Kernel methods make it relatively easy to define complex highdimensional feature spaces. This raises the question of how we can identify the relevant subspaces for a particular learning task. When two views of the same phenomenon are available kernel Canonical Correlation Analysis (KCCA) has been shown to be an effective preprocessing step that can improve the performance of classification algorithms such as the Support Vector Machine (SVM). This paper takes this observation to its logical conclusion and proposes a method that combines this two stage learning (KCCA followed by SVM) into a single optimisation termed SVM-2K. We present both experimental and theoretical analysis of the approach showing encouraging results and insights.

We prove the strongest known bound for the risk of hypotheses selected from the ensemble generated by running a learning algorithm incrementally on the training data. Our result is based on proof techniques that are remarkably different from the standard risk analysis based on uniform convergence arguments.

Neurons can have rapidly changing spike train statistics dictated by the underlying network excitability or behavioural state of an animal. To estimate the time course of such state dynamics from single-or multiple neuron recordings, we have developed an algorithm that maximizes the likelihood of observed spike trains by optimizing the state lifetimes and the state-conditional interspike-interval (ISI) distributions. Our nonparametric algorithm is free of time-binning and spike-counting problems and has the computational complexity of a Mixed-state Markov Model operating on a state sequence of length equal to the total number of recorded spikes. As an example, we fit a two-state model to paired recordings of premotor neurons in the sleeping songbird. We find that the two state-conditional ISI functions are highly similar to the ones measured during waking and singing, respectively.

In this paper, we show that the hinge loss can be interpreted as the neg-log-likelihood of a semi-parametric model of posterior probabilities. From this point of view, SVMs represent the parametric component of a semi-parametric model fitted by a maximum a posteriori estimation procedure. This connection enables to derive a mapping from SVM scores to estimated posterior probabilities. Unlike previous proposals, the suggested mapping is interval-valued, providing a set of posterior probabilities compatible with each SVM score. This framework offers a new way to adapt the SVM optimization problem to unbalanced classification, when decisions result in unequal (asymmetric) losses. Experiments show improvements over state-of-the-art procedures.

The network topology of neurons in the brain exhibits an abundance of feedback connections, but the computational function of these feedback connections is largely unknown. We present a computational theory that characterizes the gain in computational power achieved through feedback in dynamical systems with fading memory. It implies that many such systems acquire through feedback universal computational capabilities for analog computing with a non-fading memory. In particular, we show that feedback enables such systems to process time-varying input streams in diverse ways according to rules that are implemented through internal states of the dynamical system. In contrast to previous attractor-based computational models for neural networks, these flexible internal states are high-dimensional attractors of the circuit dynamics, that still allow the circuit state to absorb new information from online input streams. In this way one arrives at novel models for working memory, integration of evidence, and reward expectation in cortical circuits. We show that they are applicable to circuits of conductance-based Hodgkin-Huxley (HH) neurons with high levels of noise that reflect experimental data on invivo conditions.

We use the k-core decomposition to develop algorithms for the analysis of large scale complex networks. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by progressively focusing on their central cores. By using this strategy we develop a general visualization algorithm that can be used to compare the structural properties of various networks and highlight their hierarchical structure. The low computational complexity of the algorithm, O(n e), where n is the size of the network, and e is the number of edges, makes it suitable for the visualization of very large sparse networks. We show how the proposed visualization tool allows to find specific structural fingerprints of networks.

Fast and frugal heuristics are well studied models of bounded rationality. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-thebest searches for a sufficiently good ordering of cues (features) in a task where objects are to be compared lexicographically. We investigate the complexity of the problem of approximating optimal cue permutations for lexicographic strategies. We show that no efficient algorithm can approximate the optimum to within any constant factor, if P NP. We further consider a greedy approach for building lexicographic strategies and derive tight bounds for the performance ratio of a new and simple algorithm. This algorithm is proven to perform better than take-the-best.

We considered a gamma distribution of interspike intervals as a statistical model for neuronal spike generation. The model parameters consist of a time-dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons. Because the environment changes with time, observed data are generated from the time-dependent firing rate, which is an unknown function. A statistical model with an unknown function is called a semiparametric model, which is one of the unsolved problem in statistics and is generally very difficult to solve. We used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function. We analytically obtained an optimal estimating function for the shape parameter independent of the functional form of the firing rate. This estimation is efficient without Fisher information loss and better than maximum likelihood estimation.

Integrate-and-Fire-type models are usually criticized because of their simplicity. On the other hand, the Integrate-and-Fire model is the basis of most of the theoretical studies on spiking neuron models. Here, we develop a sequential procedure to quantitatively evaluate an equivalent Integrate-and-Fire-type model based on intracellular recordings of cortical pyramidal neurons. We find that the resulting effective model is sufficient to predict the spike train of the real pyramidal neuron with high accuracy. In in vivo-like regimes, predicted and recorded traces are almost indistinguishable and a significant part of the spikes can be predicted at the correct timing. Slow processes like spike-frequency adaptation are shown to be a key feature in this context since they are necessary for the model to connect between different driving regimes.

There has been a surge of interest in learning nonlinear manifold models to approximate high-dimensional data. Both for computational complexity reasons and for generalization capability, sparsity is a desired feature in such models. This usually means dimensionality reduction, which naturally implies estimating the intrinsic dimension, but it can also mean selecting a subset of the data to use as landmarks, which is especially important because many existing algorithms have quadratic complexity in the number of observations.