusters i.e. symbols where regularities are best captured in the learned representation, i.e. induced grammar. Our method has two-folds: 1) Create a candidate set of symbols from initial clusters, 2) Build an activity grammar and measure model complexity and likelihood to assess the quality of the candidate set of symbols. We propose a balanced model comparison method which avoids the problem commonly found in model complexity computations where one measurement term dominates the other. Our experiments on the towers of Hanoi and human dancing videos show that our method can discover the optimal number of action symbols effectively.
Chatzis SP, Demiris Y, 2012, A Reservoir-Driven Non-Stationary Hidden Markov Model, Pattern Recognition, Vol: 45, Pages: 3985-3996
In this work, we propose a novel approach towards sequential data modeling that leverages the strengths of hidden Markov models and echo-state networks (ESNs) in the context of non-parametric Bayesian inference approaches. We introduce a non-stationary hidden Markov model, the time-dependent state transition probabilities of which are driven by a high-dimensional signal that encodes the whole history of the modeled observations, namely the state vector of a postulated observations-driven ESN reservoir. We derive an efficient inference algorithm for our model under the variational Bayesian paradigm, and we examine the efficacy of our approach considering a number of sequential data modeling applications.
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