We describe a hierarchical compositional system for detecting deformable objects in images. Objects are represented by graphical models. The algorithm uses a hierarchical tree where the root of the tree corresponds to the full object and lower-level elements of the tree correspond to simpler features.

Recent neurophysiological evidence suggests the ability to interpret biological motion is facilitated by a neuronal "mirror system" which maps visual inputs to the pre-motor cortex. If the common architecture and circuitry of the cortices is taken to imply a common computation across multiple perceptual and cognitive modalities, this visual-motor interaction might be expected to have a unified computational basis. Two essential tasks underlying such visual-motor cooperation are shown here to be simply expressed and directly solved as transformation-discovery inverse problems: (a) discriminating and determining the pose of a primed 3D object in a real-world scene, and (b) interpreting the 3D configuration of an articulated kinematic object in an image. The recently developed map-seeking method provides a mathematically tractable, cortically-plausible solution to these and a variety of other inverse problems which can be posed as the discovery of a composition of transformations between two patterns. The method relies on an ordering property of superpositions and on decomposition of the transformation spaces inherent in the generating processes of the problem. 1 Introduction A variety of "brain tasks" can be tersely posed as transformation-discovery problems.

We present an infinite mixture model in which each component comprises a multivariate Gaussian distribution over an input space, and a Gaussian Process model over an output space. Our model is neatly able to deal with non-stationary covariance functions, discontinuities, multimodality and overlapping output signals. The work is similar to that by Rasmussen and Ghahramani [1]; however, we use a full generative model over input and output space rather than just a conditional model. This allows us to deal with incomplete data, to perform inference over inverse functional mappings as well as for regression, and also leads to a more powerful and consistent Bayesian specification of the effective'gating network' for the different experts.

We present a conditional temporal probabilistic framework for reconstructing 3Dhuman motion in monocular video based on descriptors encoding image silhouette observations. For computational efficiency we restrict visual inference to low-dimensional kernel induced nonlinear state spaces. Our methodology (kBME) combines kernel PCA-based nonlinear dimensionality reduction (kPCA) and Conditional Bayesian Mixture of Experts (BME) in order to learn complex multivalued predictors betweenobservations and model hidden states. This is necessary for accurate, inverse, visual perception inferences, where several probable, distant3D solutions exist due to noise or the uncertainty of monocular perspectiveprojection. Low-dimensional models are appropriate because many visual processes exhibit strong nonlinear correlations in both the image observations and the target, hidden state variables. The learned predictors are temporally combined within a conditional graphical modelin order to allow a principled propagation of uncertainty. We study several predictors and empirically show that the proposed algorithm positivelycompares with techniques based on regression, Kernel Dependency Estimation (KDE) or PCA alone, and gives results competitive tothose of high-dimensional mixture predictors at a fraction of their computational cost. We show that the method successfully reconstructs the complex 3D motion of humans in real monocular video sequences.

Long-distance language modeling is important not only in speech recognition and machine translation, but also in high-dimensional discrete sequence modeling in general.

We extend a previously developed Bayesian framework for perception to account for sensory adaptation. We first note that the perceptual effects of adaptation seems inconsistent with an adjustment of the internally represented prior distribution. Instead, we postulate that adaptation increases the signal-to-noise ratio of the measurements by adapting the operational range of the measurement stage to the input range. We show that this changes the likelihood function in such a way that the Bayesian estimator model can account for reported perceptual behavior. In particular, we compare the model's predictions to human motion discrimination data and demonstrate that the model accounts for the commonly observed perceptual adaptation effects of repulsion and enhanced discriminability.

We measure the ability of human observers to predict the next datum in a sequence that is generated by a simple statistical process undergoing change at random points in time. Accurate performance in this task requires the identification of changepoints. We assess individual differences between observers both empirically, and using two kinds of models: a Bayesian approach for change detection and a family of cognitively plausible fast and frugal models. Some individuals detect too many changes and hence perform sub-optimally due to excess variability. Other individuals do not detect enough changes, and perform sub-optimally because they fail to notice short-term temporal trends.

The problem of computing a resample estimate for the reconstruction error in PCA is reformulated as an inference problem with the help of the replica method. Using the expectation consistent (EC) approximation, the intractable inference problem can be solved efficiently using only two variational parameters. A perturbative correction to the result is computed and an alternative simplified derivation is also presented.

We consider approximate value iteration with a parameterized approximator in which the state space is partitioned and the optimal cost-to-go function over each partition is approximated by a constant. We establish performance loss bounds for policies derived from approximations associated with fixed points. These bounds identify benefits to having projection weights equal to the invariant distribution of the resulting policy. Such projection weighting leads to the same fixed points as TD(0). Our analysis also leads to the first performance loss bound for approximate value iteration with an average cost objective.

We present a model of edge and region grouping using a conditional random field built over a scale-invariant representation of images to integrate multiple cues. Our model includes potentials that capture low-level similarity, mid-level curvilinear continuity and high-level object shape. Maximum likelihood parameters for the model are learned from human labeled groundtruth on a large collection of horse images using belief propagation. Using held out test data, we quantify the information gained by incorporating generic mid-level cues and high-level shape.