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

The essence of exploration is acting to try to decrease uncertainty. We propose a new methodology for representing uncertainty in continuous-state control problems. Our approach, multi-resolution exploration (MRE), uses a hierarchical mapping to identify regions of the state space that would benefit from additional samples. We demonstrate MRE's broad utility by using it to speed up learning in a prototypical model-based and value-based reinforcement-learning method. Empirical results show that MRE improves upon state-of-the-art exploration approaches.

Kernel Principal Component Analysis (KPCA) is a popular generalization of linear PCA that allows non-linear feature extraction. In KPCA, data in the input space is mapped to higher (usually) dimensional feature space where the data can be linearly modeled. The feature space is typically induced implicitly by a kernel function, and linear PCA in the feature space is performed via the kernel trick. However, due to the implicitness of the feature space, some extensions of PCA such as robust PCA cannot be directly generalized to KPCA. This paper presents a technique to overcome this problem, and extends it to a unified framework for treating noise, missing data, and outliers in KPCA. Our method is based on a novel cost function to perform inference in KPCA. Extensive experiments, in both synthetic and real data, show that our algorithm outperforms existing methods.

Recently, fitted Q-iteration (FQI) based methods have become more popular due to their increased sample efficiency, a more stable learning process and the higher quality of the resulting policy. However, these methods remain hard to use for continuous action spaces which frequently occur in real-world tasks, e.g., in robotics and other technical applications. The greedy action selection commonly used for the policy improvement step is particularly problematic as it is expensive for continuous actions, can cause an unstable learning process, introduces an optimization bias and results in highly non-smooth policies unsuitable for real-world systems. In this paper, we show that by using a soft-greedy action selection the policy improvement step used in FQI can be simplified to an inexpensive advantage-weighted regression. With this result, we are able to derive a new, computationally efficient FQI algorithm which can even deal with high dimensional action spaces.

Uncertainty is omnipresent when we perceive or interact with our environment, and the Bayesian framework provides computational methods for dealing with it. Mathematical models for Bayesian decision making typically require datastructures that are hard to implement in neural networks. This article shows that even the simplest and experimentally best supported type of synaptic plasticity, Hebbian learning, in combination with a sparse, redundant neural code, can in principle learn to infer optimal Bayesian decisions. We present a concrete Hebbian learning rule operating on log-probability ratios. Modulated by reward-signals, this Hebbian plasticity rule also provides a new perspective for understanding how Bayesian inference could support fast reinforcement learning in the brain. In particular we show that recent experimental results by Yang and Shadlen [1] on reinforcement learning of probabilistic inference in primates can be modeled in this way.

We present a simple new Monte Carlo algorithm for evaluating probabilities of observations in complex latent variable models, such as Deep Belief Networks. While the method is based on Markov chains, estimates based on short runs are formally unbiased. In expectation, the log probability of a test set will be underestimated, and this could form the basis of a probabilistic bound. The method is much cheaper than gold-standard annealing-based methods and only slightly more expensive than the cheapest Monte Carlo methods. We give examples of the new method substantially improving simple variational bounds at modest extra cost.

Hierarchical probabilistic modeling of discrete data has emerged as a powerful tool for text analysis. Posterior inference in such models is intractable, and practitioners rely on approximate posterior inference methods such as variational inference or Gibbs sampling. There has been much research in designing better approximations, but there is yet little theoretical understanding of which of the available techniques are appropriate, and in which data analysis settings. In this paper we provide the beginnings of such understanding. We analyze the improvement that the recently proposed collapsed variational inference (CVB) provides over mean field variational inference (VB) in latent Dirichlet allocation. We prove that the difference in the tightness of the bound on the likelihood of a document decreases as $O(k-1) + \log m /m$, where $k$ is the number of topics in the model and $m$ is the number of words in a document. As a consequence, the advantage of CVB over VB is lost for long documents but increases with the number of topics. We demonstrate empirically that the theory holds, using simulated text data and two text corpora. We provide practical guidelines for choosing an approximation.

The odor transduction process has a large time constant and is susceptible to various types of noise. Therefore, the olfactory code at the sensor/receptor level is in general a slow and highly variable indicator of the input odor in both natural and artificial situations. Insects overcome this problem by using a neuronal device in their Antennal Lobe (AL), which transforms the identity code of olfactory receptors to a spatio-temporal code. This transformation improves the decision of the Mushroom Bodies (MBs), the subsequent classifier, in both speed and accuracy.Here we propose a rate model based on two intrinsic mechanisms in the insect AL, namely integration and inhibition. Then we present a MB classifier model that resembles the sparse and random structure of insect MB. A local Hebbian learning procedure governs the plasticity in the model. These formulations not only help to understand the signal conditioning and classification methods of insect olfactory systems, but also can be leveraged in synthetic problems. Among them, we consider here the discrimination of odor mixtures from pure odors. We show on a set of records from metal-oxide gas sensors that the cascade of these two new models facilitates fast and accurate discrimination of even highly imbalanced mixtures from pure odors.

Many machine learning algorithms require the summation of Gaussian kernel functions, an expensive operation if implemented straightforwardly. Several methods have been proposed to reduce the computational complexity of evaluating such sums, including tree and analysis based methods. These achieve varying speedups depending on the bandwidth, dimension, and prescribed error, making the choice between methods difficult for machine learning tasks. We provide an algorithm that combines tree methods with the Improved Fast Gauss Transform (IFGT). As originally proposed the IFGT suffers from two problems: (1) the Taylor series expansion does not perform well for very low bandwidths, and (2) parameter selection is not trivial and can drastically affect performance and ease of use. We address the first problem by employing a tree data structure, resulting in four evaluation methods whose performance varies based on the distribution of sources and targets and input parameters such as desired accuracy and bandwidth. To solve the second problem, we present an online tuning approach that results in a black box method that automatically chooses the evaluation method and its parameters to yield the best performance for the input data, desired accuracy, and bandwidth. In addition, the new IFGT parameter selection approach allows for tighter error bounds. Our approach chooses the fastest method at negligible additional cost, and has superior performance in comparisons with previous approaches.

This paper presents the first data-dependent generalization bounds for non-i.i.d. settings based on the notion of Rademacher complexity. Our bounds extend to the non-i.i.d. case existing Rademacher complexity bounds derived for the i.i.d. setting. These bounds provide a strict generalization of the ones found in the i.i.d. case, and can also be used within the standard i.i.d. scenario. They apply to the standard scenario of beta-mixing stationary sequences examined in many previous studies of non-i.i.d. settings and benefit form the crucial advantages of Rademacher complexity over other measures of the complexity of hypothesis classes. In particular, they are data-dependent and measure the complexity of a class of hypotheses based on the training sample. The empirical Rademacher complexity can be estimated from finite samples and lead to tighter bounds.