The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a L_1 norm plus a pair-wise L_inf norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where the groups are a priori unknown. The OSCAR regularizer has a non-trivial proximity operator, which limits its applicability. We reformulate this regularizer as a weighted sorted L_1 norm, and propose its grouping proximity operator (GPO) and approximate proximity operator (APO), thus making state-of-the-art proximal splitting algorithms (PSAs) available to solve inverse problems with OSCAR regularization. The GPO is in fact the APO followed by additional grouping and averaging operations, which are costly in time and storage, explaining the reason why algorithms with APO are much faster than that with GPO. The convergences of PSAs with GPO are guaranteed since GPO is an exact proximity operator. Although convergence of PSAs with APO is may not be guaranteed, we have experimentally found that APO behaves similarly to GPO when the regularization parameter of the pair-wise L_inf norm is set to an appropriately small value. Experiments on recovery of group-sparse signals (with unknown groups) show that PSAs with APO are very fast and accurate.

We consider constraint-based methods for causal structure learning, such as the PC-, FCI-, RFCI- and CCD- algorithms (Spirtes et al. (2000, 1993), Richardson (1996), Colombo et al. (2012), Claassen et al. (2013)). The first step of all these algorithms consists of the PC-algorithm. This algorithm is known to be order-dependent, in the sense that the output can depend on the order in which the variables are given. This order-dependence is a minor issue in low-dimensional settings. We show, however, that it can be very pronounced in high-dimensional settings, where it can lead to highly variable results. We propose several modifications of the PC-algorithm (and hence also of the other algorithms) that remove part or all of this order-dependence. All proposed modifications are consistent in high-dimensional settings under the same conditions as their original counterparts. We compare the PC-, FCI-, and RFCI-algorithms and their modifications in simulation studies and on a yeast gene expression data set. We show that our modifications yield similar performance in low-dimensional settings and improved performance in high-dimensional settings. All software is implemented in the R-package pcalg.

Functional magnetic resonance imaging (fMRI) produces data about activity inside the brain, from which spatial maps can be extracted by independent component analysis (ICA). In datasets, there are n spatial maps that contain p voxels. The number of voxels is very high compared to the number of analyzed spatial maps. Clustering of the spatial maps is usually based on correlation matrices. This usually works well, although such a similarity matrix inherently can explain only a certain amount of the total variance contained in the high-dimensional data where n is relatively small but p is large. For high-dimensional space, it is reasonable to perform dimensionality reduction before clustering. In this research, we used the recently developed diffusion map for dimensionality reduction in conjunction with spectral clustering. This research revealed that the diffusion map based clustering worked as well as the more traditional methods, and produced more compact clusters when needed.

We present a comprehensive study of the use of generative modeling approaches for Multiple-Instance Learning (MIL) problems. In MIL a learner receives training instances grouped together into bags with labels for the bags only (which might not be correct for the comprised instances). Our work was motivated by the task of facilitating the diagnosis of neuromuscular disorders using sets of motor unit potential trains (MUPTs) detected within a muscle which can be cast as a MIL problem. Our approach leads to a state-of-the-art solution to the problem of muscle classification. By introducing and analyzing generative models for MIL in a general framework and examining a variety of model structures and components, our work also serves as a methodological guide to modelling MIL tasks. We evaluate our proposed methods both on MUPT datasets and on the MUSK1 dataset, one of the most widely used benchmarks for MIL.

We introduce a Deep Boltzmann Machine model suitable for modeling and extracting latent semantic representations from a large unstructured collection of documents. We overcome the apparent difficulty of training a DBM with judicious parameter tying. This parameter tying enables an efficient pretraining algorithm and a state initialization scheme that aids inference. The model can be trained just as efficiently as a standard Restricted Boltzmann Machine. Our experiments show that the model assigns better log probability to unseen data than the Replicated Softmax model. Features extracted from our model outperform LDA, Replicated Softmax, and DocNADE models on document retrieval and document classification tasks.

Boosting is known to be sensitive to label noise. We studied two approaches to improve AdaBoost's robustness against labelling errors. One is to employ a label-noise robust classifier as a base learner, while the other is to modify the AdaBoost algorithm to be more robust. Empirical evaluation shows that a committee of robust classifiers, although converges faster than non label-noise aware AdaBoost, is still susceptible to label noise. However, pairing it with the new robust Boosting algorithm we propose here results in a more resilient algorithm under mislabelling.

We propose a probabilistic model to infer supervised latent variables in the Hamming space from observed data. Our model allows simultaneous inference of the number of binary latent variables, and their values. The latent variables preserve neighbourhood structure of the data in a sense that objects in the same semantic concept have similar latent values, and objects in different concepts have dissimilar latent values. We formulate the supervised infinite latent variable problem based on an intuitive principle of pulling objects together if they are of the same type, and pushing them apart if they are not. We then combine this principle with a flexible Indian Buffet Process prior on the latent variables. We show that the inferred supervised latent variables can be directly used to perform a nearest neighbour search for the purpose of retrieval. We introduce a new application of dynamically extending hash codes, and show how to effectively couple the structure of the hash codes with continuously growing structure of the neighbourhood preserving infinite latent feature space.

We seek to learn an effective policy for a Markov Decision Process (MDP) with continuous states via Q-Learning. Given a set of basis functions over state action pairs we search for a corresponding set of linear weights that minimizes the mean Bellman residual. Our algorithm uses a Kalman filter model to estimate those weights and we have developed a simpler approximate Kalman filter model that outperforms the current state of the art projected TD-Learning methods on several standard benchmark problems.

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model in the necessary manner to perform variational inference. Our ap- proach is readily extended to models with non-Gaussian likelihoods and latent variable models based around Gaussian processes. We demonstrate the approach on a simple toy problem and two real world data sets.

We propose a method for learning cyclic causal models from a combination of observational and interventional equilibrium data. Novel aspects of the proposed method are its ability to work with continuous data (without assuming linearity) and to deal with feedback loops. Within the context of biochemical reactions, we also propose a novel way of modeling interventions that modify the activity of compounds instead of their abundance. For computational reasons, we approximate the nonlinear causal mechanisms by (coupled) local linearizations, one for each experimental condition. We apply the method to reconstruct a cellular signaling network from the flow cytometry data measured by Sachs et al. (2005). We show that our method finds evidence in the data for feedback loops and that it gives a more accurate quantitative description of the data at comparable model complexity.