Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity rely on prior knowledge on how to weight (or how to penalize) individual subsets of variables during the subset selection process, which is not available in general. Inferring group weights from data is a key open research problem in structured sparsity.In this paper, we propose a Bayesian approach to the problem of group weight learning. We model the group weights as hyperparameters of heavy-tailed priors on groups of variables and derive an approximate inference scheme to infer these hyperparameters. We empirically show that we are able to recover the model hyperparameters when the data are generated from the model, and we demonstrate the utility of learning weights in synthetic and real denoising problems.

Consider a classification problem where we do not have access to labels for individual training examples, but only have average labels over subpopulations. We give practical examples of this setup and show how such a classification task can usefully be analyzed as a weakly supervised clustering problem. We propose three approaches to solving the weakly supervised clustering problem, including a latent variables model that performs well in our experiments. We illustrate our methods on an analysis of aggregated elections data and an industry data set that was the original motivation for this research.

The article is devoted to the problem of inconsistency in the pairwise comparisons based prioritization methodology. The issue of "inconsistency" in this context has gained much attention in recent years. The literature provides us with a number of different "inconsistency" indices suggested for measuring the inconsistency of the pairwise comparison matrix (PCM). The latter is understood as a deviation of the PCM from the "consistent case" - a notion that is formally well-defined in this theory. However the usage of the indices is justified only by some heuristics. It is still unclear what they really "measure". What is even more important and still not known is the relationship between their values and the "consistency" of the decision maker's judgments on one hand, and the prioritization results upon the other. We provide examples showing that it is necessary to distinguish between these three following tasks: the "measuring" of the "PCM inconsistency" and the PCM-based "measuring" of the consistency of decision maker's judgments and, finally, the "measuring" of the usefulness of the PCM as a source of information for estimation of the priority vector (PV). Next we focus on the third task, which seems to be the most important one in Multi-Criteria Decision Making. With the help of Monte Carlo experiments, we study the performance of various inconsistency indices as indicators of the final PV estimation quality. The presented results allow a deeper understanding of the information contained in these indices and help in choosing a proper one in a given situation. They also enable us to develop a new inconsistency characteristic and, based on it, to propose the PCM acceptance approach that is supported by the classical statistical methodology.

High-throughput mRNA sequencing (RNA-Seq) is widely used for transcript quantification of gene isoforms. Since RNA-Seq data alone is often not sufficient to accurately identify the read origins from the isoforms for quantification, we propose to explore protein domain-domain interactions as prior knowledge for integrative analysis with RNA-seq data. We introduce a Network-based method for RNA-Seq-based Transcript Quantification (Net-RSTQ) to integrate protein domain-domain interaction network with short read alignments for transcript abundance estimation. Based on our observation that the abundances of the neighboring isoforms by domain-domain interactions in the network are positively correlated, Net-RSTQ models the expression of the neighboring transcripts as Dirichlet priors on the likelihood of the observed read alignments against the transcripts in one gene. The transcript abundances of all the genes are then jointly estimated with alternating optimization of multiple EM problems. In simulation Net-RSTQ effectively improved isoform transcript quantifications when isoform co-expressions correlate with their interactions. qRT-PCR results on 25 multi-isoform genes in a stem cell line, an ovarian cancer cell line, and a breast cancer cell line also showed that Net-RSTQ estimated more consistent isoform proportions with RNA-Seq data. In the experiments on the RNA-Seq data in The Cancer Genome Atlas (TCGA), the transcript abundances estimated by Net-RSTQ are more informative for patient sample classification of ovarian cancer, breast cancer and lung cancer. All experimental results collectively support that Net-RSTQ is a promising approach for isoform quantification.

The Singleton Property (SP) approach has been proposed for representing and querying metadata about RDF triples such as provenance, time, location, and evidence. In this approach, one singleton property is created to uniquely represent a relationship in a particular context, and in general, generates a large property hierarchy in the schema. It has become the subject of important questions from Semantic Web practitioners. Can an existing reasoner recognize the singleton property triples? And how? If the singleton property triples describe a data triple, then how can a reasoner infer this data triple from the singleton property triples? Or would the large property hierarchy affect the reasoners in some way? We address these questions in this paper and present our study about the reasoning aspects of the singleton properties. We propose a simple mechanism to enable existing reasoners to recognize the singleton property triples, as well as to infer the data triples described by the singleton property triples. We evaluate the effect of the singleton property triples in the reasoning processes by comparing the performance on RDF datasets with and without singleton properties. Our evaluation uses as benchmark the LUBM datasets and the LUBM-SP datasets derived from LUBM with temporal information added through singleton properties.

Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as $\ell_1$ minimization and nuclear norm minimization are well understood through recent years' research. However, rigorously characterizing the phase transition of total variation (TV) minimization in recovering sparse-gradient signal is still open. In this paper, we fully characterize the phase transition curve of the TV minimization. Our proof builds on Donoho, Johnstone and Montanari's conjectured phase transition curve for the TV approximate message passing algorithm (AMP), together with the linkage between the minmax Mean Square Error of a denoising problem and the high-dimensional convex geometry for TV minimization.

In the Bayesian Reinforcement Learning (BRL) setting, agents try to maximise the collected rewards while interacting with their environment while using some prior knowledge that is accessed beforehand. Many BRL algorithms have already been proposed, but even though a few toy examples exist in the literature, there are still no extensive or rigorous benchmarks to compare them. The paper addresses this problem, and provides a new BRL comparison methodology along with the corresponding open source library. In this methodology, a comparison criterion that measures the performance of algorithms on large sets of Markov Decision Processes (MDPs) drawn from some probability distributions is defined. In order to enable the comparison of non-anytime algorithms, our methodology also includes a detailed analysis of the computation time requirement of each algorithm. Our library is released with all source code and documentation: it includes three test problems, each of which has two different prior distributions, and seven state-of-the-art RL algorithms. Finally, our library is illustrated by comparing all the available algorithms and the results are discussed.

Entity resolution (ER) is the task of identifying records belonging to the same entity (e.g. individual, group) across one or multiple databases. Ironically, it has multiple names: deduplication and record linkage, among others. In this paper we survey metrics used to evaluate ER results in order to iteratively improve performance and guarantee sufficient quality prior to deployment. Some of these metrics are borrowed from multi-class classification and clustering domains, though some key differences exist differentiating entity resolution from general clustering. Menestrina et al. empirically showed rankings from these metrics often conflict with each other, thus our primary motivation for studying them. This paper provides practitioners the basic knowledge to begin evaluating their entity resolution results.

Objective: Anemia is a frequent comorbidity in hemodialysis patients that can be successfully treated by administering erythropoiesis-stimulating agents (ESAs). ESAs dosing is currently based on clinical protocols that often do not account for the high inter- and intra-individual variability in the patient's response. As a result, the hemoglobin level of some patients oscillates around the target range, which is associated with multiple risks and side-effects. This work proposes a methodology based on reinforcement learning (RL) to optimize ESA therapy. Methods: RL is a data-driven approach for solving sequential decision-making problems that are formulated as Markov decision processes (MDPs). Computing optimal drug administration strategies for chronic diseases is a sequential decision-making problem in which the goal is to find the best sequence of drug doses. MDPs are particularly suitable for modeling these problems due to their ability to capture the uncertainty associated with the outcome of the treatment and the stochastic nature of the underlying process. The RL algorithm employed in the proposed methodology is fitted Q iteration, which stands out for its ability to make an efficient use of data. Results: The experiments reported here are based on a computational model that describes the effect of ESAs on the hemoglobin level. The performance of the proposed method is evaluated and compared with the well-known Q-learning algorithm and with a standard protocol. Simulation results show that the performance of Q-learning is substantially lower than FQI and the protocol. Conclusion: Although prospective validation is required, promising results demonstrate the potential of RL to become an alternative to current protocols.

We consider a network of agents that aim to learn some unknown state of the world using private observations and exchange of beliefs. At each time, agents observe private signals generated based on the true unknown state. Each agent might not be able to distinguish the true state based only on her private observations. This occurs when some other states are observationally equivalent to the true state from the agent's perspective. To overcome this shortcoming, agents must communicate with each other to benefit from local observations. We propose a model where each agent selects one of her neighbors randomly at each time. Then, she refines her opinion using her private signal and the prior of that particular neighbor. The proposed rule can be thought of as a Bayesian agent who cannot recall the priors based on which other agents make inferences. This learning without recall approach preserves some aspects of the Bayesian inference while being computationally tractable. By establishing a correspondence with a random walk on the network graph, we prove that under the described protocol, agents learn the truth exponentially fast in the almost sure sense. The asymptotic rate is expressed as the sum of the relative entropies between the signal structures of every agent weighted by the stationary distribution of the random walk.