We propose a new method for estimating intrinsic dimension of a dataset derived by applying the principle of maximum likelihood to the distances between close neighbors. We derive the estimator by a Poisson process approximation, assess its bias and variance theoretically andby simulations, and apply it to a number of simulated and real datasets. We also show it has the best overall performance compared with two other intrinsic dimension estimators.

We propose a new interpretation of spiking neurons as Bayesian integrators accumulatingevidence over time about events in the external world or the body, and communicating to other neurons their certainties about these events. In this model, spikes signal the occurrence of new information, i.e.what cannot be predicted from the past activity. As a result, firing statistics are close to Poisson, albeit providing a deterministic representation ofprobabilities. We proceed to develop a theory of Bayesian inference in spiking neural networks, recurrent interactions implementing avariant of belief propagation. Many perceptual and motor tasks performed by the central nervous system are probabilistic, andcan be described in a Bayesian framework [4, 3].

These models have been able to account for human responses in tasks ranging from 3D shape perception t0 Visuomotor control.

Choice-based conjoint analysis builds models of consumer preferences over products with answers gathered in questionnaires. Our main goal is to bring tools from the machine learning community to solve this problem moreefficiently. Thus, we propose two algorithms to quickly and accurately estimate consumer preferences.

We present an extension to the Jojic and Frey (2001) layered sprite model which allows for layers to undergo affine transformations. This extension allows for affine object pose to be inferred whilst simultaneously learning theobject shape and appearance. Learning is carried out by applying an augmented variational inference algorithm which includes a global search over a discretised transform space followed by a local optimisation. Toaid correct convergence, we use bottom-up cues to restrict the space of possible affine transformations. We present results on a number of video sequences and show how the model can be extended to track an object whose appearance changes throughout the sequence.

We present a novel method for learning with Gaussian process regression ina hierarchical Bayesian framework. In a first step, kernel matrices on a fixed set of input points are learned from data using a simple and efficient EM algorithm. This step is nonparametric, in that it does not require a parametric form of covariance function. In a second step, kernel functions are fitted to approximate the learned covariance matrix using a generalized Nyström method, which results in a complex, data driven kernel. We evaluate our approach as a recommendation engine for art images, where the proposed hierarchical Bayesian method leads to excellent prediction performance.

It has been demonstrated that basic aspects of human visual motion perception arequalitatively consistent with a Bayesian estimation framework, where the prior probability distribution on velocity favors slow speeds. Here, we present a refined probabilistic model that can account for the typical trial-to-trial variabilities observed in psychophysical speed perception experiments. We also show that data from such experiments can be used to constrain both the likelihood and prior functions of the model. Specifically, we measured matching speeds and thresholds in a two-alternative forced choice speed discrimination task. Parametric fits to the data reveal that the likelihood function is well approximated by a LogNormal distribution with a characteristic contrast-dependent variance, andthat the prior distribution on velocity exhibits significantly heavier tails than a Gaussian, and approximately follows a power-law function.

We present a discriminative part-based approach for the recognition of object classes from unsegmented cluttered scenes. Objects are modeled as flexible constellations of parts conditioned on local observations found by an interest operator. For each object class the probability of a given assignment of parts to local features is modeled by a Conditional Random Field(CRF). We propose an extension of the CRF framework that incorporates hidden variables and combines class conditional CRFs into a unified framework for part-based object recognition. The parameters of the CRF are estimated in a maximum likelihood framework and recognition proceedsby finding the most likely class under our model. The main advantage of the proposed CRF framework is that it allows us to relax the assumption of conditional independence of the observed data (i.e.

We present a semi-parametric latent variable model based technique for density modelling, dimensionality reduction and visualization. Unlike previous methods, we estimate the latent distribution non-parametrically which enables us to model data generated by an underlying low dimensional, multimodaldistribution. In addition, we allow the components of latent variable models to be drawn from the exponential family which makes the method suitable for special data types, for example binary or count data. Simulations on real valued, binary and count data show favorable comparisonto other related schemes both in terms of separating different populations and generalization to unseen samples.

In this paper we propose a probabilistic model for online document clustering. Weuse nonparametric Dirichlet process prior to model the growing number of clusters, and use a prior of general English language model as the base distribution to handle the generation of novel clusters. Furthermore, cluster uncertainty is modeled with a Bayesian Dirichletmultinomial distribution.We use empirical Bayes method to estimate hyperparameters based on a historical dataset. Our probabilistic model is applied to the novelty detection task in Topic Detection and Tracking (TDT) and compared with existing approaches in the literature.