The problem of support union recovery is to recover the subset of covariates that are active in at least one of the regression problems.

Graph clustering methods such as spectral clustering are defined for general weighted graphs. In machine learning, however, data often is not given in form of a graph, but in terms of similarity (or distance) values between points. In this case, first a neighborhood graph is constructed using the similarities between the points and then a graph clustering algorithm is applied to this graph. In this paper we investigate the influence of the construction of the similarity graph on the clustering results. We first study the convergence of graph clustering criteria such as the normalized cut (Ncut) as the sample size tends to infinity. We find that the limit expressions are different for different types of graph, for example the r-neighborhood graph or the k-nearest neighbor graph. In plain words: Ncut on a kNN graph does something systematically different than Ncut on an r-neighborhood graph! This finding shows that graph clustering criteria cannot be studied independently of the kind of graph they are applied to. We also provide examples which show that these differences can be observed for toy and real data already for rather small sample sizes.

Suppose we train an animal in a conditioning experiment. Can one predict how a given animal, under given experimental conditions, would perform the task? Since various factors such as stress, motivation, genetic background, and previous errors in task performance can influence animal behaviour, this appears to be a very challenging aim. Reinforcement learning (RL) models have been successful in modeling animal (and human) behaviour, but their success has been limited because of uncertainty as to how to set meta-parameters (such as learning rate, exploitation-exploration balance and future reward discount factor) that strongly influence model performance. We show that a simple RL model whose metaparameters are controlled by an artificial neural network, fed with inputs such as stress, affective phenotype, previous task performance, and even neuromodulatory manipulations, can successfully predict mouse behaviour in the "hole-box" - a simple conditioning task. Our results also provide important insights on how stress and anxiety affect animal learning, performance accuracy, and discounting of future rewards, and on how noradrenergic systems can interact with these processes.

In this theoretical contribution we provide mathematical proof that two of the most important classes of network learning - correlation-based differential Hebbian learning and reward-based temporal difference learning - are asymptotically equivalent when timing the learning with a local modulatory signal. This opens the opportunity to consistently reformulate most of the abstract reinforcement learning framework from a correlation based perspective that is more closely related to the biophysics of neurons.

Decision making lies at the very heart of many psychiatric diseases. It is also a central theoretical concern in a wide variety of fields and has undergone detailed, in-depth, analyses. We take as an example Major Depressive Disorder (MDD), applying insights from a Bayesian reinforcement learning framework. We focus on anhedonia and helplessness. Helplessness--a core element in the conceptualizations of MDD that has lead to major advances in its treatment, pharmacological and neurobiological understanding--is formalized as a simple prior over the outcome entropy of actions in uncertain environments.

Is accurate classification possible in the absence of hand-labeled data? This paper introduces the Monotonic Feature (MF) abstraction--where the probability of class membership increases monotonically with the MF's value. The paper proves that when an MF is given, PAC learning is possible with no hand-labeled data under certain assumptions. We argue that MFs arise naturally in a broad range of textual classification applications. On the classic "20 Newsgroups" data set, a learner given an MF and unlabeled data achieves classification accuracy equal to that of a state-of-the-art semi-supervised learner relying on 160 hand-labeled examples. Even when MFs are not given as input, their presence or absence can be determined from a small amount of hand-labeled data, which yields a new semi-supervised learning method that reduces error by 15% on the 20 Newsgroups data.

We show how smoother priors can preserve the benefits of these sparse priors while adding stability to the Maximum A-Posteriori (MAP) estimate that makes it more useful for prediction problems. Additionally, we show how to calculate the derivative of the MAP estimate efficiently with implicit differentiation. One prior that can be differentiated this way is KL-regularization. We demonstrate its effectiveness on a wide variety of applications, and find that online optimization of the parameters of the KL-regularized model can significantly improve prediction performance.

The problem of ranking arises ubiquitously in almost every aspect of life, and in particular in Machine Learning/Information Retrieval. A statistical model for ranking predicts how humans rank subsets V of some universe U. In this work we define a statistical model for ranking that satisfies certain desirable properties. The model automatically gives rise to a logistic regression based approach to learning how to rank, for which the score and comparison based approaches are dual views. This offers a new generative approach to ranking which can be used for IR.

In this paper lower and upper bounds for the number of support vectors are derived for support vector machines (SVMs) based on the epsilon-insensitive loss function. It turns out that these bounds are asymptotically tight under mild assumptions on the data generating distribution. Finally, we briefly discuss a trade-off in epsilon between sparsity and accuracy if the SVM is used to estimate the conditional median.

We introduces a new probability distribution over a potentially infinite number of binary Markov chains which we call the Markov Indian buffet process. This process extends the IBP to allow temporal dependencies in the hidden variables. We use this stochastic process to build a nonparametric extension of the factorial hidden Markov model. After working out an inference scheme which combines slice sampling and dynamic programming we demonstrate how the infinite factorial hidden Markov model can be used for blind source separation.