Stochastic Syncing in Sinusoidally Driven Atomic Orbital Memory

Stochastically fluctuating multiwell systems are a promising route toward physical implementations of energy-based machine learning and neuromorphic hardware. One of the challenges is finding tunable material platforms that exhibit such multiwell behavior and understanding how complex dynamic input signals influence their stochastic response. One such platform is the recently discovered atomic Boltzmann machine, where each stochastic unit is represented by a binary orbital memory state of an individual atom. Here, we investigate the stochastic response of binary orbital memory states to sinusoidal input voltages. Using scanning tunneling microscopy, we investigated orbital memory derived from individual Fe and Co atoms on black phosphorus. We quantify the state residence times as a function of various input parameters such as frequency, amplitude, and offset voltage. The state residence times for both species, when driven by a sinusoidal signal, exhibit synchronization that can be quantitatively modeled by a Poisson process based on the switching rates in the absence of a sinusoidal signal. For individual Fe atoms, we also observe a frequency-dependent response of the state favorability, which can be tuned by the input parameters. In contrast to Fe, there is no significant frequency dependence in the state favorability for individual Co atoms. Based on the Poisson model, the difference in the response of the state favorability can be traced to the difference in the voltage-dependent switching rates of the two different species. This platform provides a tunable way to induce population changes in stochastic systems and provides a foundation toward understanding driven stochastic multiwell systems.

Postoperative Delirium After Intracranial Surgery: A Retrospective Cohort Study

BACKGROUND

The clinical relevance of postoperative delirium (POD) in neurosurgery remains unclear and should be investigated because these patients are vulnerable. Hence, we investigated the impact of POD, by means of incidence and health outcomes, and identified independent risk factors.

METHODS

Adult patients undergoing an intracranial surgical procedure in the Erasmus Medical Center Rotterdam between June 2017 and September 2020 were retrospectively included. POD incidence, defined by a Delirium Observation Screening Scale (DOSS) ≥3 or antipsychotic treatment for delirium within 5 days after surgery, was calculated. Logistic regression analysis on the full data set was conducted for the multivariable risk factor and health outcome analyses.

RESULTS

After including 2901 intracranial surgical procedures, POD was present in 19.4% with a mean onset in days of 2.62 (standard deviation, 1.22) and associated with more intensive care unit admissions and more discharge toward residential care. Onset of POD was not associated with increased length of hospitalization or mortality. We identified several independent nonmodifiable risk factors such as age, preexisting memory problems, emergency operations, craniotomy compared with burr-hole surgery, and severe blood loss. Moreover, we identified modifiable risk factors such as low preoperative potassium and opioid and dexamethasone administration.

CONCLUSIONS

Our POD incidence rates and correlation with more intensive care unit admission and discharge toward residential care suggest a significant impact of POD on neurosurgical patients. We identified several modifiable and nonmodifiable risk factors, which shed light on the pathophysiologic mechanisms of POD in this cohort and could be targeted for future intervention studies.

OS10.3.A Predicting delirium after craniotomy in neuro-oncology

BACKGROUND

Post-operative delirium (POD) is a frequent and severe complication after neurosurgical operations. Good prediction of POD after craniotomy in neuro-oncologic patients is important to install prophylactic measures, increase recognition and apply early treatment. Hence, we compared logistic regression with machine learning to build an accurate predictive model in a large dataset.

MATERIAL AND METHODS

POD was defined in case of a Delirium Observation Scale (DOS) ≥ 3 or start of antipsychotic treatment for delirium within 10 days after surgery. Adult patients undergoing a craniotomy for a neuro-oncologic disease in the Erasmus Medical Centre in Rotterdam were retrospectively included. The cohort was split into a training (75%), after three-fold cross validation, and test set (25%). Logistic regression and Lasso Elastic-Net Regularized Generalized Linear Models (GLMNet) were trained based on 19 pre- and intra-operative features and risk factors were identified based on the superior model.

RESULTS

We included 1025 neuro-oncologic craniotomies between June 2017 and September 2020. Overall incidence of POD was 18.6% (95%CI 17.4–19.8). Compared to logistic regression, Lasso GLMNet performed superior (AUC 0.73 vs. 0.76) based on the optimal tuning parameters (α=1, λ=0.014). Several non-modifiable risk factors such as age (OR1.01), prior delirium (OR1.04), memory problems (OR1.12), surgery duration (OR1.01) and modifiable risk factors, such as low potassium (OR0.97) levels and opioid administration (OR1.03), were identified.

