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Structured recurrent temporal restricted Boltzmann machines
- In ICML
, 2014
"... Abstract The recurrent temporal restricted Boltzmann machine (RTRBM) is a probabilistic time-series model. The topology of the RTRBM graphical model, however, assumes full connectivity between all the pairs of visible units and hidden units, thereby ignoring the dependency structure within the obse ..."
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Abstract The recurrent temporal restricted Boltzmann machine (RTRBM) is a probabilistic time-series model. The topology of the RTRBM graphical model, however, assumes full connectivity between all the pairs of visible units and hidden units, thereby ignoring the dependency structure within the observations. Learning this structure has the potential for not only improving the prediction performance, but also revealing important dependency patterns in the data. For example, given a meteorological dataset, we could identify regional weather patterns. In this work, we propose a new class of RTRBM, which we refer to as the structured RTRBM (SRTRBM), which explicitly uses a graph to model the dependency structure. Our technique is related to methods such as graphical lasso, which are used to learn the topology of Gaussian graphical models. We also develop a spike-and-slab version of the RTRBM, and combine it with the SRTRBM to learn dependency structures in datasets with real-valued observations. Our experimental results using synthetic and real datasets demonstrate that the SRTRBM can significantly improve the prediction performance of the RTRBM, particularly when the number of visible units is large and the size of the training set is small. It also reveals the dependency structures underlying our benchmark datasets.
Reasoning with uncertainties over existence of objects
- In AAAI Fall Symposium: How Should Intelligence Be Abstracted in AI Research
, 2013
"... In this paper we consider planning problems in relational Markov processes where objects may “appear ” or “disap-pear”, perhaps depending on previous actions or properties of other objects. For instance, problems which require to ex-plicitly generate or discover objects fall into this category. In o ..."
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In this paper we consider planning problems in relational Markov processes where objects may “appear ” or “disap-pear”, perhaps depending on previous actions or properties of other objects. For instance, problems which require to ex-plicitly generate or discover objects fall into this category. In our formulation this requires to explicitly represent the un-certainty over the number of objects (dimensions or factors) in a dynamic Bayesian networks (DBN). Many formalisms (also existing ones) are conceivable to formulate such prob-lems. We aim at a formulation that facilitates inference and planning. Based on a specific formulation we investigate two inference methods—rejection sampling and reversible-jump MCMC—to compute a posterior over the process conditioned on the first and last time slice (start and goal state). We will discuss properties, efficiency, and appropriateness of each one.
Parsing epileptic events using a Markov switching process model for correlated time series Supplementary Materials
"... A.1 Channel i conditional likelihood at time t............................. 2 A.2 Channel i conditional marginal likelihood over t = 1,..., T................... 2 A.3 Conditional event likelihood..................................... 2 ..."
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A.1 Channel i conditional likelihood at time t............................. 2 A.2 Channel i conditional marginal likelihood over t = 1,..., T................... 2 A.3 Conditional event likelihood..................................... 2
Multiagent Planning and Learning Using Random Decompositions and Adaptive Representations
, 2015
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MONDRIAN HIDDEN MARKOVMODEL FOR MUSIC SIGNAL PROCESSING
"... This paper discusses a new extension of hidden Markov mod-els that can capture clusters embedded in transitions between the hidden states. In our model, the state-transition matrices are viewed as representations of relational data reflecting a network structure between the hidden states. We specifi ..."
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This paper discusses a new extension of hidden Markov mod-els that can capture clusters embedded in transitions between the hidden states. In our model, the state-transition matrices are viewed as representations of relational data reflecting a network structure between the hidden states. We specifically present a nonparametric Bayesian approach to the proposed state-space model whose network structure is represented by a Mondrian Process-based relational model. We show an appli-cation of the proposed model to music signal analysis through some experimental results. Index Terms — Bayesian nonparametrics, hiddenMarkov model, Mondrian process
Modelling mechanisms with causal cycles
, 2013
"... Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et a ..."
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Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et al. (2011) put forward the Recursive Bayesian Net (RBN) formalism as well suited to this end. The RBN formalism is an extension of the standard Bayesian net formalism, an extension that allows for modelling the hierarchical nature of mechanisms. Like the standard Bayesian net formalism, it models causal relationships using directed acyclic graphs. Given this appeal to acyclicity, causal cycles pose a prima facie problem for the RBN approach. This paper argues that the problem is a significant one given the ubiquity of causal cycles in mechanisms, but that the problem can be solved by combining two sorts of solution strategy in a judicious way. §1
Modeling the Complex Dynamics and Changing Correlations of Epileptic Events
"... Patients with epilepsy can manifest short, sub-clinical epileptic “bursts ” in addition to full-blown clinical seizures. We believe the relationship between these two classes of events—something not previously studied quantitatively— could yield important insights into the nature and intrinsic dynam ..."
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Patients with epilepsy can manifest short, sub-clinical epileptic “bursts ” in addition to full-blown clinical seizures. We believe the relationship between these two classes of events—something not previously studied quantitatively— could yield important insights into the nature and intrinsic dynamics of seizures. A goal of our work is to parse these complex epileptic events into distinct dynamic regimes. A challenge posed by the intracranial EEG (iEEG) data we study is the fact that the number and placement of electrodes can vary between patients. We develop a Bayesian nonparametric Markov switch-ing process that allows for (i) shared dynamic regimes between a variable numbers of channels, (ii) asynchronous regime-switching, and (iii) an un-known dictionary of dynamic regimes. We encode a sparse and changing set of dependencies between the channels using a Markov-switching Gaussian graphical model for the innovations process driving the channel dynamics and demonstrate the importance of this model in parsing and out-of-sample predictions of iEEG data. We show that our model produces intuitive state assignments that can help automate clinical analysis of seizures and enable the comparison of sub-clinical bursts and full clinical seizures.
5a. CONTRACT NUMBER
"... Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comment ..."
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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing
Acting and Bayesian reinforcement structure learning of partially observable environment
"... Abstract: This article shows how to learn both the structure and the parameters of partially observable en-vironment simultaneously while also online performing near-optimal sequence of actions taking into account exploration-exploitation tradeoff. It combines two re-sults of recent research: The fo ..."
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Abstract: This article shows how to learn both the structure and the parameters of partially observable en-vironment simultaneously while also online performing near-optimal sequence of actions taking into account exploration-exploitation tradeoff. It combines two re-sults of recent research: The former extends model-based Bayesian reinforcement learning of fully observable envi-ronment to bigger domains by learning the structure. The latter shows how a known structure can be exploited to model-based Bayesian reinforcement learning of partially observable domains. This article shows that merging both approaches is possible without too excessive increase in computational complexity. 1
