Bayesian networks in biomedicine and health-care.
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Classification of inhibitors of protein tyrosine phosphatase 1B using molecular structure based descriptors.
Loss of Protein Tyrosine Phosphatase 1B (PTP 1B) activity is known to enhance insulin sensitivity and resistance to weight gain. So potent and orally active PTP1B inhibitors could be potential pharmacological agents for the treatment of Type 2 diabetes and obesity. Classification models of PTP1B inhibitors are developed using a data set containing 128 compounds. Their inhibitory concentrations ranged from -1.59 to 1.68 log units. Initially a two-class (active, inactive) problem is tackled using a number of different methods. The data set was divided into active and inactive classes on the basis of inhibitory activity of the compounds. Molecular structure-based descriptors were calculated and used in the model development. Descriptors encoding the flexibility of the molecules were investigated. Classification models were generated using k-nearest neighbors (k-NN), linear discriminant analysis (LDA), and radial basis function neural network (RBFNN). All models are tested using an external prediction set, compounds not used anywhere during the model development procedure. A five-descriptor model is developed that produces a classification rate of 85.7% for an external prediction set. Then a three-class (active, moderately active, inactive) problem was explored. This time the data set was divided into highly active, moderate, and inactive classes on the basis of inhibitory activity of the compounds. The best classification rate achieved for an external prediction set was 85%. The classification rates achieved indicate that these models could serve as a screening mechanism, to identify potentially useful PTP 1B inhibitors. In addition multiple linear regression and computational neural network models are also developed for prediction of log IC(50) values. All QSAR models are tested using the same external prediction set.
Benzofurans↗
Digital VLSI algorithms and architectures for support vector machines.
In this paper, we propose some very simple algorithms and architectures for a digital VLSI implementation of Support Vector Machines. We discuss the main aspects concerning the realization of the learning phase of SVMs, with special attention on the effects of fixed-point math for computing and storing the parameters of the network. Some experiments on two classification problems are described that show the efficiency of the proposed methods in reaching optimal solutions with reasonable hardware requirements.
Algorithms↗
Computational constraints between retrieving the past and predicting the future, and the CA3-CA1 differentiation.
The differentiation between the CA3 and CA1 fields of the mammalian hippocampus is one of the salient traits that set it apart from the organization of the homologue medial wall in reptiles and birds. CA3 is widely thought to function as an autoassociator, but what do we need CA1 for? Based on evidence for a specific role of CA1 in temporal processing, I have explored the hypothesis that the differentiation between CA3 and CA1 may help solve a computational conflict. The conflict is between pattern completion, or integrating current sensory information on the basis of memory, and prediction, or moving from one pattern to the next in a stored sequence. CA3 would take care of the former, while CA1 would concentrate on the latter. I have found the hypothesis to be only weakly supported by neural network simulations. The conflict indeed exists, but two mechanisms that would relate more directly to a functional CA3-CA1 differentiation were found unable to produce genuine prediction. Instead, a simple mechanism based on firing frequency adaptation in pyramidal cells was found to be sufficient for prediction, with the degree of adaptation as the crucial parameter balancing retrieval with prediction. The differentiation between the architectures of CA3 and CA1 has a minor but significant, and positive, effect on this balance. In particular, for a fixed anticipatory interval in the model, it increases significantly the information content of hippocampal outputs. There may therefore be just a simple quantitative advantage in differentiating the connectivity of the two fields. Moreover, different degrees of adaptation in CA3 and CA1 cells were not found to lead to better performance, further undermining the notion of a functional dissociation.
Action Potentials↗
A connectionist model of left-right sound discrimination by the Mauthner system.
Artificial neural networks were used to explore the auditory function of the Mauthner system, the brainstem circuit in teleost fishes that initiates fast-start escape responses. The artificial neural networks were trained with backpropagation to assign connectivity and receptive fields in an architecture consistent with the known anatomy of the Mauthner system. Our first goal was to develop neurally specific hypotheses for how the Mauthner system discriminates right from left in the onset of a sound. Our model was consistent with the phase model for directional hearing underwater, the prevalent theory for sound source localization by fishes. Our second goal was to demonstrate how the neural mechanisms that permit sound localization according to the phase model can coexist with the mechanisms that permit the Mauthner system to discriminate between stimuli based on amplitude. Our results indicate possible computational roles for elements of the Mauthner system, which has provided us a theoretical context within which to consider past and future experiments on the cellular physiology. Thus, these findings demonstrate the potential significance of this approach in generating experimentally testable hypotheses for small systems of identified cells.