CONCLUSION

POD is a frequent complication after craniotomy in neuro-oncologic patients. Lasso GLMNet was useful in predicting POD in this cohort. Validation in a prospective cohort of this model should be applied to further evaluate its value in diminishing POD.

An atomic Boltzmann machine capable of self-adaption

The quest to implement machine learning algorithms in hardware has focused on combining various materials, each mimicking a computational primitive, to create device functionality. Ultimately, these piecewise approaches limit functionality and efficiency, while complicating scaling and on-chip learning, necessitating new approaches linking physical phenomena to machine learning models. Here, we create an atomic spin system that emulates a Boltzmann machine directly in the orbital dynamics of one well-defined material system. Utilizing the concept of orbital memory based on individual cobalt atoms on black phosphorus, we fabricate the prerequisite tuneable multi-well energy landscape by gating patterned atomic ensembles using scanning tunnelling microscopy. Exploiting the anisotropic behaviour of black phosphorus, we realize plasticity with multi-valued and interlinking synapses that lead to tuneable probability distributions. Furthermore, we observe an autonomous reorganization of the synaptic weights in response to external electrical stimuli, which evolves at a different time scale compared to neural dynamics. This self-adaptive architecture paves the way for autonomous learning directly in atomic-scale machine learning hardware.

Bayesian neural networks with variable selection for prediction of genotypic values

BACKGROUND

Estimating the genetic component of a complex phenotype is a complicated problem, mainly because there are many allele effects to estimate from a limited number of phenotypes. In spite of this difficulty, linear methods with variable selection have been able to give good predictions of additive effects of individuals. However, prediction of non-additive genetic effects is challenging with the usual prediction methods. In machine learning, non-additive relations between inputs can be modeled with neural networks. We developed a novel method (NetSparse) that uses Bayesian neural networks with variable selection for the prediction of genotypic values of individuals, including non-additive genetic effects.

RESULTS

We simulated several populations with different phenotypic models and compared NetSparse to genomic best linear unbiased prediction (GBLUP), BayesB, their dominance variants, and an additive by additive method. We found that when the number of QTL was relatively small (10 or 100), NetSparse had 2 to 28 percentage points higher accuracy than the reference methods. For scenarios that included dominance or epistatic effects, NetSparse had 0.0 to 3.9 percentage points higher accuracy for predicting phenotypes than the reference methods, except in scenarios with extreme overdominance, for which reference methods that explicitly model dominance had 6 percentage points higher accuracy than NetSparse.

CONCLUSIONS

Bayesian neural networks with variable selection are promising for prediction of the genetic component of complex traits in animal breeding, and their performance is robust across different genetic models. However, their large computational costs can hinder their use in practice.

Role of Synaptic Stochasticity in Training Low-Precision Neural Networks

Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights naturally gives prominence to exponentially rare dense regions of solutions with a number of desirable properties such as robustness and good generalization performance, while typical solutions are isolated and hard to find. Binary solutions of the standard perceptron problem are obtained from a simple gradient descent procedure on a set of real values parametrizing a probability distribution over the binary synapses. Both analytical and numerical results are presented. An algorithmic extension that allows to train discrete deep neural networks is also investigated.

Learning Universal Computations with Spikes

Providing the neurobiological basis of information processing in higher animals, spiking neural networks must be able to learn a variety of complicated computations, including the generation of appropriate, possibly delayed reactions to inputs and the self-sustained generation of complex activity patterns, e.g. for locomotion. Many such computations require previous building of intrinsic world models. Here we show how spiking neural networks may solve these different tasks. Firstly, we derive constraints under which classes of spiking neural networks lend themselves to substrates of powerful general purpose computing. The networks contain dendritic or synaptic nonlinearities and have a constrained connectivity. We then combine such networks with learning rules for outputs or recurrent connections. We show that this allows to learn even difficult benchmark tasks such as the self-sustained generation of desired low-dimensional chaotic dynamics or memory-dependent computations. Furthermore, we show how spiking networks can build models of external world systems and use the acquired knowledge to control them.

Path integral control and state-dependent feedback

In this paper we address the problem of computing state-dependent feedback controls for path integral control problems. To this end we generalize the path integral control formula and utilize this to construct parametrized state-dependent feedback controllers. In addition, we show a relation between control and importance sampling: Better control, in terms of control cost, yields more efficient importance sampling, in terms of effective sample size. The optimal control provides a zero-variance estimate.

