17,811 research outputs found
Information-theoretic methods for studying population codes
Population coding is the quantitative study of which algorithms or representations are used by the brain to combine together and evaluate the messages carried by different neurons. Here, we review an information-theoretic approach to population coding. We first discuss how to compute the information carried by simultaneously recorded neural populations, and in particular how to reduce the limited sampling bias which affects the calculation of information from a limited amount of experimental data.
We then discuss how to quantify the contribution of individual members of the population, or the interaction between them, to the overall information encoded by the considered group of neurons. We focus in particular on evaluating what is the contribution of interactions up to any given order to the total information. We illustrate this formalism with applications to simulated data with realistic neuronal statistics and to real simultaneous recordings of multiple spike trains.Instituto de Física La PlataInstituto de Investigaciones Fisicoquímicas Teóricas y Aplicada
Optimal Population Coding, Revisited
Cortical circuits perform the computations underlying rapid perceptual decisions within a few dozen milliseconds with each neuron emitting only a few spikes. Under these conditions, the theoretical analysis of neural population codes is challenging, as the most commonly used theoretical tool – Fisher information – can lead to erroneous conclusions about the optimality of different coding schemes. Here we revisit the effect of tuning function width and correlation structure on neural population codes based on ideal observer analysis in both a discrimination and reconstruction task. We show that the optimal tuning function width and the optimal correlation structure in both paradigms strongly depend on the available decoding time in a very similar way. In contrast, population codes optimized for Fisher information do not depend on decoding time and are severely suboptimal when only few spikes are available. In addition, we use the neurometric functions of the ideal observer in the classification task to investigate the differential coding properties of these Fisher-optimal codes for fine and coarse discrimination. We find that the discrimination error for these codes does not decrease to zero with increasing population size, even in simple coarse discrimination tasks. Our results suggest that quite different population codes may be optimal for rapid decoding in cortical computations than those inferred from the optimization of Fisher information
Visual Concepts and Compositional Voting
It is very attractive to formulate vision in terms of pattern theory
\cite{Mumford2010pattern}, where patterns are defined hierarchically by
compositions of elementary building blocks. But applying pattern theory to real
world images is currently less successful than discriminative methods such as
deep networks. Deep networks, however, are black-boxes which are hard to
interpret and can easily be fooled by adding occluding objects. It is natural
to wonder whether by better understanding deep networks we can extract building
blocks which can be used to develop pattern theoretic models. This motivates us
to study the internal representations of a deep network using vehicle images
from the PASCAL3D+ dataset. We use clustering algorithms to study the
population activities of the features and extract a set of visual concepts
which we show are visually tight and correspond to semantic parts of vehicles.
To analyze this we annotate these vehicles by their semantic parts to create a
new dataset, VehicleSemanticParts, and evaluate visual concepts as unsupervised
part detectors. We show that visual concepts perform fairly well but are
outperformed by supervised discriminative methods such as Support Vector
Machines (SVM). We next give a more detailed analysis of visual concepts and
how they relate to semantic parts. Following this, we use the visual concepts
as building blocks for a simple pattern theoretical model, which we call
compositional voting. In this model several visual concepts combine to detect
semantic parts. We show that this approach is significantly better than
discriminative methods like SVM and deep networks trained specifically for
semantic part detection. Finally, we return to studying occlusion by creating
an annotated dataset with occlusion, called VehicleOcclusion, and show that
compositional voting outperforms even deep networks when the amount of
occlusion becomes large.Comment: It is accepted by Annals of Mathematical Sciences and Application
Bootstrap methods for the empirical study of decision-making and information flows in social systems
Abstract: We characterize the statistical bootstrap for the estimation of information theoretic quantities from data, with particular reference to its use in the study of large-scale social phenomena. Our methods allow one to preserve, approximately, the underlying axiomatic relationships of information theory—in particular, consistency under arbitrary coarse-graining—that motivate use of these quantities in the first place, while providing reliability comparable to the state of the art for Bayesian estimators. We show how information-theoretic quantities allow for rigorous empirical study of the decision-making capacities of rational agents, and the time-asymmetric flows of information in distributed systems. We provide illustrative examples by reference to ongoing collaborative work on the semantic structure of the British Criminal Court system and the conflict dynamics of the contemporary Afghanistan insurgency
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
Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation
We investigate an encoding scheme for lossy compression of a binary symmetric
source based on simple spatially coupled Low-Density Generator-Matrix codes.
The degree of the check nodes is regular and the one of code-bits is Poisson
distributed with an average depending on the compression rate. The performance
of a low complexity Belief Propagation Guided Decimation algorithm is
excellent. The algorithmic rate-distortion curve approaches the optimal curve
of the ensemble as the width of the coupling window grows. Moreover, as the
check degree grows both curves approach the ultimate Shannon rate-distortion
limit. The Belief Propagation Guided Decimation encoder is based on the
posterior measure of a binary symmetric test-channel. This measure can be
interpreted as a random Gibbs measure at a "temperature" directly related to
the "noise level of the test-channel". We investigate the links between the
algorithmic performance of the Belief Propagation Guided Decimation encoder and
the phase diagram of this Gibbs measure. The phase diagram is investigated
thanks to the cavity method of spin glass theory which predicts a number of
phase transition thresholds. In particular the dynamical and condensation
"phase transition temperatures" (equivalently test-channel noise thresholds)
are computed. We observe that: (i) the dynamical temperature of the spatially
coupled construction saturates towards the condensation temperature; (ii) for
large degrees the condensation temperature approaches the temperature (i.e.
noise level) related to the information theoretic Shannon test-channel noise
parameter of rate-distortion theory. This provides heuristic insight into the
excellent performance of the Belief Propagation Guided Decimation algorithm.
The paper contains an introduction to the cavity method
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