Acoustic Stimulation↗
Assignment of folds for proteins of unknown function in three microbial genomes.
Analysis of DNA sequences of several microbial genomes has revealed that a large fraction of predicted coding regions has no known protein function. Information about the three-dimensional folds of these proteins may provide insight into their possible functions. To predict the folds for protein sequences with little or no homology to proteins of known function, we used computational neural networks trained on the database of proteins with known three-dimensional structures. Global descriptions of protein sequences based on physical and structural properties of the constituent amino acids were used as inputs for neural networks. Of the 131, 498, and 868 protein sequences of unknown function from Mycoplasma genitalium, Haemophilus influenzae, and Methanococcus jannaschii (Fleischmann et al. 1995), we have made high-confidence fold assignments for 4, 10, and 19 sequences, respectively.
Amino Acid Sequence↗
A connectionist model of septohippocampal dynamics during conditioning: closing the loop.
Septohippocampal interactions determine how stimuli are encoded during conditioning. This study extends a previous neurocomputational model of corticohippocampal processing to incorporate hippocamposeptal feedback and examines how the presence or absence of such feedback affects learning in the model. The effects of septal modulation in conditioning were simulated by dynamically adjusting the hippocampal learning rate on the basis of how well the hippocampal system encoded stimuli. The model successfully accounts for changes in behavior and septohippocampal activity observed in studies of the acquisition, retention, and generalization of conditioned responses and accounts for the effects of septal disruption on conditioning. The model provides a computational, neurally based synthesis of prior learning theories that predicts changes in medial septal activity based on the novelty of stimulus events.
Animals↗
Decoding a temporal population code.
Encoding of sensory events in internal states of the brain requires that this information can be decoded by other neural structures. The encoding of sensory events can involve both the spatial organization of neuronal activity and its temporal dynamics. Here we investigate the issue of decoding in the context of a recently proposed encoding scheme: the temporal population code. In this code, the geometric properties of visual stimuli become encoded into the temporal response characteristics of the summed activities of a population of cortical neurons. For its decoding, we evaluate a model based on the structure and dynamics of cortical microcircuits that is proposed for computations on continuous temporal streams: the liquid state machine. Employing the original proposal of the decoding network results in a moderate performance. Our analysis shows that the temporal mixing of subsequent stimuli results in a joint representation that compromises their classification. To overcome this problem, we investigate a number of initialization strategies. Whereas we observe that a deterministically initialized network results in the best performance, we find that in case the network is never reset, that is, it continuously processes the sequence of stimuli, the classification performance is greatly hampered by the mixing of information from past and present stimuli. We conclude that this problem of the mixing of temporally segregated information is not specific to this particular decoding model but relates to a general problem that any circuit that processes continuous streams of temporal information needs to solve. Furthermore, as both the encoding and decoding components of our network have been independently proposed as models of the cerebral cortex, our results suggest that the brain could solve the problem of temporal mixing by applying reset signals at stimulus onset, leading to a temporal segmentation of a continuous input stream.
Action Potentials↗
Population coding and decoding in a neural field: a computational study.