Quantitative analysis of task selection for brain-computer interfaces

OBJECTIVE

To assess quantitatively the impact of task selection in the performance of brain-computer interfaces (BCI).

APPROACH

We consider the task-pairs derived from multi-class BCI imagery movement tasks in three different datasets. We analyze for the first time the benefits of task selection on a large-scale basis (109 users) and evaluate the possibility of transferring task-pair information across days for a given subject.

MAIN RESULTS

Selecting the subject-dependent optimal task-pair among three different imagery movement tasks results in approximately 20% potential increase in the number of users that can be expected to control a binary BCI. The improvement is observed with respect to the best task-pair fixed across subjects. The best task-pair selected for each subject individually during a first day of recordings is generally a good task-pair in subsequent days. In general, task learning from the user side has a positive influence in the generalization of the optimal task-pair, but special attention should be given to inexperienced subjects.

SIGNIFICANCE

These results add significant evidence to existing literature that advocates task selection as a necessary step towards usable BCIs. This contribution motivates further research focused on deriving adaptive methods for task selection on larger sets of mental tasks in practical online scenarios.

Adaptive Multiclass Classification for Brain Computer Interfaces

We consider the problem of multiclass adaptive classification for brain-computer interfaces and propose the use of multiclass pooled mean linear discriminant analysis (MPMLDA), a multiclass generalization of the adaptation rule introduced by Vidaurre, Kawanabe, von Bünau, Blankertz, and Müller ( 2010 ) for the binary class setting. Using publicly available EEG data sets and tangent space mapping (Barachant, Bonnet, Congedo, & Jutten, 2012 ) as a feature extractor, we demonstrate that MPMLDA can significantly outperform state-of-the-art multiclass static and adaptive methods. Furthermore, efficient learning rates can be achieved using data from different subjects.

Emerging phenomena in neural networks with dynamic synapses and their computational implications

In this paper we review our research on the effect and computational role of dynamical synapses on feed-forward and recurrent neural networks. Among others, we report on the appearance of a new class of dynamical memories which result from the destabilization of learned memory attractors. This has important consequences for dynamic information processing allowing the system to sequentially access the information stored in the memories under changing stimuli. Although storage capacity of stable memories also decreases, our study demonstrated the positive effect of synaptic facilitation to recover maximum storage capacity and to enlarge the capacity of the system for memory recall in noisy conditions. Possibly, the new dynamical behavior can be associated with the voltage transitions between up and down states observed in cortical areas in the brain. We investigated the conditions for which the permanence times in the up state are power-law distributed, which is a sign for criticality, and concluded that the experimentally observed large variability of permanence times could be explained as the result of noisy dynamic synapses with large recovery times. Finally, we report how short-term synaptic processes can transmit weak signals throughout more than one frequency range in noisy neural networks, displaying a kind of stochastic multi-resonance. This effect is due to competition between activity-dependent synaptic fluctuations (due to dynamic synapses) and the existence of neuron firing threshold which adapts to the incoming mean synaptic input.

Irregular dynamics in up and down cortical states

Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a biologically motivated stochastic model of up and down transitions. The model is constituted by a simple bistable rate dynamics, where the synaptic current is modulated by short-term synaptic processes which introduce stochasticity and temporal correlations. A complete analysis of our model, both with mean-field approaches and numerical simulations, shows the appearance of complex transitions between high (up) and low (down) neural activity states, driven by the synaptic noise, with permanence times in the up state distributed according to a power-law. We show that the experimentally observed large fluctuation in up and down permanence times can be explained as the result of sufficiently noisy dynamical synapses with sufficiently large recovery times. Static synapses cannot account for this behavior, nor can dynamical synapses in the absence of noise.

Multipoint approximations of identity-by-descent probabilities for accurate linkage analysis of distantly related individuals

We propose an analytical approximation method for the estimation of multipoint identity by descent (IBD) probabilities in pedigrees containing a moderate number of distantly related individuals. We show that in large pedigrees where cases are related through untyped ancestors only, it is possible to formulate the hidden Markov model of the Lander-Green algorithm in terms of the IBD configurations of the cases. We use a first-order Markov approximation to model the changes in this IBD-configuration variable along the chromosome. In simulated and real data sets, we demonstrate that estimates of parametric and nonparametric linkage statistics based on the first-order Markov approximation are accurate. The computation time is exponential in the number of cases instead of in the number of meioses separating the cases. We have implemented our approach in the computer program ALADIN (accurate linkage analysis of distantly related individuals). ALADIN can be applied to general pedigrees and marker types and has the ability to model marker-marker linkage disequilibrium with a clustered-markers approach. Using ALADIN is straightforward: It requires no parameters to be specified and accepts standard input files.

