On the context tree maximizing algorithm

Volf, Petr; Willems, F.M.J.

doi:10.1109/isit.1995.531122

Cited by 12 publications

(13 citation statements)

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“…A tree with the same number of leaves but a higher order requires more bits to detail all the layers of the longer branches. This condition often arises in compression where an optimal trade-off between the code length of the sequence and the cost of the model is desired (Volf and Willems 1995). With this penalty term, we construct our objective function as a trade-off between the model complexity and finding a tree model that maximizes the a posteriori probability:…”

Section: Context Tree Estimationmentioning

confidence: 99%

“…minimized among set I. This objective function can be solved recursively, and the penalty term can be readily broken down and incorporated into the recursive optimization process (Volf and Willems 1995). We define the maximized probability P s ‫ء‬ at node s as P s…”

Section: Context Tree Estimationmentioning

confidence: 99%

“…Also, CTW assumes that all firing patterns are equally likely, and this method of assigning all patterns equal weight is very data intensive and does not provide insight into the data structure. In this study, we implemented a different method that utilizes the context tree framework-context tree maximizing (CTM), which, in addition to being data driven, also automatically finds the appropriate tree depth as well as the best tree structure that fits the data in the a posteriori sense and prevents overfitting (Csiszár and Talata 2006;Volf and Willems 1995), in which case the model tends to fit the noise other than the underlying patterns and relationships of the signals. Because it is data driven, CTM is not constrained by model types and is able to detect both linear and nonlinear relationships between spike train sequences.…”

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confidence: 99%

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Inferring neuronal network functional connectivity with directed information

Cai

Neveu

Baxter

et al. 2017

Journal of Neurophysiology

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A major challenge in neuroscience is to develop effective tools that infer the circuit connectivity from large-scale recordings of neuronal activity patterns. In this study, context tree maximizing (CTM) was used to estimate directed information (DI), which measures causal influences among neural spike trains in order to infer putative synaptic connections. In contrast to existing methods, the method presented here is data driven and can readily identify both linear and nonlinear relations between neurons. This CTM-DI method reliably identified circuit structures underlying simulations of realistic conductance-based networks. It also inferred circuit properties from voltage-sensitive dye recordings of the buccal ganglion of This method can be applied to other large-scale recordings as well. It offers a systematic tool to map network connectivity and to track changes in network structure such as synaptic strengths as well as the degrees of connectivity of individual neurons, which in turn could provide insights into how modifications produced by learning are distributed in a neural network. This study brings together the techniques of voltage-sensitive dye recording and information theory to infer the functional connectome of the feeding central pattern generating network of In contrast to current statistical approaches, the inference method developed in this study is data driven and validated by conductance-based model circuits, can distinguish excitatory and inhibitory connections, is robust against synaptic plasticity, and is capable of detecting network structures that mediate motor patterns.

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Section: Context Tree Estimationmentioning

confidence: 99%

Section: Context Tree Estimationmentioning

confidence: 99%

mentioning

confidence: 99%

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Inferring neuronal network functional connectivity with directed information

Cai

Neveu

Baxter

et al. 2017

Journal of Neurophysiology

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“…As we found in extensive simulation studies, the bias of the CTW estimator converges much faster than the biases of the LZ estimators, while keeping the advantage of dealing with long-range dependence. Moreover, from the CTW we can obtain an explicit statistical model for the data, the "maximum a posteriori probability" (MAP) tree described in [14]. The importance of these models comes from the fact that, in the information-theoretic context, they can be operationally interpreted as the "best" tree models for the data at hand.…”

Section: A Entropy Estimatesmentioning

confidence: 99%

“…We computed the MAP tree models [14] derived from spike train data using the CTW algorithm with depth D = 100. Figure 3 shows the suffix sets of two cells' MAP trees, sorted in descending order of suffix frequency.…”

Section: B Map Tree Models For Spike Trainsmentioning

confidence: 99%

From the Entropy to the Statistical Structure of Spike Trains

Gao

Kontoyiannis

Bienenstock

2006

2006 IEEE International Symposium on Information Theory

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We use statistical estimates of the entropy rate of individual spike train data in order to make inferences about the underlying structure of the spike train itself. We first examine a number of different parametric and nonparametric estimators (some known and some new), including the "plug-in" method, several versions of Lempel-Ziv-based compression algorithms, a maximum likelihood estimator tailored to renewal processes, and the natural estimator derived from the Context-Tree Weighting method (CTW). The theoretical properties of these estimators are examined, several new theoretical results are developed, and all estimators are systematically applied to various types of simulated data under different conditions. Our main focus is on the performance of these entropy estimators on the (binary) spike trains of 28 neurons recorded simultaneously for a one-hour period from the primary motor and dorsal premotor cortices of a monkey. We show how the entropy estimates can be used to test for the existence of longterm structure in the data, and we construct a hypothesis test for whether the renewal process model is appropriate for these spike trains. Further, by applying the CTW algorithm we derive the maximum a posterior (MAP) tree model of our empirical data, and comment on the underlying structure it reveals.

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Inferring functional connectivity through graphical directed information

et al. 2021

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Objective. Accurate inference of functional connectivity is critical for understanding brain function. Previous methods have limited ability distinguishing between direct and indirect connections because of inadequate scaling with dimensionality. This poor scaling performance reduces the number of nodes that can be included in conditioning. Our goal was to provide a technique that scales better and thereby enables minimization of indirect connections. Approach. Our major contribution is a powerful model-free framework, graphical directed information (GDI), that enables pairwise directed functional connections to be conditioned on the activity of substantially more nodes in a network, producing a more accurate graph of functional connectivity that reduces indirect connections. The key technology enabling this advancement is a recent advance in the estimation of mutual information (MI), which relies on multilayer perceptrons and exploiting an alternative representation of the Kullback–Leibler divergence definition of MI. Our second major contribution is the application of this technique to both discretely valued and continuously valued time series. Main results. GDI correctly inferred the circuitry of arbitrary Gaussian, nonlinear, and conductance-based networks. Furthermore, GDI inferred many of the connections of a model of a central pattern generator circuit in Aplysia, while also reducing many indirect connections. Significance. GDI is a general and model-free technique that can be used on a variety of scales and data types to provide accurate direct connectivity graphs and addresses the critical issue of indirect connections in neural data analysis.

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On the context tree maximizing algorithm

Cited by 12 publications

References 1 publication

Inferring neuronal network functional connectivity with directed information

Inferring neuronal network functional connectivity with directed information

From the Entropy to the Statistical Structure of Spike Trains

Inferring functional connectivity through graphical directed information

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