Recent work has examined the estimation of models of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a noisy, leaky, integrate-and-fire mechanism with a spike-dependent aftercurrent. This model is a biophysically plausible alternative to models with Poisson (memory-less) spiking, and has been shown to effectively reproduce various spiking statistics of neurons in vivo. However, the problem of estimating the model from extracellular spike train data has not been examined in depth. We formulate the problem in terms of maximum likelihood estimation, and show that the computational problem of maximizing the likelihood is tractable.

Figure l(Dl-Gl)* depict some of the main STDP findings/ of which the best-investigated are shown in figure l(Dl;El), and are variants of based a'standard' STDP rule. Earlier work considered rate-based rather than spike temporal rules, and so we adopt the broader term'time dependent plasticity' or TDP. Note the strong temporal asymmetry in both the standard rules. Although the theoretical studies have provided us with excellent tools for modeling the detailed consequences of different time-dependent rules, and understanding characteristics such as long-run stability and the relationship with non-temporal learning rules such as BCM,6 specifically computational ideas about TDP are rather thinner on the ground. Two main qualitative notions explored in various of the works cited above are that the temporal asymmetries in TDP rules are associated with causality or prediction. However, looking specifically at the standard STDP rules, models interested in prediction *We refer to graphs in this figure by row and column.

Dopamine exerts two classes of effect on the sustained neural activity in prefrontal cortex that underlies working memory. Direct release in the cortex increases the contrast of prefrontal neurons, enhancing the robustness of storage. Release of dopamine in the striatum is associated with salient stimuli and makes medium spiny neurons bistable; this modulation of the output of spiny neurons affects prefrontal cortex so as to indirectly gate access to working memory and additionally damp sensitivity to noise. Existing models have treated dopamine in one or other structure, or have addressed basal ganglia gating of working memory exclusive of dopamine effects. In this paper we combine these mechanisms and explore their joint effect. We model a memory-guided saccade task to illustrate how dopamine's actions lead to working memory that is selective for salient input and has increased robustness to distraction.

We employ an efficient method using Bayesian and linear classifiers for analyzing the dynamics of information in high-dimensional states of generic cortical microcircuit models. It is shown that such recurrent circuits of spiking neurons have an inherent capability to carry out rapid computations on complex spike patterns, merging information contained in the order of spike arrival with previously acquired context information.

A balanced network leads to contradictory constraints on memory models, as exemplified in previous work on accommodation of synfire chains. Here we show that these constraints can be overcome by introducing a'shadow' inhibitory pattern for each excitatory pattern of the model. This is interpreted as a doublebalance principle, whereby there exists both global balance between average excitatory and inhibitory currents and local balance between the currents carrying coherent activity at any given time frame. This principle can be applied to networks with Hebbian cell assemblies, leading to a high capacity of the associative memory. The number of possible patterns is limited by a combinatorial constraint that turns out to be P 0.06N within the specific model that we employ. This limit is reached by the Hebbian cell assembly network. To the best of our knowledge this is the first time that such high memory capacities are demonstrated in the asynchronous state of models of spiking neurons.

We present a unified view for online classification, regression, and uniclass problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the non-realizable case. A conversion of our main online algorithm to the setting of batch learning is also discussed. The end result is new algorithms and accompanying loss bounds for the hinge-loss.

We compute approximate analytical bootstrap averages for support vector classification using a combination of the replica method of statistical physics and the TAP approach for approximate inference. We test our method on a few datasets and compare it with exact averages obtained by extensive Monte-Carlo sampling.

We derive the limiting form of the eigenvalue spectrum for sample covariance matrices produced from non-isotropic data. For the analysis of standard PCA we study the case where the data has increased variance along a small number of symmetry-breaking directions. The spectrum depends on the strength of the symmetry-breaking signals and on a parameter α which is the ratio of sample size to data dimension. Results are derived in the limit of large data dimension while keeping α fixed. As α increases there are transitions in which delta functions emerge from the upper end of the bulk spectrum, corresponding to the symmetry-breaking directions in the data, and we calculate the bias in the corresponding eigenvalues. For kernel PCA the covariance matrix in feature space may contain symmetry-breaking structure even when the data components are independently distributed with equal variance. We show examples of phase-transition behaviour analogous to the PCA results in this case.

A general linear response method for deriving improved estimates of correlations in the variational Bayes framework is presented. Three applications are given and it is discussed how to use linear response as a general principle for improving mean field approximations.

We interpret nonnegative matrix factorization geometrically, as the problem of finding a simplicial cone which contains a cloud of data points and which is contained in the positive orthant. We show that under certain conditions, basically requiring that some of the data are spread across the faces of the positive orthant, there is a unique such simplicial cone. We give examples of synthetic image articulation databases which obey these conditions; these require separated support and factorial sampling. For such databases there is a generative model in terms of'parts' and NMF correctly identifies the'parts'. We show that our theoretical results are predictive of the performance of published NMF code, by running the published algorithms on one of our synthetic image articulation databases.