Modeling linkage disequilibrium in exact linkage computations: a comparison of first-order Markov approaches and the clustered-markers approach

Recent studies have shown that linkage disequilibrium (LD) between single-nucleotide polymorphism (SNP) markers is widespread. Assuming linkage equilibrium has been shown to cause false positives in linkage studies where parental genotypes are not available. Therefore, linkage analysis methods that can deal with LD are required to accurately analyze SNP marker data sets. We compared three approaches to deal with LD between markers: 1) The clustered-markers approach implemented in the computer program MERLIN; 2) The standard hidden Markov model (HMM) multipoint model augmented with a first-order Markov model for the allele frequencies of the founders, in which we considered both a Bayesian and a maximum-likelihood implementation of this approach; 3) The 'independent' SNPs approach, i.e., removing SNPs from the data set until the remaining SNPs have low levels of LD.

We evaluated these approaches on the Illumina 6K SNP data set of affected sib-pairs of Problem 2. We found that the first-order Markov model was able to account for most of the strong LD in this data set. The difference between the Bayesian and maximum- likelihood implementation was small. An advantage of the first-order Markov model is that it does not require the user to specify parameters.

Competition between synaptic depression and facilitation in attractor neural networks

We study the effect of competition between short-term synaptic depression and facilitation on the dynamic properties of attractor neural networks, using Monte Carlo simulation and a mean-field analysis. Depending on the balance of depression, facilitation, and the underlying noise, the network displays different behaviors, including associative memory and switching of activity between different attractors. We conclude that synaptic facilitation enhances the attractor instability in a way that (1) intensifies the system adaptability to external stimuli, which is in agreement with experiments, and (2) favors the retrieval of information with less error during short time intervals.

Haplotype inference in general pedigrees using the cluster variation method

We present CVMHAPLO, a probabilistic method for haplotyping in general pedigrees with many markers. CVMHAPLO reconstructs the haplotypes by assigning in every iteration a fixed number of the ordered genotypes with the highest marginal probability, conditioned on the marker data and ordered genotypes assigned in previous iterations. CVMHAPLO makes use of the cluster variation method (CVM) to efficiently estimate the marginal probabilities. We focused on single-nucleotide polymorphism (SNP) markers in the evaluation of our approach. In simulated data sets where exact computation was feasible, we found that the accuracy of CVMHAPLO was high and similar to that of maximum-likelihood methods. In simulated data sets where exact computation of the maximum-likelihood haplotype configuration was not feasible, the accuracy of CVMHAPLO was similar to that of state of the art Markov chain Monte Carlo (MCMC) maximum-likelihood approximations when all ordered genotypes were assigned and higher when only a subset of the ordered genotypes was assigned. CVMHAPLO was faster than the MCMC approach and provided more detailed information about the uncertainty in the inferred haplotypes. We conclude that CVMHAPLO is a practical tool for the inference of haplotypes in large complex pedigrees.

Input-Driven Oscillations in Networks with Excitatory and Inhibitory Neurons with Dynamic Synapses

Previous work has shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons can reveal oscillatory activity. For example, Börgers and Kopell (2003) have shown that oscillations occur when the excitatory neurons receive a sufficiently large input. A constant drive to the excitatory neurons is sufficient for oscillatory activity. Other studies (Doiron, Chacron, Maler, Longtin, & Bastian, 2003; Doiron, Lindner, Longtin, Maler, & Bastian, 2004) have shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons reveal oscillatory activity only if the excitatory neurons receive correlated input, regardless of the amount of excitatory input. In this study, we show that these apparently contradictory results can be explained by the behavior of a single model operating in different regimes of parameter space. Moreover, we show that adding dynamic synapses in the inhibitory feedback loop provides a robust network behavior over a broad range of stimulus intensities, contrary to that of previous models. A remarkable property of the introduction of dynamic synapses is that the activity of the network reveals synchronized oscillatory components in the case of correlated input, but also reflects the temporal behavior of the input signal to the excitatory neurons. This allows the network to encode both the temporal characteristics of the input and the presence of spatial correlations in the input simultaneously.

