Online learning algorithms are typically fast, memory efficient, and simple to implement. However, many common learning problems fit more naturally in the batch learning setting. The power of online learning algorithms can be exploited in batch settings by using online-to-batch conversions techniques which build a new batch algorithm from an existing online algorithm. We first give a unified overview of three existing online-to-batch conversion techniques which do not use training data in the conversion process. We then build upon these data-independent conversions to derive and analyze data-driven conversions. Our conversions find hypotheses with a small risk by explicitly minimizing datadependent generalization bounds. We experimentally demonstrate the usefulness of our approach and in particular show that the data-driven conversions consistently outperform the data-independent conversions.

We present an efficient algorithm to actively select queries for learning the boundaries separating a function domain into regions where the function is above and below a given threshold. We develop experiment selection methods based on entropy, misclassification rate, variance, and their combinations, and show how they perform on a number of data sets. We then show how these algorithms are used to determine simultaneously valid 1 α confidence intervals for seven cosmological parameters. Experimentation shows that the algorithm reduces the computation necessary for the parameter estimation problem by an order of magnitude.

We address the problem of robust, computationally-efficient design of biological experiments. Classical optimal experiment design methods have not been widely adopted in biological practice, in part because the resulting designs can be very brittle if the nominal parameter estimates for the model are poor, and in part because of computational constraints. We present a method for robust experiment design based on a semidefinite programming relaxation. We present an application of this method to the design of experiments for a complex calcium signal transduction pathway, where we have found that the parameter estimates obtained from the robust design are better than those obtained from an "optimal" design.

Lasso regression tends to assign zero weights to most irrelevant or redundant features, and hence is a promising technique for feature selection. Its limitation, however, is that it only offers solutions to linear models. Kernel machines with feature scaling techniques have been studied for feature selection with nonlinear models. However, such approaches require to solve hard non-convex optimization problems. This paper proposes a new approach named the Feature Vector Machine (FVM). It reformulates the standard Lasso regression into a form isomorphic to SVM, and this form can be easily extended for feature selection with nonlinear models by introducing kernels defined on feature vectors. FVM generates sparse solutions in the nonlinear feature space and it is much more tractable compared to feature scaling kernel machines. Our experiments with FVM on simulated data show encouraging results in identifying the small number of dominating features that are non-linearly correlated to the response, a task the standard Lasso fails to complete.

It is well-known that everything that is learnable in the difficult online setting, where an arbitrary sequences of examples must be labeled one at a time, is also learnable in the batch setting, where examples are drawn independently from a distribution. We show a result in the opposite direction. We give an efficient conversion algorithm from batch to online that is transductive: it uses future unlabeled data. This demonstrates the equivalence between what is properly and efficiently learnable in a batch model and a transductive online model.

Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a non invasive method for brain neuronal fibers delineation. Here we show a modification for DT-MRI that allows delineation of neuronal fibers which are infiltrated by edema. We use the Muliple Tensor Variational (MTV) framework which replaces the diffusion model of DT-MRI with a multiple component model and fits it to the signal attenuation with a variational regularization mechanism. In order to reduce free water contamination we estimate the free water compartment volume fraction in each voxel, remove it, and then calculate the anisotropy of the remaining compartment. The variational framework was applied on data collected with conventional clinical parameters, containing only six diffusion directions. By using the variational framework we were able to overcome the highly ill posed fitting. The results show that we were able to find fibers that were not found by DT-MRI.

We investigate under what conditions a neuron can learn by experimentally supported rules for spike timing dependent plasticity (STDP) to predict the arrival times of strong "teacher inputs" to the same neuron. It turns out that in contrast to the famous Perceptron Convergence Theorem, which predicts convergence of the perceptron learning rule for a simplified neuron model whenever a stable solution exists, no equally strong convergence guarantee can be given for spiking neurons with STDP. But we derive a criterion on the statistical dependency structure of input spike trains which characterizes exactly when learning with STDP will converge on average for a simple model of a spiking neuron. This criterion is reminiscent of the linear separability criterion of the Perceptron Convergence Theorem, but it applies here to the rows of a correlation matrix related to the spike inputs. In addition we show through computer simulations for more realistic neuron models that the resulting analytically predicted positive learning results not only hold for the common interpretation of STDP where STDP changes the weights of synapses, but also for a more realistic interpretation suggested by experimental data where STDP modulates the initial release probability of dynamic synapses.

We present an algorithm for learning a quadratic Gaussian metric (Mahalanobis distance) for use in classification tasks. Our method relies on the simple geometric intuition that a good metric is one under which points in the same class are simultaneously near each other and far from points in the other classes. We construct a convex optimization problem whose solution generates such a metric by trying to collapse all examples in the same class to a single point and push examples in other classes infinitely far away. We show that when the metric we learn is used in simple classifiers, it yields substantial improvements over standard alternatives on a variety of problems. We also discuss how the learned metric may be used to obtain a compact low dimensional feature representation of the original input space, allowing more efficient classification with very little reduction in performance.

A model of bottom-up overt attention is proposed based on the principle of maximizing information sampled from a scene. The proposed operation is based on Shannon's self-information measure and is achieved in a neural circuit, which is demonstrated as having close ties with the circuitry existent in the primate visual cortex. It is further shown that the proposed saliency measure may be extended to address issues that currently elude explanation in the domain of saliency based models. Results on natural images are compared with experimental eye tracking data revealing the efficacy of the model in predicting the deployment of overt attention as compared with existing efforts. 1 Introduction There has long been interest in the nature of eye movements and fixation behavior following early studies by Buswell [I] and Yarbus [2]. However, a complete description of the mechanisms underlying these peculiar fixation patterns remains elusive.

Experimental data indicate that norepinephrine is critically involved in aspects of vigilance and attention. Previously, we considered the function of this neuromodulatory system on a time scale of minutes and longer, and suggested that it signals global uncertainty arising from gross changes in environmental contingencies. However, norepinephrine is also known to be activated phasically by familiar stimuli in welllearned tasks. Here, we extend our uncertainty-based treatment of norepinephrine to this phasic mode, proposing that it is involved in the detection and reaction to state uncertainty within a task. This role of norepinephrine can be understood through the metaphor of neural interrupts.