In this paper, a simple yet interpretable, probabilistic model is proposed for the prediction of reported case counts of infectious diseases. A spatio-temporal kernel is derived from training data to capture the typical interaction effects of reported infections across time and space, which provides insight into the dynamics of the spread of infectious diseases. Testing the model on a one-week-ahead prediction task for campylobacteriosis and rotavirus infections across Germany, as well as Lyme borreliosis across the federal state of Bavaria, shows that the proposed model performs on-par with the state-of-the-art hhh4 model. However, it provides a full posterior distribution over parameters in addition to model predictions, which aides in the assessment of the model. The employed Bayesian Monte Carlo regression framework is easily extensible and allows for incorporating prior domain knowledge, which makes it suitable for use on limited, yet complex datasets as often encountered in epidemiology.
A neuronal population is a computational unit that receives a multivariate, time-varying input signal and creates a related multivariate output. These neural signals are modeled as stochastic processes that transmit information in real time, subject to stochastic noise. In a stationary environment, where the input signals can be characterized by constant statistical properties, the systematic relationship between its input and output processes determines the computation carried out by a population. When these statistical characteristics unexpectedly change, the population needs to adapt to its new environment if it is to maintain stable operation. Based on the general concept of homeostatic plasticity, we propose a simple compositional model of adaptive networks that achieve invariance with regard to undesired changes in the statistical properties of their input signals and maintain outputs with well-defined joint statistics. To achieve such invariance, the network model combines two functionally distinct types of plasticity. An abstract stochastic process neuron model implements a generalized form of intrinsic plasticity that adapts marginal statistics, relying only on mechanisms locally confined within each neuron and operating continuously in time, while a simple form of Hebbian synaptic plasticity operates on synaptic connections, thus shaping the interrelation between neurons as captured by a copula function. The combined effect of both mechanisms allows a neuron population to discover invariant representations of its inputs that remain stable under a wide range of transformations (e.g., shifting, scaling and (affine linear) mixing). The probabilistic model of homeostatic adaptation on a population level as presented here allows us to isolate and study the individual and the interaction dynamics of both mechanisms of plasticity and could guide the future search for computationally beneficial types of adaptation.
In this paper, a simple yet interpretable, probabilistic model is proposed for the prediction of reported case counts of infectious diseases. A spatio-temporal kernel is derived from training data to capture the typical interaction effects of reported infections across time and space, which provides insight into the dynamics of the spread of infectious diseases. Testing the model on a one-week-ahead prediction task for campylobacteriosis and rotavirus infections across Germany, as well as Lyme borreliosis across the federal state of Bavaria, shows that the proposed model performs on-par with the state-of-the-art hhh4 model. However, it provides a full posterior distribution over parameters in addition to model predictions, which aides in the assessment of the model. The employed Bayesian Monte Carlo regression framework is easily extensible and allows for incorporating prior domain knowledge, which makes it suitable for use on limited, yet complex datasets as often encountered in epidemiology. Author summaryWhy was this study done?• Statistical modeling is invaluable to public-health policy as it helps understand and anticipate the dynamics of the spread of infectious diseases. The available training data is often limited and reported with a low spatial and temporal resolution. This poses a challenge and makes it particularly important to incorporate domain knowledge and prior assumptions to guide the modeling process.• In order to evaluate the trustworthiness and reliability of a model's predictions, it is crucial to be able to interpret the model and quantify the model uncertainty.• To address this, we develop an interpretable model that uses Bayesian inference (rather than commonly used maximum likelihood estimation) and provides a probability distribution over inferred parameters.• We develop and test a single probabilistic model that learns to predict the number of weekly case counts for three different diseases (campylobacteriosis, rotaviral enteritis and Lyme borreliosis) at the county level one week ahead of time.• We employ a Bayesian Monte Carlo regression approach that provides an estimate of the full probability distribution over inferred parameters as well as model predictions.• The model learns an interpretable spatio-temporal kernel that captures typical interactions between infection cases of the tested diseases.• The predictive performance of our model compares favorably with a contemporary reference model for all diseases tested.What do these findings mean?• Interpretable predictive models can be applied to surveillance data to gain insights into the dynamics of infectious diseases.• Probabilistic modeling approaches provide a suitable framework for many challenges of working with epidemiological data. Public-health agencies have the responsibility to detect, prevent and control infections in 2 the population. In Germany, the Robert Koch Institute collects a wide range of factors, 3 such as location, age, gender, pathogen, and further specifics, of laboratory confirmed 4 cases for approximately ...
The brain constantly processes information encoded in temporal sequences of spiking activity. This sequential activity emerges from sensory inputs as well as from the brain's own recurrent connectivity and spans multiple dynamically changing timescales. Decoding the temporal order of spiking activity across these varying timescales is a critical function of the brain, but we do not yet understand its neural implementation. The problem is, that the passive dynamics of neural membrane potentials occur on a short millisecond timescale, whereas many cognitive tasks require the integration of information across much slower behavioral timescales. However, actively generated dendritic plateau potentials do occur on such longer timescales, and their essential role for many aspects of cognition has been firmly established by recent experiments. Here, we build on these discoveries and propose a new model of neural computation that emerges from the interaction of localized plateau potentials across a functionally compartmentalized dendritic tree. We show how this interaction offers a robust solution to the timing invariant detection and processing of sequential spike patterns in single neurons. Stochastic synaptic transmission complements the deterministic all-or-none plateau process and improves information transmission by allowing ensembles of neurons to produce graded responses to continuous combinations of features. We found that networks of such neurons can solve highly complex sequence detection tasks by breaking down long inputs into sequences of shorter, random features that can be classified reliably. These results suggest that active dendritic processes are fundamental to neural computation.
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