In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously known bounds for algorithms like GP-UCB. We also introduce the novel Gaussian Process Mutual Information algorithm (GP-MI), which significantly improves further these upper bounds for the cumulative regret. We confirm the efficiency of this algorithm on synthetic and real tasks against the natural competitor, GP-UCB, and also the Expected Improvement heuristic. After the publication of our article, we found an error in the proof of Lemma 1 which invalidates the main theorem.

In this paper, we consider voxel selection for functional Magnetic Resonance Imaging (fMRI) brain data with the aim of finding a more complete set of probably correlated discriminative voxels, thus improving interpretation of the discovered potential biomarkers. The main difficulty in doing this is an extremely high dimensional voxel space and few training samples, resulting in unreliable feature selection. In order to deal with the difficulty, stability selection has received a great deal of attention lately, especially due to its finite sample control of false discoveries and transparent principle for choosing a proper amount of regularization. However, it fails to make explicit use of the correlation property or structural information of these discriminative features and leads to large false negative rates. In other words, many relevant but probably correlated discriminative voxels are missed. Thus, we propose a new variant on stability selection "randomized structural sparsity", which incorporates the idea of structural sparsity. Numerical experiments demonstrate that our method can be superior in controlling for false negatives while also keeping the control of false positives inherited from stability selection.

Variable selection is a challenging issue in statistical applications when the number of predictors $p$ far exceeds the number of observations $n$. In this ultra-high dimensional setting, the sure independence screening (SIS) procedure was introduced to significantly reduce the dimensionality by preserving the true model with overwhelming probability, before a refined second stage analysis. However, the aforementioned sure screening property strongly relies on the assumption that the important variables in the model have large marginal correlations with the response, which rarely holds in reality. To overcome this, we propose a novel and simple screening technique called the high-dimensional ordinary least-squares projection (HOLP). We show that HOLP possesses the sure screening property and gives consistent variable selection without the strong correlation assumption, and has a low computational complexity. A ridge type HOLP procedure is also discussed. Simulation study shows that HOLP performs competitively compared to many other marginal correlation based methods. An application to a mammalian eye disease data illustrates the attractiveness of HOLP.

Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance is poor in nonparametric models. We take a small-variance asymptotics (SVA) approach to overcome these limitations. We derive the small-variance asymptotics for parametric and nonparametric MJPs for both directly observed and hidden state models. In the parametric case we obtain a novel objective function which leads to non-degenerate trajectories. To derive the nonparametric version we introduce the gamma-gamma process, a novel extension to the gamma-exponential process. We propose algorithms for each of these formulations, which we call \emph{JUMP-means}. Our experiments demonstrate that JUMP-means is competitive with or outperforms widely used MJP inference approaches in terms of both speed and reconstruction accuracy.

We design mechanisms for online procurement of data held by strategic agents for machine learning tasks. The challenge is to use past data to actively price future data and give learning guarantees even when an agent's cost for revealing her data may depend arbitrarily on the data itself. We achieve this goal by showing how to convert a large class of no-regret algorithms into online posted-price and learning mechanisms. Our results in a sense parallel classic sample complexity guarantees, but with the key resource being money rather than quantity of data: With a budget constraint $B$, we give robust risk (predictive error) bounds on the order of $1/\sqrt{B}$. Because we use an active approach, we can often guarantee to do significantly better by leveraging correlations between costs and data. Our algorithms and analysis go through a model of no-regret learning with $T$ arriving pairs (cost, data) and a budget constraint of $B$. Our regret bounds for this model are on the order of $T/\sqrt{B}$ and we give lower bounds on the same order.

The winning team of MOL Group's Freshhh 2015 competition truly learned the value of hard work. "Just ask Siri," the first-place winner of the competition in which students from across the globe compete in technology and business strategy simulations related to the oil and gas industry was made up of three students from the University of Economics, Prague and Czech Technical University in Prague, Czech Republic. MOL Group experts are a part of the game development, so they make sure tasks are aligned with real-life situations, said Zdravka Demeter Bubalo, HR vice president of MOL Group. The top teams are invited to compete in the Live Final and present case studies connected to recent industry trends and issues. This strategy allows MOL Group to find the best global talent to join the company.

We provide a rigorous definition of the visual cause of a behavior that is broadly applicable to the visually driven behavior in humans, animals, neurons, robots and other perceiving systems. Our framework generalizes standard accounts of causal learning to settings in which the causal variables need to be constructed from micro-variables. We prove the Causal Coarsening Theorem, which allows us to gain causal knowledge from observational data with minimal experimental effort. The theorem provides a connection to standard inference techniques in machine learning that identify features of an image that correlate with, but may not cause, the target behavior. Finally, we propose an active learning scheme to learn a manipulator function that performs optimal manipulations on the image to automatically identify the visual cause of a target behavior. We illustrate our inference and learning algorithms in experiments based on both synthetic and real data.

We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a Hidden Markov Model (HMM); we model the relationship between multiple cell types by connecting their hidden states by a fixed tree of known structure. The main challenge with learning parameters of such models is that iterative methods such as EM are very slow, while naive spectral methods result in time and space complexity exponential in the number of cell types. We exploit properties of the tree structure of the hidden states to provide spectral algorithms that are more computationally efficient for current biological datasets. We provide sample complexity bounds for our algorithm and evaluate it experimentally on biological data from nine human cell types. Finally, we show that beyond our specific model, some of our algorithmic ideas can be applied to other graphical models.

Fine-grained visual categorization (FGVC) is to categorize objects into subordinate classes instead of basic classes. One major challenge in FGVC is the co-occurrence of two issues: 1) many subordinate classes are highly correlated and are difficult to distinguish, and 2) there exists the large intra-class variation (e.g., due to object pose). This paper proposes to explicitly address the above two issues via distance metric learning (DML). DML addresses the first issue by learning an embedding so that data points from the same class will be pulled together while those from different classes should be pushed apart from each other; and it addresses the second issue by allowing the flexibility that only a portion of the neighbors (not all data points) from the same class need to be pulled together. However, feature representation of an image is often high dimensional, and DML is known to have difficulty in dealing with high dimensional feature vectors since it would require $\mathcal{O}(d^2)$ for storage and $\mathcal{O}(d^3)$ for optimization. To this end, we proposed a multi-stage metric learning framework that divides the large-scale high dimensional learning problem to a series of simple subproblems, achieving $\mathcal{O}(d)$ computational complexity. The empirical study with FVGC benchmark datasets verifies that our method is both effective and efficient compared to the state-of-the-art FGVC approaches.

We present a new, fully generative model of optical telescope image sets, along with a variational procedure for inference. Each pixel intensity is treated as a Poisson random variable, with a rate parameter dependent on latent properties of stars and galaxies. Key latent properties are themselves random, with scientific prior distributions constructed from large ancillary data sets. We check our approach on synthetic images. We also run it on images from a major sky survey, where it exceeds the performance of the current state-of-the-art method for locating celestial bodies and measuring their colors.