This activity often manifests itself as dynamically coordinated sequences of action potentials. Since multiple electrode recordings are now a standard tool in neuroscience research, it is important to have a measure of such network-wide behavioral coordinationand information sharing, applicable to multiple neural spike train data. We propose a new statistic, informational coherence, which measures how much better one unit can be predicted by knowing the dynamical state of another. We argue informational coherence is a measure of association and shared information which is superior to traditional pairwisemeasures of synchronization and correlation. To find the dynamical states, we use a recently-introduced algorithm which reconstructs effectivestate spaces from stochastic time series.

Multiple visual cues are used by the visual system to analyze a scene; achromatic cues include luminance, texture, contrast and motion. Singlecell recordingshave shown that the mammalian visual cortex contains neurons that respond similarly to scene structure (e.g., orientation of a boundary), regardless of the cue type conveying this information. This paper shows that cue-invariant response properties of simple-and complex-type cells can be learned from natural image data in an unsupervised manner.In order to do this, we also extend a previous conceptual model of cue invariance so that it can be applied to model simple-and complex-cell responses. Our results relate cue-invariant response properties tonatural image statistics, thereby showing how the statistical modeling approachcan be used to model processing beyond the elemental response properties visual neurons. This work also demonstrates how to learn, from natural image data, more sophisticated feature detectors than those based on changes in mean luminance, thereby paving the way for new data-driven approaches to image processing and computer vision.

We study the problem of maximum entropy density estimation in the presence of known sample selection bias. We propose three bias correction approaches.The first one takes advantage of unbiased sufficient statistics which can be obtained from biased samples. The second one estimates thebiased distribution and then factors the bias out. The third one approximates the second by only using samples from the sampling distribution. Weprovide guarantees for the first two approaches and evaluate the performance of all three approaches in synthetic experiments and on real data from species habitat modeling, where maxent has been successfully appliedand where sample selection bias is a significant problem.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lankriet et al. (2004) considered conic combinations of kernel matrices for classification, leadingto a convex quadratically constraint quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations. Moreover,we generalize the formulation and our method to a larger class of problems, including regression and one-class classification. Experimentalresults show that the proposed algorithm helps for automatic model selection, improving the interpretability of the learning resultand works for hundred thousands of examples or hundreds of kernels to be combined.

We present a new connectionist model for constructive, intuitionistic modal reasoning. We use ensembles of neural networks to represent intuitionistic modaltheories, and show that for each intuitionistic modal program there exists a corresponding neural network ensemble that computes theprogram. This provides a massively parallel model for intuitionistic modalreasoning, and sets the scene for integrated reasoning, knowledge representation, and learning of intuitionistic theories in neural networks, since the networks in the ensemble can be trained by examples using standard neural learning algorithms.

We discuss two intrinsic weaknesses of the spectral graph partitioning method, both of which have practical consequences. The first is that spectral embeddings tend to hide the best cuts from the commonly used hyperplane rounding method. Rather than cleaning up the resulting suboptimal cutswith local search, we recommend the adoption of flow-based rounding. The second weakness is that for many "power law" graphs, the spectral method produces cuts that are highly unbalanced, thus decreasing theusefulness of the method for visualization (see figure 4(b)) or as a basis for divide-and-conquer algorithms. These balance problems, which occur even though the spectral method's quotient-style objective function does encourage balance, can be fixed with a stricter balance constraint thatturns the spectral mathematical program into an SDP that can be solved for million-node graphs by a method of Burer and Monteiro.

Separation of music signals is an interesting but difficult problem. It is helpful for many other music researches such as audio content analysis. In this paper, a new music signal separation method is proposed, which is based on harmonic structure modeling. The main idea of harmonic structure modelingis that the harmonic structure of a music signal is stable, so a music signal can be represented by a harmonic structure model. Accordingly, acorresponding separation algorithm is proposed. The main idea is to learn a harmonic structure model for each music signal in the mixture, and then separate signals by using these models to distinguish harmonic structures of different signals. Experimental results show that the algorithm can separate signals and obtain not only a very high Signalto-Noise Ratio(SNR) but also a rather good subjective audio quality.

There is a longstanding controversy on the site of the cerebellar motor learning. Different theories and experimental results suggest that either the cerebellar flocculus or the brainstem learns the task and stores the memory. With a dynamical system approach, we clarify the mechanism of transferring the memory generated in the flocculus to the brainstem and that of so-called savings phenomena. The brainstem learning must comply with a sort of Hebbian rule depending on Purkinje-cell activities. In contrast to earlier numerical models, our model is simple but it accommodates explanationsand predictions of experimental situations as qualitative features of trajectories in the phase space of synaptic weights, without fine parameter tuning.

We describe a generative model for handwritten digits that uses two pairs of opposing springs whose stiffnesses are controlled by a motor program. We show how neural networks can be trained to infer the motor programs required to accurately reconstruct the MNIST digits. The inferred motor programs can be used directly for digit classification, but they can also be used in other ways. By adding noise to the motor program inferred from an MNIST image we can generate a large set of very different images of the same class, thus enlarging the training set available to other methods. We can also use the motor programs as additional, highly informative outputs which reduce overfitting when training a feed-forward classifier.

Ridge regression can "fix" such problems numerically,