Object detection and multi-class image segmentation are two closely related tasks that can be greatly improved when solved jointly by feeding information from one task to the other [10, 11]. However, current state-of-the-art models use a separate representation for each task making joint inference clumsy and leaving the classification of many parts of the scene ambiguous. In this work, we propose a hierarchical region-based approach to joint object detection and image segmentation. Our approach simultaneously reasons about pixels, regions and objects in a coherent probabilistic model. Pixel appearance features allow us to perform well on classifying amorphous background classes, while the explicit representation of regions facilitate the computation of more sophisticated featuresnecessary for object detection. Importantly, our model gives a single unified description of the scene--we explain every pixel in the image and enforce global consistency between all random variables in our model. We run experiments on the challenging Street Scene dataset [2] and show significant improvementover state-of-the-art results for object detection accuracy.

Image representation based on image bases provides a framework for understanding neural representation of visual perception. A recent fMRI study has shown that arbitrary contrast-defined visual images can be reconstructed from fMRI activity patterns using a combination of multi-scale local image bases. In the reconstruction model, the mapping from an fMRI activity pattern to the contrasts of the image bases was learned from measured fMRI responses to visual images. But the shapes of the images bases were fixed, and thus may not be optimal for reconstruction. Here, we propose a method to build a reconstruction model in which image bases are automatically extracted from the measured data. We constructed a probabilistic model that relates the fMRI activity space to the visual image space via a set of latent variables. The mapping from the latent variables to the visual image space can be regarded as a set of image bases. We found that spatially localized, multi-scale image bases were estimated near the fovea, and that the model using the estimated image bases was able to accurately reconstruct novel visual images. The proposed method provides a means to discover a novel functional mapping between stimuli and brain activity patterns.

A non-parametric Bayesian model is proposed for processing multiple images. The analysis employs image features and, when present, the words associated with accompanying annotations. The model clusters the images into classes, and each image is segmented into a set of objects, also allowing the opportunity to assign a word to each object (localized labeling). Each object is assumed to be represented as a heterogeneous mix of components, with this realized via mixture models linking image features to object types. The number of image classes, number of object types, and the characteristics of the object-feature mixture models are inferred non-parametrically. To constitute spatially contiguous objects, a new logistic stick-breaking process is developed. Inference is performed efficiently via variational Bayesian analysis, with example results presented on two image databases.

We devise a graphical model that supports the process of debugging software by guiding developers to code that is likely to contain defects. The model is trained using execution traces of passing test runs; it reflects the distribution over transitional patterns of code positions. Given a failing test case, the model determines the least likely transitional pattern in the execution trace. The model is designed such that Bayesian inference has a closed-form solution. We evaluate the Bernoulli graph model on data of the software projects AspectJ and Rhino.

The Indian Buffet Process is a Bayesian nonparametric approach that models objects as arising from an infinite number of latent factors. Here we extend the latent factor model framework to two or more unbounded layers of latent factors. From a generative perspective, each layer defines a conditional \emph{factorial} prior distribution over the binary latent variables of the layer below via a noisy-or mechanism. We explore the properties of the model with two empirical studies, one digit recognition task and one music tag data experiment.

This paper considers a sensitivity analysis in Hidden Markov Models with continuous state and observation spaces. We propose an Infinitesimal Perturbation Analysis (IPA) on the filtering distribution with respect to some parameters of the model. We describe a methodology for using any algorithm that estimates the filtering density, such as Sequential Monte Carlo methods, to design an algorithm that estimates its gradient. The resulting IPA estimator is proven to be asymptotically unbiased, consistent and has computational complexity linear in the number of particles. We consider an application of this analysis to the problem of identifying unknown parameters of the model given a sequence of observations. We derive an IPA estimator for the gradient of the log-likelihood, which may be used in a gradient method for the purpose of likelihood maximization. We illustrate the method with several numerical experiments.

A central hypothesis about early visual processing is that it represents inputs in a coordinate system matched to the statistics of natural scenes. Simple versions of this lead to Gabor-like receptive fields and divisive gain modulation from local surrounds; these have led to influential neural and psychological models of visual processing. However, these accounts are based on an incomplete view of the visual context surrounding each point. Here, we consider an approximate model of linear and non-linear correlations between the responses of spatially distributed Gabor-like receptive fields, which, when trained on an ensemble of natural scenes, unifies a range of spatial context effects. The full model accounts for neural surround data in primary visual cortex (V1), provides a statistical foundation for perceptual phenomena associated with Lis (2002) hypothesis that V1 builds a saliency map, and fits data on the tilt illusion.

We describe probability distributions, dubbed compressible priors, whose independent and identically distributed (iid) realizations result in compressible signals. A signal is compressible when sorted magnitudes of its coefficients exhibit a power-law decay so that the signal can be well-approximated by a sparse signal. Since compressible signals live close to sparse signals, their intrinsic information can be stably embedded via simple non-adaptive linear projections into a much lower dimensional space whose dimension grows logarithmically with the ambient signal dimension. By using order statistics, we show that N-sample iid realizations of generalized Pareto, Student’s t, log-normal, Frechet, and log-logistic distributions are compressible, i.e., they have a constant expected decay rate, which is independent of N. In contrast, we show that generalized Gaussian distribution with shape parameter q is compressible only in restricted cases since the expected decay rate of its N-sample iid realizations decreases with N as 1/[q log(N/q)]. We use compressible priors as a scaffold to build new iterative sparse signal recovery algorithms based on Bayesian inference arguments. We show how tuning of these algorithms explicitly depends on the parameters of the compressible prior of the signal, and how to learn the parameters of the signal’s compressible prior on the fly during recovery.

In cognitive science, empirical data collected from participants are the arbiters in model selection. Model discrimination thus depends on designing maximally informative experiments. It has been shown that adaptive design optimization (ADO) allows one to discriminate models as efficiently as possible in simulation experiments. In this paper we use ADO in a series of experiments with people to discriminate the Power, Exponential, and Hyperbolic models of memory retention, which has been a long-standing problem in cognitive science, providing an ideal setting in which to test the application of ADO for addressing questions about human cognition. Using an optimality criterion based on mutual information, ADO is able to find designs that are maximally likely to increase our certainty about the true model upon observation of the experiment outcomes. Results demonstrate the usefulness of ADO and also reveal some challenges in its implementation.

Over recent years Dirichlet processes and the associated Chinese restaurant process (CRP) have found many applications in clustering while the Indian buffet process (IBP) is increasingly used to describe latent feature models. In the clustering case, we associate to each data point a latent allocation variable. These latent variables can share the same value and this induces a partition of the data set. The CRP is a prior distribution on such partitions. In latent feature models, we associate to each data point a potentially infinite number of binary latent variables indicating the possession of some features and the IBP is a prior distribution on the associated infinite binary matrix. These prior distributions are attractive because they ensure exchangeability (over samples). We propose here extensions of these models to decomposable graphs. These models have appealing properties and can be easily learned using Monte Carlo techniques.