A new Bayesian modeling method is proposed by combining the maximization of the marginal likelihood with a momentum-space renormalization group transformation for Gaussian graphical models. Moreover, we present a scheme for computint the statistical averages of hyperparameters and mean square errors in our proposed method based on a momentumspace renormalization transformation.

Policy gradient methods have enjoyed great success in deep reinforcement learning but suffer from high variance of gradient estimates. The high variance problem is particularly exasperated in problems with long horizons or high-dimensional action spaces. To mitigate this issue, we derive a bias-free action-dependent baseline for variance reduction which fully exploits the structural form of the stochastic policy itself and does not make any additional assumptions about the MDP. We demonstrate and quantify the benefit of the action-dependent baseline through both theoretical analysis as well as numerical results, including an analysis of the suboptimality of the optimal state-dependent baseline. The result is a computationally efficient policy gradient algorithm, which scales to high-dimensional control problems, as demonstrated by a synthetic 2000-dimensional target matching task. Our experimental results indicate that action-dependent baselines allow for faster learning on standard reinforcement learning benchmarks and high-dimensional hand manipulation and synthetic tasks. Finally, we show that the general idea of including additional information in baselines for improved variance reduction can be extended to partially observed and multi-agent tasks.

The article is devoted to investigating the application of aggregating algorithms to the problem of the long-term forecasting. We examine the classic aggregating algorithms based on the exponential reweighing. For the general Vovk's aggregating algorithm we provide its generalization for the long-term forecasting. For the special basic case of Vovk's algorithm we provide its two modifications for the long-term forecasting. The first one is theoretically close to an optimal algorithm and is based on replication of independent copies. It provides the time-independent regret bound with respect to the best expert in the pool. The second one is not optimal but is more practical and has O( T) regret bound, where T is the length of the game. Keywords: aggregating algorithm, long-term forecasting, prediction with experts' advice, delayed feedback.

The positive-unlabeled (PU) classification is a common scenario in real-world applications such as healthcare, text classification, and bioinformatics, in which we only observe a few samples labeled as "positive" together with a large volume of "unlabeled" samples that may contain both positive and negative samples. Building robust classifier for the PU problem is very challenging, especially for complex data where the negative samples overwhelm and mislabeled samples or corrupted features exist. To address these three issues, we propose a robust learning framework that unifies AUC maximization (a robust metric for biased labels), outlier detection (for excluding wrong labels), and feature selection (for excluding corrupted features). The generalization error bounds are provided for the proposed model that give valuable insight into the theoretical performance of the method and lead to useful practical guidance, e.g., to train a model, we find that the included unlabeled samples are sufficient as long as the sample size is comparable to the number of positive samples in the training process. Empirical comparisons and two real-world applications on surgical site infection (SSI) and EEG seizure detection are also conducted to show the effectiveness of the proposed model.

The use of formal statistical methods to analyse quantitative data in data science has increased considerably over the last few years. One such approach, Bayesian Decision Theory (BDT), also known as Bayesian Hypothesis Testing and Bayesian inference, is a fundamental statistical approach that quantifies the tradeoffs between various decisions using distributions and costs that accompany such decisions. In pattern recognition it is used for designing classifiers making the assumption that the problem is posed in probabilistic terms, and that all of the relevant probability values are known. Generally, we don't have such perfect information but it is a good place to start when studying machine learning, statistical inference, and detection theory in signal processing. BDT also has many applications in science, engineering, and medicine.

Distribution grid is the medium and low voltage part of a large power system. Structurally, the majority of distribution networks operate radially, such that energized lines form a collection of trees, i.e. forest, with a substation being at the root of any tree. The operational topology/forest may change from time to time, however tracking these changes, even though important for the distribution grid operation and control, is hindered by limited real-time monitoring. This paper develops a learning framework to reconstruct radial operational structure of the distribution grid from synchronized voltage measurements in the grid subject to the exogenous fluctuations in nodal power consumption. To detect operational lines our learning algorithm uses conditional independence tests for continuous random variables that is applicable to a wide class of probability distributions of the nodal consumption and Gaussian injections in particular. Moreover, our algorithm applies to the practical case of unbalanced three-phase power flow. Algorithm performance is validated on AC power flow simulations over IEEE distribution grid test cases.

We introduce interactive structure learning, an abstract problem that encompasses many interactive learning tasks that have traditionally been studied in isolation, including active learning of binary classifiers, interactive clustering, interactive embedding, and active learning of structured output predictors. These problems include variants of both supervised and unsupervised tasks, and allow many different types of feedback, from binary labels to must-link/cannot-link constraints to similarity assessments to structured outputs. Despite these surface differences, they conform to a common template that allows them to be fruitfully unified. In interactive structure learning, there is a space of items X --for instance, an input space on which a classifier is to be learned, or points to cluster, or points to embed in a metric space--and the goal is to learn a structure on X, chosen from a family G. This set G could consist, for example, of all linear classifiers on X, or all hierarchical clusterings of X, or all knowledge graphs on X.

In this paper we study the frequentist convergence rate for the Latent Dirichlet Allocation (Blei et al., 2003) topic models. We show that the maximum likelihood estimator converges to one of the finitely many equivalent parameters in Wasserstein's distance metric at a rate of $n^{-1/4}$ without assuming separability or non-degeneracy of the underlying topics and/or the existence of more than three words per document, thus generalizing the previous works of Anandkumar et al. (2012, 2014) from an information-theoretical perspective. We also show that the $n^{-1/4}$ convergence rate is optimal in the worst case.

In order to alleviate data sparsity and over-fitting problems in maximum likelihood estimation (MLE) for sequence prediction tasks, we propose the Generative Bridging Network (GBN), in which a novel bridge module is introduced to assist the training of the sequence prediction model (the generator network). Unlike MLE directly maximizing the conditional likelihood, the bridge extends the point-wise ground truth to a bridge distribution conditioned on it, and the generator is optimized to minimize their KL-divergence. Three different GBNs, namely uniform GBN, language-model GBN and coaching GBN, are proposed to penalize confidence, enhance language smoothness and relieve learning burden. Experiments conducted on two recognized sequence prediction tasks (machine translation and abstractive text summarization) show that our proposed GBNs can yield significant improvements over strong baselines. Furthermore, by analyzing samples drawn from different bridges, expected influences on the generator are verified.

Markov decision processes (MDPs) (Bellman, 1957; Puterman, 2014) are the primary mathematical model for representing sequential decision problems with an indefinite time horizon (Bertsekas and Tsitsiklis, 1996; Sutton and Barto, 1998; Bather, 2000; Si, 2004; Powell, 2007; Wiering and Van Otterlo, 2012). This class of models is quite general as almost any decision process can be made into an MDP by concatenating data over multiple decision points (see Section 2 for a precise statement); however, coercing a decision process into the MDP framework in this way can lead to high-dimensional system state information that is difficult to model effectively. One common approach to construct a low-dimensional decision process from a high-dimensional MDP is to create a finite discretization of the space of possible system states and to treat the resultant process as a finite MDP (Gordon, 1995; Murao and Kitamura, 1997; Sutton and Barto, 1998; Kamio et al., 2004; Whiteson et al., 2007). However, such discretization can result in a significant loss of information and can be difficult to apply when the system state information is continuous and high-dimensional. Another common approach to dimension reduction is to construct a low-dimensional summary of the underlying system states, e.g., by applying principal components analysis (Jolliffe, 1986), multidimensional scaling (Borg and Groenen, 1997), or by constructing a local linear embedding (Roweis and Saul, 2000).