We develop a statistical framework for the simultaneous, unsupervised segmentation and discovery of visual object categories from image databases. Examining a large set of manually segmented scenes, we use chi--square tests to show that object frequencies and segment sizes both follow power law distributions, which are well modeled by the Pitman--Yor (PY) process. This nonparametric prior distribution leads to learning algorithms which discover an unknown set of objects, and segmentation methods which automatically adapt their resolution to each image. Generalizing previous applications of PY processes, we use Gaussian processes to discover spatially contiguous segments which respect image boundaries. Using a novel family of variational approximations, our approach produces segmentations which compare favorably to state--of--the--art methods, while simultaneously discovering categories shared among natural scenes.

We show how improved sequences for magnetic resonance imaging can be found through automated optimization of Bayesian design scores. Combining recent advances in approximate Bayesian inference and natural image statistics with high-performance numerical computation, we propose the first scalable Bayesian experimental design framework for this problem of high relevance to clinical and brain research. Our solution requires approximate inference for dense, non-Gaussian models on a scale seldom addressed before. We propose a novel scalable variational inference algorithm, and show how powerful methods of numerical mathematics can be modified to compute primitives in our framework. Our approach is evaluated on a realistic setup with raw data from a 3T MR scanner.

Pattern classification approaches to analyzing functional neuroimaging data have become increasingly popular [12] [3] [4].

Polysemy is a problem for methods that exploit image search engines to build object category models. Existing unsupervised approaches do not take word sense into consideration. We propose a new method that uses a dictionary to learn models of visual word sense from a large collection of unlabeled web data. The use of LDA to discover a latent sense space makes the model robust despite the very limited nature of dictionary definitions. The definitions are used to learn a distribution in the latent space that best represents a sense. The algorithm then uses the text surrounding image links to retrieve images with high probability of a particular dictionary sense. An object classifier is trained on the resulting sense-specific images. We evaluate our method on a dataset obtained by searching the web for polysemous words. Category classification experiments show that our dictionary-based approach outperforms baseline methods.

We describe a novel class of distributions, called Mondrian processes, which can be interpreted as probability distributions over kd-tree data structures. Mondrian processesare multidimensional generalizations of Poisson processes and this connection allows us to construct multidimensional generalizations of the stickbreaking processdescribed by Sethuraman (1994), recovering the Dirichlet process in one dimension. After introducing the Aldous-Hoover representation for jointly and separately exchangeable arrays, we show how the process can be used as a nonparametric prior distribution in Bayesian models of relational data.

Cognitive control refers to the flexible deployment of memory and attention in response to task demands and current goals. Control is often studied experimentally by presenting sequences of stimuli, some demanding a response, and others modulating the stimulus-response mapping. In these tasks, participants must maintain information about the current stimulus-response mapping in working memory. Prominent theories of cognitive control use recurrent neural nets to implement working memory, and optimize memory utilization via reinforcement learning. We present a novel perspective on cognitive control in which working memory representations are intrinsically probabilistic, and control operations that maintain and update working memory are dynamically determined via probabilistic inference. We show that our model provides a parsimonious account of behavioral and neuroimaging data, and suggest that it offers an elegant conceptualization of control in which behavior can be cast as optimal, subject to limitations on learning and the rate of information processing. Moreover, our model provides insight into how task instructions can be directly translated into appropriate behavior and then efficiently refined with subsequent task experience.

This paper describes a recursive estimation procedure for multivariate binary densities using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients to estimate, which renders conventional approaches computationally prohibitive when $d$ is large. However, for a wide class of densities that satisfy a certain sparsity condition, our estimator runs in probabilistic polynomial time and adapts to the unknown sparsity of the underlying density in two key ways: (1) it attains near-minimax mean-squared error, and (2) the computational complexity is lower for sparser densities. Our method also allows for flexible control of the trade-off between mean-squared error and computational complexity.

This paper studies global ranking problem by learning to rank methods. Conventional learning to rank methods are usually designed for `local ranking', in the sense that the ranking model is defined on a single object, for example, a document in information retrieval. For many applications, this is a very loose approximation. Relations always exist between objects and it is better to define the ranking model as a function on all the objects to be ranked (i.e., the relations are also included). This paper refers to the problem as global ranking and proposes employing a Continuous Conditional Random Fields (CRF) for conducting the learning task. The Continuous CRF model is defined as a conditional probability distribution over ranking scores of objects conditioned on the objects. It can naturally represent the content information of objects as well as the relation information between objects, necessary for global ranking. Taking two specific information retrieval tasks as examples, the paper shows how the Continuous CRF method can perform global ranking better than baselines.

Causal structure-discovery techniques usually assume that all causes of more than one variable are observed. This is the so-called causal sufficiency assumption. In practice, it is untestable, and often violated. In this paper, we present an efficient causal structure-learning algorithm, suited for causally insufficient data. Similar to algorithms such as IC* and FCI, the proposed approach drops the causal sufficiency assumption and learns a structure that indicates (potential) latent causes for pairs of observed variables. Assuming a constant local density of the data-generating graph, our algorithm makes a quadratic number of conditional-independence tests w.r.t. the number of variables. We show with experiments that our algorithm is comparable to the state-of-the-art FCI algorithm in accuracy, while being several orders of magnitude faster on large problems. We conclude that MBCS* makes a new range of causally insufficient problems computationally tractable.

A series of corrections is developed for the fixed points of Expectation Propagation (EP),which is one of the most popular methods for approximate probabilistic inference. These corrections can lead to improvements of the inference approximation orserve as a sanity check, indicating when EP yields unrealiable results.