This study uses a neural field model to investigate computational aspects of population coding and decoding when the stimulus is a single variable. A general prototype model for the encoding process is proposed, in which neural responses are correlated, with strength specified by a gaussian function of their difference in preferred stimuli. Based on the model, we study the effect of correlation on the Fisher information, compare the performances of three decoding methods that differ in the amount of encoding information being used, and investigate the implementation of the three methods by using a recurrent network. This study not only rediscovers main results in existing literatures in a unified way, but also reveals important new features, especially when the neural correlation is strong. As the neural correlation of firing becomes larger, the Fisher information decreases drastically. We confirm that as the width of correlation increases, the Fisher information saturates and no longer increases in proportion to the number of neurons. However, we prove that as the width increases further--wider than (sqrt)2 times the effective width of the turning function--the Fisher information increases again, and it increases without limit in proportion to the number of neurons. Furthermore, we clarify the asymptotic efficiency of the maximum likelihood inference (MLI) type of decoding methods for correlated neural signals. It shows that when the correlation covers a nonlocal range of population (excepting the uniform correlation and when the noise is extremely small), the MLI type of method, whose decoding error satisfies the Cauchy-type distribution, is not asymptotically efficient. This implies that the variance is no longer adequate to measure decoding accuracy.
Neural Networks, Computer↗
Spatio-temporal autoregressive models defined over brain manifolds.
Multivariate Autoregressive time series models (MAR) are an increasingly used tool for exploring functional connectivity in Neuroimaging. They provide the framework for analyzing the Granger Causality of a given brain region on others. In this article, we shall limit our attention to linear MAR models, in which a set of matrices of autoregressive coefficients Ak (k = 1,...,p) describe the dependence of present values of the image on lagged values of its past. Methods for estimating the Ak and determining which elements that are zero are well-known and are the basis for directed measures of influence. However, to date, MAR models are limited in the number of time series they can handle, forcing the a priori selection of a (small) number of voxels or regions of interest for analysis. This ignores the full spatio-temporal nature of functional brain data which are, in fact, collections of time series sampled over an underlying continuous spatial manifold the brain. A fully spatio-temporal MAR model (ST-MAR) is developed within the framework of functional data analysis. For spatial data, each row of a matrix Ak is the influence field of a given voxel. A Bayesian ST-MAR model is specified in which the influence fields for all voxels are required to vary smoothly over space. This requirement is enforced by penalizing the spatial roughness of the influence fields. This roughness is calculated with a discrete version of the spatial Laplacian operator. A massive reduction in dimensionality of computations is achieved via the singular value decomposition, making an interactive exploration of the model feasible. Use of the model is illustrated with an fMRI time series that was gathered concurrently with EEG in order to analyze the origin of resting brain rhythms.
Bayes Theorem↗
Application of a data-mining method based on Bayesian networks to lesion-deficit analysis.
Although lesion-deficit analysis (LDA) has provided extensive information about structure-function associations in the human brain, LDA has suffered from the difficulties inherent to the analysis of spatial data, i.e., there are many more variables than subjects, and data may be difficult to model using standard distributions, such as the normal distribution. We herein describe a Bayesian method for LDA; this method is based on data-mining techniques that employ Bayesian networks to represent structure-function associations. These methods are computationally tractable, and can represent complex, nonlinear structure-function associations. When applied to the evaluation of data obtained from a study of the psychiatric sequelae of traumatic brain injury in children, this method generates a Bayesian network that demonstrates complex, nonlinear associations among lesions in the left caudate, right globus pallidus, right side of the corpus callosum, right caudate, and left thalamus, and subsequent development of attention-deficit hyperactivity disorder, confirming and extending our previous statistical analysis of these data. Furthermore, analysis of simulated data indicates that methods based on Bayesian networks may be more sensitive and specific for detecting associations among categorical variables than methods based on chi-square and Fisher exact statistics.
Algorithms↗
Computation of inverse functions in a model of cerebellar and reflex pathways allows to control a mobile mechanical segment.