Cavity approximation for graphical models

We reformulate the cavity approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our formulation, which allows for the treatment of multivalued variables, a further generalization to factor graphs with arbitrary order of interaction factors is explicitly carried out, and a message passing algorithm that implements the first order correction to the Bethe approximation is described. Furthermore, we investigate an implementation of the CA for pairwise interactions. In all cases considered we could confirm that CA[k] with increasing k provides a sequence of approximations of markedly increasing precision. Furthermore, in some cases we could also confirm the general expectation that the approximation of order k , whose computational complexity is O(N(k+1)) has an error that scales as 1/N(k+1) with the size of the system. We discuss the relation between this approach and some recent developments in the field.

Effects of fast presynaptic noise in attractor neural networks

We study both analytically and numerically the effect of presynaptic noise on the transmission of information in attractor neural networks. The noise occurs on a very short timescale compared to that for the neuron dynamics and it produces short-time synaptic depression. This is inspired in recent neurobiological findings that show that synaptic strength may either increase or decrease on a short timescale depending on presynaptic activity. We thus describe a mechanism by which fast presynaptic noise enhances the neural network sensitivity to an external stimulus. The reason is that, in general, presynaptic noise induces nonequilibrium behavior and, consequently, the space of fixed points is qualitatively modified in such a way that the system can easily escape from the attractor. As a result, the model shows, in addition to pattern recognition, class identification and categorization, which may be relevant to the understanding of some of the brain complex tasks.

The cluster variation method for efficient linkage analysis on extended pedigrees

Background

Computing exact multipoint LOD scores for extended pedigrees rapidly becomes infeasible as the number of markers and untyped individuals increase. When markers are excluded from the computation, significant power may be lost. Therefore accurate approximate methods which take into account all markers are desirable.

Methods

We present a novel method for efficient estimation of LOD scores on extended pedigrees. Our approach is based on the Cluster Variation Method, which deterministically estimates likelihoods by performing exact computations on tractable subsets of variables (clusters) of a Bayesian network. First a distribution over inheritances on the marker loci is approximated with the Cluster Variation Method. Then this distribution is used to estimate the LOD score for each location of the trait locus.

Results

First we demonstrate that significant power may be lost if markers are ignored in the multi-point analysis. On a set of pedigrees where exact computation is possible we compare the estimates of the LOD scores obtained with our method to the exact LOD scores. Secondly, we compare our method to a state of the art MCMC sampler. When both methods are given equal computation time, our method is more efficient. Finally, we show that CVM scales to large problem instances.

Conclusion

We conclude that the Cluster Variation Method is as accurate as MCMC and generally is more efficient. Our method is a promising alternative to approaches based on MCMC sampling.

Linear theory for control of nonlinear stochastic systems

We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of nonlinear control problems that can be formulated as a path integral and where the noise plays the role of temperature. The path integral displays symmetry breaking and there exists a critical noise value that separates regimes where optimal control yields qualitatively different solutions. The path integral can be computed efficiently by Monte Carlo integration or by a Laplace approximation, and can therefore be used to solve high dimensional stochastic control problems.

Coincidence detection with dynamic synapses

Recent experimental findings show that the efficacy of transmission in cortical synapses depends on presynaptic activity. In most neural models, however, the synapses are regarded as static entities where this dependence is not included. We study the role of activity-dependent (dynamic) synapses in neuronal responses to temporal patterns of afferent activity. Our results demonstrate that, for suitably chosen threshold values, dynamic synapses are capable of coincidence detection (CD) over a much larger range of frequencies than static synapses. The phenomenon appears to be valid for an integrate-and-fire as well as a Hodgkin-Huxley neuron and various types of CD tasks.

Associative memory with dynamic synapses

We have examined a role of dynamic synapses in the stochastic Hopfield-like network behavior. Our results demonstrate an appearance of a novel phase characterized by quick transitions from one memory state to another. The network is able to retrieve memorized patterns corresponding to classical ferromagnetic states but switches between memorized patterns with an intermittent type of behavior. This phenomenon might reflect the flexibility of real neural systems and their readiness to receive and respond to novel and changing external stimuli.

Storage capacity of attractor neural networks with depressing synapses

We compute the capacity of a binary neural network with dynamic depressing synapses to store and retrieve an infinite number of patterns. We use a biologically motivated model of synaptic depression and a standard mean-field approach. We find that at T=0 the critical storage capacity decreases with the degree of the depression. We confirm the validity of our main mean-field results with numerical simulations.

