Reinforcement learning has gained wide popularity as a technique for simulation-driven approximate dynamic programming. A less known aspect is that the very reasons that make it effective in dynamic programming can also be leveraged for using it for distributed schemes for certain matrix computations involving non-negative matrices. In this spirit, we propose a reinforcement learning algorithm for PageRank computation that is fashioned after analogous schemes for approximate dynamic programming. The algorithm has the advantage of ease of distributed implementation and more importantly, of being model-free, i.e., not dependent on any specific assumptions about the transition probabilities in the random web-surfer model. We analyze its convergence and finite time behavior and present some supporting numerical experiments.

Iterative thresholding algorithms are well-suited for high-dimensional problems in sparse recovery and compressive sensing. The performance of this class of algorithms depends heavily on the tuning of certain threshold parameters. In particular, both the final reconstruction error and the convergence rate of the algorithm crucially rely on how the threshold parameter is set at each step of the algorithm. In this paper, we propose a parameter-free approximate message passing (AMP) algorithm that sets the threshold parameter at each iteration in a fully automatic way without either having an information about the signal to be reconstructed or needing any tuning from the user. We show that the proposed method attains both the minimum reconstruction error and the highest convergence rate. Our method is based on applying the Stein unbiased risk estimate (SURE) along with a modified gradient descent to find the optimal threshold in each iteration. Motivated by the connections between AMP and LASSO, it could be employed to find the solution of the LASSO for the optimal regularization parameter. To the best of our knowledge, this is the first work concerning parameter tuning that obtains the fastest convergence rate with theoretical guarantees.

The sequential posterior updates play a central role in many Bayesian inference procedures. As an example, in Bayesian inference one is interested in the posterior probability of variables of interest given the data observed sequentially up to a given time point. As a more specific example which provides the motivation for this work, in a sequential change point detection problem [1], the key quantity is the posterior probability that a change has occurred given the data observed up to present time. When the underlying probability model is complex, e.g., a large-scale graphical model, the calculation of such quantities in a fast and online manner is a formidable challenge. In such situations approximate inference methods are required - for graphical models, message-passing variational inference algorithms present a viable option [2, 3].

The kernel least-mean-square (KLMS) algorithm is an appealing tool for online identification of nonlinear systems due to its simplicity and robustness. In addition to choosing a reproducing kernel and setting filter parameters, designing a KLMS adaptive filter requires to select a so-called dictionary in order to get a finite-order model. This dictionary has a significant impact on performance, and requires careful consideration. Theoretical analysis of KLMS as a function of dictionary setting has rarely, if ever, been addressed in the literature. In an analysis previously published by the authors, the dictionary elements were assumed to be governed by the same probability density function of the input data. In this paper, we modify this study by considering the dictionary as part of the filter parameters to be set. This theoretical analysis paves the way for future investigations on KLMS dictionary design.

Incorporating spatial information into hyperspectral unmixing procedures has been shown to have positive effects, due to the inherent spatial-spectral duality in hyperspectral scenes. Current research works that consider spatial information are mainly focused on the linear mixing model. In this paper, we investigate a variational approach to incorporating spatial correlation into a nonlinear unmixing procedure. A nonlinear algorithm operating in reproducing kernel Hilbert spaces, associated with an $\ell_1$ local variation norm as the spatial regularizer, is derived. Experimental results, with both synthetic and real data, illustrate the effectiveness of the proposed scheme.

The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation processes, but these, being Markov processes, are restricted to linear or tree structured covariate spaces. We define a partition-valued process on an arbitrary covariate space using Gaussian processes. We use the process to construct a multitask clustering model which partitions datapoints in a similar way across multiple data sources, and a time series model of network data which allows cluster assignments to vary over time. We describe sampling algorithms for inference and apply our method to defining cancer subtypes based on different types of cellular characteristics, finding regulatory modules from gene expression data from multiple human populations, and discovering time varying community structure in a social network.

We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and can be heavy-tailed. The objects of interest have unknown varying intensities. No boundary shape constraints are imposed on the objects, only a set of weak bulk conditions is required. We view the object detection problem as a multiple hypothesis testing for discrete statistical inverse problems. We present an algorithm that allows to detect greyscale objects of various shapes in noisy images. We prove results on consistency and algorithmic complexity of our procedures. Applications to cryo-electron microscopy are presented.

Concept-to-text generation refers to the task of automatically producing textual output from non-linguistic input. We present a joint model that captures content selection ("what to say") and surface realization ("how to say") in an unsupervised domain-independent fashion. Rather than breaking up the generation process into a sequence of local decisions, we define a probabilistic context-free grammar that globally describes the inherent structure of the input (a corpus of database records and text describing some of them). We recast generation as the task of finding the best derivation tree for a set of database records and describe an algorithm for decoding in this framework that allows to intersect the grammar with additional information capturing fluency and syntactic well-formedness constraints. Experimental evaluation on several domains achieves results competitive with state-of-the-art systems that use domain specific constraints, explicit feature engineering or labeled data.

The SPARQL query language is currently being extended by the World Wide Web Consortium (W3C) with so-called entailment regimes. An entailment regime defines how queries are evaluated under more expressive semantics than SPARQL's standard simple entailment, which is based on subgraph matching. The queries are very expressive since variables can occur within complex concepts and can also bind to concept or role names. In this paper, we describe a sound and complete algorithm for the OWL Direct Semantics entailment regime. We further propose several novel optimizations such as strategies for determining a good query execution order, query rewriting techniques, and show how specialized OWL reasoning tasks and the concept and role hierarchy can be used to reduce the query execution time. For determining a good execution order, we propose a cost-based model, where the costs are based on information about the instances of concepts and roles that are extracted from a model abstraction built by an OWL reasoner. We present two ordering strategies: a static and a dynamic one. For the dynamic case, we improve the performance by exploiting an individual clustering approach that allows for computing the cost functions based on one individual sample from a cluster. We provide a prototypical implementation and evaluate the efficiency of the proposed optimizations. Our experimental study shows that the static ordering usually outperforms the dynamic one when accurate statistics are available. This changes, however, when the statistics are less accurate, e.g., due to nondeterministic reasoning decisions. For queries that go beyond conjunctive instance queries we observe an improvement of up to three orders of magnitude due to the proposed optimizations.

This paper provides new algorithms for distributed clustering for two popular center-based objectives, k-median and k-means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following a classic approach in clustering by \cite{har2004coresets}, we reduce the problem of finding a clustering with low cost to the problem of finding a coreset of small size. We provide a distributed method for constructing a global coreset which improves over the previous methods by reducing the communication complexity, and which works over general communication topologies. Experimental results on large scale data sets show that this approach outperforms other coreset-based distributed clustering algorithms.