The command and control of limb movements by the cerebellar and reflex pathways are modeled by means of a circuit whose structure is deduced from functional constraints. One constraint is that fast limb movements must be accurate although they cannot be continuously controlled in closed loop by use of sensory signals. Thus, the pathways which process the motor orders must contain approximate inverse functions of the bio-mechanical functions of the limb and of the muscles. This can be achieved by means of parallel feedback loops, whose pattern turns out to be comparable to the anatomy of the cerebellar pathways. They contain neural networks able to anticipate the motor consequences of the motor orders, modeled by artificial neural networks whose connectivity is similar to that of the cerebellar cortex. These networks learn the direct biomechanical functions of the limbs and muscles by means of a supervised learning process. Teaching signals calculated from motor errors are sent to the learning sites, as, in the cerebellum, complex spikes issued from the inferior olive are conveyed to the Purkinje cells by climbing fibers. Learning rules are deduced by a differential calculation, as classical gradient rules, and they account for the long term depression which takes place in the dendritic arborizations of the Purkinje cells. Another constraint is that reflexes must not impede voluntary movements while remaining at any instant ready to oppose perturbations. Therefore, efferent copies of the motor orders are sent to the interneurones of the reflexes, where they cancel the sensory-motor consequences of the voluntary movements. After learning, the model is able to drive accurately, both in velocity and position, angular movements of a rod actuated by two pneumatic McKibben muscles. Reflexes comparable to the myotatic and tendinous reflexes, and stabilizing reactions comparable to the cerebellar sensory-motor reactions, reduce efficiently the effects of perturbing torques. These results allow to link the behavioral concepts of the equilibrium-point "lambda model" [J Motor Behav 18 (1986) 17] with anatomical and physiological features: gains of reflexes and sensori-motor reactions set the slope of the "invariant characteristic," and efferent copies set the "threshold of the stretch reflex." Thus, mathematical and physical laws account for the raison d'etre of the inhibitory nature of Purkinje cells and for the conspicuous anatomical pattern of the cerebellar pathways. These properties of these pathways allow to perform approximate inverse calculations after learning of direct functions, and insure also the coordination of voluntary and reflex motor orders.
Algorithms↗
Data mining of inputs: analysing magnitude and functional measures.
The problem of data encoding and feature selection for training back-propagation neural networks is well known. The basic principles are to avoid encrypting the underlying structure of the data, and to avoid using irrelevant inputs. This is not easy in the real world, where we often receive data which has been processed by at least one previous user. The data may contain too many instances of some class, and too few instances of other classes. Real data sets often include many irrelevant or redundant input fields. This paper examines the use of weight matrix analysis techniques and functional measures using two real (and hence noisy) data sets. The first part of this paper examines the use of the weight matrix of the trained neural network itself to determine which inputs are significant. A new technique is introduced and compared with two other techniques from the literature. We present our experience and results on some satellite data augmented by a terrain model. The task was to predict the forest supra-type based on the available information. A brute force technique eliminating randomly selected inputs was used to validate our approach. The second part of this paper examines the use of measures to determine the functional contribution of inputs to outputs. Inputs which include minor but unique information to the network are more significant than inputs with higher magnitude contribution but providing redundant information, which is also provided by another input. A comparison is made to sensitivity analysis, where the sensitivity of outputs to input perturbation is used as a measure of the significance of inputs. This paper presents a novel functional analysis of the weight matrix based on a technique developed for determining the behavioral significance of hidden neurons. This is compared with the application of the same technique to the training and test data. Finally, a novel aggregation technique is introduced.
Algorithms↗
Entorhinal cortex grid cells can map to hippocampal place cells by competitive learning.
'Grid cells' in the dorsocaudal medial entorhinal cortex (dMEC) are activated when a rat is located at any of the vertices of a grid of equilateral triangles covering the environment. dMEC grid cells have different frequencies and phase offsets. However, cells in the dentate gyrus (DG) and hippocampal area CA3 of the rodent typically display place fields, where individual cells are active over only a single portion of the space. In a model of the hippocampus, we have shown that the connectivity from the entorhinal cortex to the dentate granule cells could allow the dentate granule cells to operate as a competitive network to recode their inputs to produce sparse orthogonal representations, and this includes spatial pattern separation. In this paper we show that the same computational hypothesis can account for the mapping of EC grid cells to dentate place cells. We show that the learning in the competitive network is an important part of the way in which the mapping can be achieved. We further show that incorporation of a short term memory trace into the associative learning can help to produce the relatively broad place fields found in the hippocampus.
Action Potentials↗
A neural network simulation of the outgroup homogeneity effect.
