We study the convergence and the rate of convergence of a local manifold learning algorithm: LTSA [13]. The main technical tool is the perturbation analysis on the linear invariant subspace that corresponds to the solution of LTSA. We derive a worst-case upper bound of errors for LTSA which naturally leads to a convergence result. We then derive the rate of convergence for LTSA in a special case.

Randomly connected recurrent neural circuits have proven to be very powerful models for online computations when a trained memoryless readout function is appended. Such Reservoir Computing (RC) systems are commonly used in two flavors: with analog or binary (spiking) neurons in the recurrent circuits. Previous work showed a fundamental difference between these two incarnations of the RC idea. The performance of a RC system built from binary neurons seems to depend strongly on the network connectivity structure. In networks of analog neurons such dependency has not been observed. In this article we investigate this apparent dichotomy in terms of the in-degree of the circuit nodes. Our analyses based amongst others on the Lyapunov exponent reveal that the phase transition between ordered and chaotic network behavior of binary circuits qualitatively differs from the one in analog circuits. This explains the observed decreased computational performance of binary circuits of high node in-degree. Furthermore, a novel mean-field predictor for computational performance is introduced and shown to accurately predict the numerically obtained results.

Neuroimaging datasets often have a very large number of voxels and a very small number of training cases, which means that overfitting of models for this data can become a very serious problem. Working with a set of fMRI images from a study on stroke recovery, we consider a classification task for which logistic regression performs poorly, even when L1-or L2-regularized. We show that much better discrimination can be achieved by fitting a generative model to each separate condition and then seeing which model is most likely to have generated the data. We compare discriminative training of exactly the same set of models, and we also consider convex blends of generative and discriminative training.

We consider the problem of estimating the graph structure associated with a Gaussian Markov random field (GMRF) from i.i.d.

The problem of support union recovery is to recover the subset of covariates that are active in at least one of the regression problems.

We explore a recently proposed mixture model approach to understanding interactions between conflicting sensory cues. Alternative model formulations, differing in their sensory noise models and inference methods, are compared based on their fit to experimental data. Heavy-tailed sensory likelihoods yield a better description of the subjects' response behavior than standard Gaussian noise models. We study the underlying cause for this result, and then present several testable predictions of these models.

Graph clustering methods such as spectral clustering are defined for general weighted graphs. In machine learning, however, data often is not given in form of a graph, but in terms of similarity (or distance) values between points. In this case, first a neighborhood graph is constructed using the similarities between the points and then a graph clustering algorithm is applied to this graph. In this paper we investigate the influence of the construction of the similarity graph on the clustering results. We first study the convergence of graph clustering criteria such as the normalized cut (Ncut) as the sample size tends to infinity. We find that the limit expressions are different for different types of graph, for example the r-neighborhood graph or the k-nearest neighbor graph. In plain words: Ncut on a kNN graph does something systematically different than Ncut on an r-neighborhood graph! This finding shows that graph clustering criteria cannot be studied independently of the kind of graph they are applied to. We also provide examples which show that these differences can be observed for toy and real data already for rather small sample sizes.

Suppose we train an animal in a conditioning experiment. Can one predict how a given animal, under given experimental conditions, would perform the task? Since various factors such as stress, motivation, genetic background, and previous errors in task performance can influence animal behaviour, this appears to be a very challenging aim. Reinforcement learning (RL) models have been successful in modeling animal (and human) behaviour, but their success has been limited because of uncertainty as to how to set meta-parameters (such as learning rate, exploitation-exploration balance and future reward discount factor) that strongly influence model performance. We show that a simple RL model whose metaparameters are controlled by an artificial neural network, fed with inputs such as stress, affective phenotype, previous task performance, and even neuromodulatory manipulations, can successfully predict mouse behaviour in the "hole-box" - a simple conditioning task. Our results also provide important insights on how stress and anxiety affect animal learning, performance accuracy, and discounting of future rewards, and on how noradrenergic systems can interact with these processes.

We consider multi-label prediction problems with large output spaces under the assumption of output sparsity - that the target (label) vectors have small support. We develop a general theory for a variant of the popular error correcting output code scheme, using ideas from compressed sensing for exploiting this sparsity. The method can be regarded as a simple reduction from multi-label regression problems to binary regression problems. We show that the number of subproblems need only be logarithmic in the total number of possible labels, making this approach radically more efficient than others. We also state and prove robustness guarantees for this method in the form of regret transform bounds (in general), and also provide a more detailed analysis for the linear prediction setting.

In this theoretical contribution we provide mathematical proof that two of the most important classes of network learning - correlation-based differential Hebbian learning and reward-based temporal difference learning - are asymptotically equivalent when timing the learning with a local modulatory signal. This opens the opportunity to consistently reformulate most of the abstract reinforcement learning framework from a correlation based perspective that is more closely related to the biophysics of neurons.