In dynamic topic modeling, the proportional contribution of a topic to a document depends on the temporal dynamics of that topic's overall prevalence in the corpus. We extend the Dynamic Topic Model of Blei and Lafferty (2006) by explicitly modeling document level topic proportions with covariates and dynamic structure that includes polynomial trends and periodicity. A Markov Chain Monte Carlo (MCMC) algorithm that utilizes Polya-Gamma data augmentation is developed for posterior inference. Conditional independencies in the model and sampling are made explicit, and our MCMC algorithm is parallelized where possible to allow for inference in large corpora. To address computational bottlenecks associated with Polya-Gamma sampling, we appeal to the Central Limit Theorem to develop a Gaussian approximation to the Polya-Gamma random variable. This approximation is fast and reliable for parameter values relevant in the text mining domain. Our model and inference algorithm are validated with multiple simulation examples, and we consider the application of modeling trends in PubMed abstracts. We demonstrate that sharing information across documents is critical for accurately estimating document-specific topic proportions. We also show that explicitly modeling polynomial and periodic behavior improves our ability to predict topic prevalence at future time points.

Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for an observation matrix with p features across n samples. We develop a structured Bayesian group factor analysis model that extends the factor model to multiple coupled observation matrices; in the case of two observations, this reduces to a Bayesian model of canonical correlation analysis. The main contribution of this work is to carefully define a structured Bayesian prior that encourages both element-wise and column-wise shrinkage and leads to desirable behavior on high-dimensional data. In particular, our model puts a structured prior on the joint factor loading matrix, regularizing at three levels, which enables element-wise sparsity and unsupervised recovery of latent factors corresponding to structured variance across arbitrary subsets of the observations. In addition, our structured prior allows for both dense and sparse latent factors so that covariation among either all features or only a subset of features can both be recovered. We use fast parameter-expanded expectation-maximization for parameter estimation in this model. We validate our method on both simulated data with substantial structure and real data, comparing against a number of state-of-the-art approaches. These results illustrate useful properties of our model, including i) recovering sparse signal in the presence of dense effects; ii) the ability to scale naturally to large numbers of observations; iii) flexible observation- and factor-specific regularization to recover factors with a wide variety of sparsity levels and percentage of variance explained; and iv) tractable inference that scales to modern genomic and document data sizes.

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to incorporate prior information such as sparsity or structure. To address this problem, we present a new view of dynamical system learning: we show how to learn dynamical systems by solving a sequence of ordinary supervised learning problems, thereby allowing users to incorporate prior knowledge via standard techniques such as L1 regularization. Many existing spectral methods are special cases of this new framework, using linear regression as the supervised learner. We demonstrate the effectiveness of our framework by showing examples where nonlinear regression or lasso let us learn better state representations than plain linear regression does; the correctness of these instances follows directly from our general analysis.

This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time $t_{\text{mix}}$ of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require the knowledge of any parameters of the chain. This stands in contrast to previous approaches, which either only provide point estimates, or require a reset mechanism, or additional prior knowledge. The interval is constructed around the relaxation time $t_{\text{relax}}$, which is strongly related to the mixing time, and the width of the interval converges to zero roughly at a $\sqrt{n}$ rate, where $n$ is the length of the sample path. Upper and lower bounds are given on the number of samples required to achieve constant-factor multiplicative accuracy. The lower bounds indicate that, unless further restrictions are placed on the chain, no procedure can achieve this accuracy level before seeing each state at least $\Omega(t_{\text{relax}})$ times on the average. Finally, future directions of research are identified.

This paper analyzes repeated multimarket contact with observation errors where two players operate in multiple markets simultaneously. Multimarket contact has received much attention from the literature of economics,management, and information systems. Despite vast empirical studies that examine whether multimarket contact fosters cooperation/collusion, little is theoretically known as to how players behave in an equilibrium when each player receives a noisy observation of other firms’ actions. This paper tackles an essentially realistic situation where the players do not share common information; each player may observe a different signal (private monitoring). Thus, players have difficulty in having a common understanding about which market their opponent should be punished in and when punishment should be started and ended. We first theoretically show that an extension of 1-period mutual punishment (1MP) for an arbitrary number of markets can be an equilibrium. Second, by applying a verification method, we identify a simple equilibrium strategy called "locally cautioning (LC)" that restores collusion after observation error or deviation. We then numerically reveal that LC significantly outperforms 1MP and achieves the highest degree of collusion.

The number of applications of service robotics in public spaces such as hospitals, museums and malls is a growing trend. Public spaces, however, provide several challenges to the robot, and specifically with its planning capabilities: they need to cope with a dynamic and uncertain environment and are subject to particular human-robot interaction constraints. A major challenge is the Joint Intention problem. When cooperating with humans, a persistent commitment to achieve a shared goal cannot be always assumed, since they have an unpredictable behavior and may be distracted in environments as dynamic and uncertain as public spaces, and even more so if the human agents are customers,visitors or bystanders. In order to address such issues in a decision-making context, we present a framework based on Hierarchical Factored POMDPs. We describe the general method for ensuring the Joint Intention between human and robot , the hierarchical structure and the Value Decomposition method adopted to build it.We also provide an example application scenario: an Escort Task in a shopping mall for guiding a customer towards a desired point of interest.

This paper proposes an online transfer framework to capture the interaction among agents and shows that current transfer learning in reinforcement learning is a special case of online transfer. Furthermore, this paper re-characterizes existing agents-teaching-agents methods as online transfer and analyze one such teaching method in three ways. First, the convergence of Q-learning and Sarsa with tabular representation with a finite budget is proven. Second, the convergence of Q-learning and Sarsa with linear function approximation is established. Third, the we show the asymptotic performance cannot be hurt through teaching. Additionally, all theoretical results are empirically validated.

We parallelize the Point-Based Value Iteration (PBVI) algorithm, which approximates the solution to Partially Observable Markov Decision Processes (POMDPs), using a Graphics Processing Unit (GPU). We detail additional optimizations, such as leveraging the bounded size of non-zero values over all belief point vectors, usable by serial and parallel algorithms. We compare serial (CPU) and parallel (GPU) implementations on 10 distinct problem domains, and demonstrate that our approach provides an order of magnitude improvement.

The Markov Decision Process (MDP) framework is a versatile method for addressing single and multiagent sequential decision making problems. Many exact and approximate solution methods attempt to exploit structure in the problem and are based on value factorization. Especially multiagent settings (MAS), however, are known to suffer from an exponential increase in value component sizes as interactions become denser, meaning that approximation architectures are overly restricted in the problem sizes and types they can handle. We present an approach to mitigate this limitation for certain types of MASs, exploiting a property that can be thought of as "anonymous influence" in the factored MDP. In particular, we show how anonymity can lead to representational and computational efficiencies, both for general variable elimination in a factor graph but also for the approximate linear programming solution to factored MDPs. The latter allows to scale linear programming to factored MDPs that were previously unsolvable. Our results are shown for a disease control domain over a graph with 50 nodes that are each connected with up to 15 neighbors.

In this paper, we present the conceptual model of a realworld application of Markov Decision Processes to dam management. The idea is to demonstrate that it is possible to efficiently automate the construction of operation policies by modelling the problem as a sequential decision problem that can be easily solved using stochastic dynamic programming. We will explain the problem domain and provide an analysis of the resulting value and policy functions. We will also present a useful discussion about the issues that will appear when the conceptual model to be extended into a real-world application.