This article presents a neural network simulation of the out-group homogeneity effect (OHE). The model is a feedback network with delta-rule learning that has been previously used to simulate other aspects of stereotype learning, as well as causal learning and reasoning, and human memory. This simulation achieves 2 goals: First, we show that the model could successfully simulate the OHE. We argue that this is due to the error-correcting nature of delta-rule learning. Second, we show that each of 5 aspects of the simulation influences the size of the OHE: (a) the ratio of in-group to out-group size, (b) the overall population size, (c) the learning rate, (d) the decay rate for weights, and (e) increased learning for extreme cases. The psychological relevance of these parameters and ways to study them are presented. Advantages of the model in terms of breadth of coverage for studying social cognitive phenomena are discussed.
Group Processes↗
Population coding in somatosensory cortex.
Computational analyses have begun to elucidate which components of somatosensory cortical population activity may encode basic stimulus features. Recent results from rat barrel cortex suggest that the essence of this code is not synergistic spike patterns, but rather the precise timing of single neuron's first post-stimulus spikes. This may form the basis for a fast, robust population code.
Action Potentials↗
Functional holography of recorded neuronal networks activity.
We present a new approach for analyzing multi-channel recordings, such as ECoG (electrocorticograph) recordings of cortical brain activity and of individual neuron dynamics, in cultured networks. The latter are used here to illustrate the method and its ability to discover hidden functional connectivity motifs in the recorded activity. The cultured networks are formed from dissociated mixtures of cortical neurons and glia-cells that are homogeneously spread over multi-electrode array for recording of the neuronal activity. Rich, spontaneous dynamical behavior is detected, marked by the formation of temporal sequences of synchronized bursting events (SBEs), partitioned into statistically distinguishable subgroups, each with its own characteristic spatio-temporal pattern of activity.In analogy with coherence connectivity networks for multi-location cortical recordings, we evaluated the inter-neuron correlation-matrix for each subgroup. Ordinarily such matrices are mapped onto a connectivity network between neuron positions in real space. In our functional holography, the correlations are normalized by the correlation distances Euclidian distances between the matrix columns. Then, we project the N-dimensional (for N channels) space spanned by the matrix of the normalized correlations, or correlation affinities, onto a corresponding 3D manifold (3D Cartesian space constructed by the three leading principal vectors of the principal component algorithm). The neurons are located by their principal eigenvalues and linked by their original (not normalized) correlations. By looking at these holograms, hidden causal motifs are revealed: each SBEs subgroup generates its characteristic connectivity diagram (network) in the 3D manifold, where the neuron locations and their links form simple structures. Moreover, the computed temporal ordering of neuron activity, when projected onto the connectivity diagrams, also exhibits simple patterns of causal propagation. We show that the method can expose functional connectivity motifs like the co-existence of subneuronal functional networks in the space of affinities. The method can be directly utilized to construct similar causal holograms for recorded brain activity. We expect that by doing so, hidden functional connectivity motifs with relevance to the understanding of brain activity might be discovered.
Animals↗
On the analysis and interpretation of inhomogeneous quadratic forms as receptive fields.
In this letter, we introduce some mathematical and numerical tools to analyze and interpret inhomogeneous quadratic forms. The resulting characterization is in some aspects similar to that given by experimental studies of cortical cells, making it particularly suitable for application to second-order approximations and theoretical models of physiological receptive fields. We first discuss two ways of analyzing a quadratic form by visualizing the coefficients of its quadratic and linear term directly and by considering the eigenvectors of its quadratic term. We then present an algorithm to compute the optimal excitatory and inhibitory stimuli--those that maximize and minimize the considered quadratic form, respectively, given a fixed energy constraint. The analysis of the optimal stimuli is completed by considering their invariances, which are the transformations to which the quadratic form is most insensitive, and by introducing a test to determine which of these are statistically significant. Next we propose a way to measure the relative contribution of the quadratic and linear term to the total output of the quadratic form. Furthermore, we derive simpler versions of the above techniques in the special case of a quadratic form without linear term. In the final part of the letter, we show that for each quadratic form, it is possible to build an equivalent two-layer neural network, which is compatible with (but more general than) related networks used in some recent articles and with the energy model of complex cells. We show that the neural network is unique only up to an arbitrary orthogonal transformation of the excitatory and inhibitory subunits in the first layer.
Action Potentials↗