Stimulus-dependent maximum entropy models of neural population codes

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. To be able to infer a model for this distribution from large-scale neural recordings, we introduce a stimulus-dependent maximum entropy (SDME) model---a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. The model is able to capture the single-cell response properties as well as the correlations in neural spiking due to shared stimulus and due to effective neuron-to-neuron connections. Here we show that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. As a result, the SDME model gives a more accurate account of single cell responses and in particular outperforms uncoupled models in reproducing the distributions of codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like surprise and information transmission in a neural population.Comment: 11 pages, 7 figure

Artificial Neural Networks in Financial Modelling

The study of Artificial Neural Networks derives from first trials to translate in mathematical models the principles of biological processing. An Artificial Neural Network deals with generating, in the fastest times, an implicit and predictive model of the evolution of a system. In particular, it derives from experience its ability to be able to recognize some behaviours or situations and to suggest how to take them into account. This work illustrates an approach to the use of Artificial Neural Networks for Financial Modelling; we aim to explore the structural differences (and implications) between one- and multi- agent and population models. In one-population models, ANNs are involved as forecasting devices with wealth-maximizing agents (in which agents make decisions so as to achieve an utility maximization following non-linear models to do forecasting), while in multipopulation models agents do not follow predetermined rules, but tend to create their own behavioural rules as market data are collected. In particular, it is important to analyze diversities between one-agent and one-population models; in fact, in building one-population model it is possible to illustrate the market equilibrium endogenously, which is not possible in one-agent model where all the environmental characteristics are taken as given and beyond the control of the single agent.artificial neural network, financial modelling, population model, market equilibrium.

Artificial Neural Networks in Finance Modelling

The study of Artificial Neural Networks derives from first trials to translate in mathematical models the principles of biological “processing”. An Artificial Neural Network deals with generating, in the fastest times, an implicit and predictive model of the evolution of a system. In particular, it derives from experience its ability to be able to recognize some behaviours or situations and to “suggest” how to take them into account. This work illustrates an approach to the use of Artificial Neural Networks for Financial Modelling; we aim to explore the structural differences (and implications) between one- and multi- agent and population models. In one-population models, ANNs are involved as forecasting devices with wealth-maximizing agents (in which agents make decisions so as to achieve an utility maximization following non- linear models to do forecasting), while in multi-population models agents do not follow predetermined rules, but tend to create their own behavioural rules as market data are collected. In particular, it is important to analyze diversities between one-agent and one-population models; in fact, in building one-population model it is possible to illustrate the market equilibrium endogenously, which is not possible in one-agent model where all the environmental characteristics are taken as given and beyond the control of the single agent. A particular application we aim to study is the one regarding “customer profiling”, in which (based on personal and direct relationships) the “buying” behaviour of each customer can be defined, making use of behavioural inference models such as the ones offered by Artificial Neural Networks much better than traditional statistical methodologies.Artificial Neural Network, Financial Modelling, Customer Profiling