In fact, for many of the kernels used (not the polynomial kernels) like Gaussian rbf-kernels it can be shown [6] that SV machines are universal approximators. While this is advantageous in general, parametric models are useful techniques in their own right. Especially if one happens to have additional knowledge about the problem, it would be unwise not to take advantage of it.

We introduce a novel framework for simultaneous structure and parameter learning in hidden-variable conditional probability models, based on an entropic prior and a solution for its maximum a posteriori (MAP) estimator. The MAP estimate minimizes uncertainty in all respects: cross-entropy between model and data; entropy of the model; entropy of the data's descriptive statistics. Iterative estimation extinguishes weakly supported parameters, compressing and sparsifying the model. Trimming operators accelerate this process by removing excess parameters and, unlike most pruning schemes, guarantee an increase in posterior probability. Entropic estimation takes a overcomplete random model and simplifies it, inducing the structure of relations between hidden and observed variables. Applied to hidden Markov models (HMMs), it finds a concise finite-state machine representing the hidden structure of a signal. We entropically model music, handwriting, and video time-series, and show that the resulting models are highly concise, structured, predictive, and interpretable: Surviving states tend to be highly correlated with meaningful partitions of the data, while surviving transitions provide a low-perplexity model of the signal dynamics.

Visually-guided arm reaching movements are produced by distributed neural networks within parietal and frontal regions of the cerebral cortex. Experimental data indicate that (I) single neurons in these regions are broadly tuned to parameters of movement; (2) appropriate commands are elaborated by populations of neurons; (3) the coordinated action of neurons canbe visualized using a neuronal population vector (NPV). However, theNPV provides only a rough estimate of movement parameters (direction, velocity) and may even fail to reflect the parameters of movement whenarm posture is changed. We designed a model of the cortical motor command to investigate the relation between the desired direction of the movement, the actual direction of movement and the direction of the NPV in motor cortex. The model is a two-layer self-organizing neural network which combines broadly-tuned (muscular) proprioceptive and (cartesian) visual information to calculate (angular) motor commands for the initial part of the movement of a two-link arm.

Structure in a visual scene can be described at many levels of granularity. Ata coarse level, the scene is composed of objects; at a finer level, each object is made up of parts, and the parts of subparts. In this work, I propose a simple principle by which such hierarchical structure can be extracted from visual scenes: Regularity in the relations among different parts of an object is weaker than in the internal structure of a part. This principle can be applied recursively to define part-whole relationships among elements in a scene. The principle does not make use of object models, categories, or other sorts of higher-level knowledge; rather, part-whole relationships can be established based on the statistics of a set of sample visual scenes. I illustrate with a model that performs unsupervised decompositionof simple scenes. The model can account for the results from a human learning experiment on the ontogeny of partwhole relationships.

W is often taken to be diagonal, but if we allow W to be a general positive definite matrix which can be tuned on the basis of training data, then an eigen-analysis of W shows that we are effectively creating hidden features, where the dimensionality of the hidden-feature space is determined by the data. We demonstrate the superiority of predictions usi ng the general matrix over those based on a diagonal matrix on two test problems.

The learning of many visual perceptual tasks has been shown to be specific to practiced stimuli, while new stimuli require re-Iearning from scratch. Here we demonstrate generalization using a novel paradigm in motion discrimination where learning has been previously shown to be specific. We trained subjects to discriminate the directions of moving dots, and verified the previous results that learning does not transfer from the trained direction to a new one. However, by tracking the subjects' performance across time in the new direction, we found that their rate of learning doubled. Therefore, learning generalized in a task previously considered too difficult for generalization.

AR-NNs are a natural generalization of the classic linear autoregressive AR(p) process (2) See, e.g., Brockwell & Davis (1987) for a comprehensive introduction into AR and ARMA (autoregressive moving average) models.

We seek the scene interpretation that best explains image data. For example, we may want to infer the projected velocities (scene) which best explain two consecutive image frames (image).

We consider recurrent analog neural nets where each gate is subject to Gaussian noise, or any other common noise distribution whose probability density function is nonzero on a large set.

Computer animation through the numerical simulation of physics-based graphics models offers unsurpassed realism, but it can be computationally demanding. This paper demonstrates the possibility of replacing the numerical simulation of nontrivial dynamic models with a dramatically more efficient "NeuroAnimator" that exploits neural networks. NeuroAnimators are automatically trained off-line to emulate physical dynamics through the observation of physics-based models in action. Depending on the model, its neural network emulator can yield physically realistic animation one or two orders of magnitude faster than conventional numerical simulation. We demonstrate NeuroAnimators for a variety of physics-based models.