A tighter bound for graphical models

We present a method to bound the partition function of a Boltzmann machine neural network with any odd-order polynomial. This is a direct extension of the mean-field bound, which is first order. We show that the third-order bound is strictly better than mean field. Additionally, we derive a third-order bound for the likelihood of sigmoid belief networks. Numerical experiments indicate that an error reduction of a factor of two is easily reached in the region where expansion-based approximations are useful.

Nonmonotonic generalization bias of Gaussian mixture models

Theories of learning and generalization hold that the generalization bias, defined as the difference between the training error and the generalization error, increases on average with the number of adaptive parameters. This article, however, shows that this general tendency is violated for a gaussian mixture model. For temperatures just below the first symmetry breaking point, the effective number of adaptive parameters increases and the generalization bias decreases. We compute the dependence of the neural information criterion on temperature around the symmetry breaking. Our results are confirmed by numerical cross-validation experiments.

Mean field theory for asymmetric neural networks

The computation of mean firing rates and correlations is intractable for large neural networks. For symmetric networks one can derive mean field approximations using the Taylor series expansion of the free energy as proposed by Plefka. In asymmetric networks, the concept of free energy is absent. Therefore, it is not immediately obvious how to extend this method to asymmetric networks. In this paper we extend Plefka's approach to asymmetric networks and in fact to arbitrary probability distributions. The method is based on an information geometric argument. The method is illustrated for asymmetric neural networks with sequential dynamics. We compare our approximate analytical results with Monte Carlo simulations for a network of 100 neurons. It is shown that the quality of the approximation for asymmetric networks is as good as for symmetric networks.

Learning in higher order Boltzmann machines using linear response

We introduce an efficient method for learning and inference in higher order Boltzmann machines. The method is based on mean field theory with the linear response correction. We compute the correlations using the exact and the approximated method for a fully connected third order network of ten neurons. In addition, we compare the results of the exact and approximate learning algorithm. Finally we use the presented method to solve the shifter problem. We conclude that the linear response approximation gives good results as long as the couplings are not too large.

A development protocol for a diagnostic DSS

A diagnostic decision support system (DSS) in medicine is an expert system that aids the physician in the determination of the diagnosis based on findings and test results. The DSS can be divided into 2 different types of components: the knowledge component and the information system component. Methods from software engineering, knowledge engineering and management are combined into a dynamic development cycle that allows stepwise update and refinement. The development of the knowledge component is based on knowledge engineering. In the starting phases, rapid prototyping is convenient to determine and evaluate the specification. The content of the knowledge base is frequently updated during its life time. For this purpose, a knowledge modelling protocol is supplied.

Symmetry breaking and training from incomplete data with Radial Basis Boltzmann Machines

A Radial Basis Boltzmann Machine (RBBM) is a specialized Boltzmann Machine architecture that combines feed-forward mapping with probability estimation in the input space, and for which very efficient learning rules exist. The hidden representation of the network displays symmetry breaking as a function of the noise in the dynamics. Thus, generalization can be studied as a function of the noise in the neuron dynamics instead of as a function of the number of hidden units. We show that the RBBM can be seen as an elegant alternative of k-nearest neighbor, leading to comparable performance without the need to store all data. We show that the RBBM has good classification performance compared to the MLP. The main advantage of the RBBM is that simultaneously with the input-output mapping, a model of the input space is obtained which can be used for learning with missing values. We derive learning rules for the case of incomplete data, and show that they perform better on incomplete data than the traditional learning rules on a 'repaired' data set.

Advanced ovarian cancer. Neural network analysis to predict treatment outcome

BACKGROUND

Quantitative methods for the analysis of prognostic information are important in order to use this knowledge optimally. The neural network is a new quantitative method where the fundamental building blocks are units which can be likened to neurons, and weighted connections which can be likened to synapses. The more the hidden units, the more complex the patterns that can be learnt.

MATERIALS AND METHODS

Data from two Dutch studies in ovarian cancer were used to compare the previously reported survival rates predicted by the Cox's prognostic index with the prediction obtained by a neural network.

RESULTS

Both the Cox's analysis and the neural network agreed on residual tumour size, stage, and performance status as being important for survival. The neural network identified additional predictive factors such as place of diagnosis and age. As the Cox's prognostic index has not been tested to predict survival on an independent data set a comparison with the results obtained in the neural network test set could not be performed.

CONCLUSIONS

Neural networks perform at least as well as Cox's method for the prediction of survival, and prognostic factors can easily be identified. The analysis not only revealed the predictive power of some characteristics, but also the non-predictive power of the others.