This paper introduces a novel classification method for functional magnetic resonance imaging datasets with tens of classes. The method is designed to make predictions using information from as many brain locations as possible, instead of resorting to feature selection, and does this by decomposing the pattern of brain activation into differently informative sub-regions. We provide results over a complex semantic processing dataset that show that the method is competitive with state-of-the-art feature selection and also suggest how the method may be used to perform group or exploratory analyses of complex class structure.

This paper discusses the problem of calibrating posterior class probabilities from partially labelled data. Each instance is assumed to be labelled as belonging to one of several candidate categories, at most one of them being true. We generalize the concept of proper loss to this scenario, establish a necessary and sufficient condition for a loss function to be proper, and we show a direct procedure to construct a proper loss for partial labels from a conventional proper loss. The problem can be characterized by the mixing probability matrix relating the true class of the data and the observed labels. An interesting result is that the full knowledge of this matrix is not required, and losses can be constructed that are proper in a subset of the probability simplex.

We present a new model based on Gaussian processes (GPs) for learning pairwise preferences expressed by multiple users. Inference is simplified by using a \emph{preference kernel} for GPs which allows us to combine supervised GP learning of user preferences with unsupervised dimensionality reduction for multi-user systems. The model not only exploits collaborative information from the shared structure in user behavior, but may also incorporate user features if they are available. Approximate inference is implemented using a combination of expectation propagation and variational Bayes. Finally, we present an efficient active learning strategy for querying preferences. The proposed technique performs favorably on real-world data against state-of-the-art multi-user preference learning algorithms.

While compressive sensing (CS) has been one of the most vibrant and active research fields in the past few years, most development only applies to linear models. This limits its application and excludes many areas where CS ideas could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique -- CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery. We further provide scalable numerical solvers to accelerate its implementation. The source code of our algorithms will be provided to the public.

We propose a novel stochastic process that is with probability $\alpha_i$ being absorbed at current state $i$, and with probability $1-\alpha_i$ follows a random edge out of it. We analyze its properties and show its potential for exploring graph structures. We prove that under proper absorption rates, a random walk starting from a set $\mathcal{S}$ of low conductance will be mostly absorbed in $\mathcal{S}$. Moreover, the absorption probabilities vary slowly inside $\mathcal{S}$, while dropping sharply outside $\mathcal{S}$, thus implementing the desirable cluster assumption for graph-based learning. Remarkably, the partially absorbing process unifies many popular models arising in a variety of contexts, provides new insights into them, and makes it possible for transferring findings from one paradigm to another. Simulation results demonstrate its promising applications in graph-based learning.

The expected return is a widely used objective in decision making under uncertainty. Manyalgorithms, such as value iteration, have been proposed to optimize it. In risk-aware settings, however, the expected return is often not an appropriate objective to optimize. We propose a new optimization objective for risk-aware planning and show that it has desirable theoretical properties. We also draw connections topreviously proposed objectives for risk-aware planing: minmax, exponential utility,percentile and mean minus variance. Our method applies to an extended class of Markov decision processes: we allow costs to be stochastic as long as they are bounded. Additionally, we present an efficient algorithm for optimizing theproposed objective. Synthetic and real-world experiments illustrate the effectiveness of our method, at scale.

Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Continuous relaxations of balanced cut problems yield excellent clustering results. This paper provides rigorous convergence results for two algorithms that solve the relaxed Cheeger Cut minimization. The first algorithm is a new steepest descent algorithm and the second one is a slight modification of the Inverse Power Method algorithm \cite{pro:HeinBuhler10OneSpec}. While the steepest descent algorithm has better theoretical convergence properties, in practice both algorithm perform equally. We also completely characterize the local minima of the relaxed problem in terms of the original balanced cut problem, and relate this characterization to the convergence of the algorithms.

We present a new algorithm for Independent Component Analysis (ICA) which has provable performance guarantees. In particular, suppose we are given samples of the form y Ax η where A is an unknown n n matrix and x is a random variable whose components are independent and have a fourth moment strictly less than that of a standard Gaussian random variable and η is an n-dimensional Gaussian random variable with unknown covariance Σ: We give an algorithm that provable recovers A and Σ up to an additive ɛ and whose running time and sample complexityare polynomial in n and 1/ɛ. To accomplish this, we introduce a novel "quasi-whitening" step that may be useful in other contexts in which the covariance of Gaussian noise is not known in advance. We also give a general framework for finding all local optima of a function (given an oracle for approximately findingjust one) and this is a crucial step in our algorithm, one that has been overlooked in previous attempts, and allows us to control the accumulation of error when we find the columns of A one by one via local search.

We propose a Deep Boltzmann Machine for learning a generative model of multimodal data. We show how to use the model to extract a meaningful representation of multimodal data. We find that the learned representation is useful for classification and information retreival tasks, and hence conforms to some notion of semantic similarity. The model defines a probability density over the space of multimodal inputs. By sampling from the conditional distributions over each data modality, it possible to create the representation even when some data modalities are missing. Our experimental results on bi-modal data consisting of images and text show that the Multimodal DBM can learn a good generative model of the joint space of image and text inputs that is useful for information retrieval from both unimodal and multimodal queries. We further demonstrate that our model can significantly outperform SVMs and LDA on discriminative tasks. Finally, we compare our model to other deep learning methods, including autoencoders and deep belief networks, and show that it achieves significant gains.

The sum-product network (SPN) is a recently-proposed deep model consisting of a network of sum and product nodes, and has been shown to be competitive with state-of-the-art deep models on certain difficult tasks such as image completion. Designing an SPN network architecture that is suitable for the task at hand is an open question. We propose an algorithm for learning the SPN architecture from data. The idea is to cluster variables (as opposed to data instances) in order to identify variable subsets that strongly interact with one another. Nodes in the SPN network are then allocated towards explaining these interactions. Experimental evidence shows that learning the SPN architecture significantly improves its performance compared to using a previously-proposed static architecture.