Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the significance of this problem, statistical characterization of the proposed metrics has been limited. We introduce and develop a class of techniques for analyzing random walks on graphs using stochastic calculus. Using these techniques we generalize results on the degeneracy of hitting times and analyze a metric based on the Laplace transformed hitting time (LTHT). The metric serves as a natural, provably well-behaved alternative to the expected hitting time. We establish a general correspondence between hitting times of the Brownian motion and analogous hitting times on the graph. We show that the LTHT is consistent with respect to the underlying metric of a geometric graph, preserves clustering tendency, and remains robust against random addition of non-geometric edges. Tests on simulated and real-world data show that the LTHT matches theoretical predictions and outperforms alternatives.

This research studies the impact of Time-Of-Use (TOU) tariffs in a competitive electricity market place. Specifically, it focuses on the question of how should an autonomous broker agent optimize TOU tariffs in a competitive retail market, and what is the impact of such tariffs on the economy. We formalize the problem of TOU tariff optimization and propose an algorithm for approximating its solution. We extensively experiment with our algorithm in a large-scale, detailed electricity retail markets simulation of the Power Trading Agent Competition (Power TAC) and: 1) find that our algorithm results in 15\% peak-demand reduction, 2) find that its peak-flattening results in greater profits and/or profit-share for the broker and allows it to win in head-to-head competition against the 1st and 2nd place brokers from the Power TAC 2014 finals, and 3) analyze several economic implications of using TOU tariffs in competitive retail markets.

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.

External factors are hard to model using a Markovian state in several real-world planning domains. Although planning can be difficult in such domains, it may be possible to exploit long-term dependencies between states of the environment during planning. We introduce weighted state scenarios to model long-term sequences of states, and we use a model based on a Partially Observable Markov Decision Process to reason about scenarios during planning. Experiments show that our model outperforms other methods for decision making in two real-world domains.

A key contribution of this paper is to introduce an extended BO setting, called Bayesian Optimization with Resources We consider optimizing an unknown function f by running (BOR), that explicitly models experimental resources experiments that each take an input x and return a noisy output and activities. In particular, our model specifies f(x). In particular, we focus on the setting where experiments the following: 1) resource requirements for experiments, are expensive, limiting the number of experiments which may vary across different experiments, 2) resourceproduction that can be run. Bayesian Optimization (BO) addresses this actions, which produce the various resources and setting by maintaining a Bayesian posterior over f to capture can require varying amounts of time, and 3) a set of "labs" our uncertainty about f given prior experiments (Jones for running concurrent experiments and a set of "production 2001; Brochu, Cora, and de Freitas 2010). The posterior is lines" for concurrent resource production. The problem is then used to select new experiments that trades-off exploring then to select and schedule the experiments and resourceproduction uncertain areas of the experimental space and exploiting actions in order to optimize the unknown objective promising areas.

The updating is accomplished using Bayes'

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an optimization problem over an appropriately selected family of distributions. The goal is two-fold. Firstly, to find lower-dimensional representations of the unknown parameter vector that capture as much as possible of the associated posterior density, and secondly to enable the computation of the approximate posterior density with as few forward calls as possible. We discuss how these objectives can be achieved by using a fully Bayesian argumentation and employing the marginal likelihood or evidence as the ultimate model validation metric for any proposed dimensionality reduction. We demonstrate the performance of the proposed methodology for problems in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. An Importance Sampling scheme is finally employed in order to validate the results and assess the efficacy of the approximations provided.

In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to integrate both types of models. Methods such as posterior regularization follow the idea of generalized moment matching, in that they allow matching expectations between two models, but sometimes both models are most conveniently expressed as latent variable models. We propose latent Bayesian melding, which is motivated by averaging the distributions over populations statistics of both the individual-level and the population-level models under a logarithmic opinion pool framework. In a case study on electricity disaggregation, which is a type of single-channel blind source separation problem, we show that latent Bayesian melding leads to significantly more accurate predictions than an approach based solely on generalized moment matching.

We study contextual bandits with budget and time constraints, referred to as constrained contextual bandits.The time and budget constraints significantly complicate the exploration and exploitation tradeoff because they introduce complex coupling among contexts over time.Such coupling effects make it difficult to obtain oracle solutions that assume known statistics of bandits. To gain insight, we first study unit-cost systems with known context distribution. When the expected rewards are known, we develop an approximation of the oracle, referred to Adaptive-Linear-Programming (ALP), which achieves near-optimality and only requires the ordering of expected rewards. With these highly desirable features, we then combine ALP with the upper-confidence-bound (UCB) method in the general case where the expected rewards are unknown {\it a priori}. We show that the proposed UCB-ALP algorithm achieves logarithmic regret except for certain boundary cases. Further, we design algorithms and obtain similar regret analysis results for more general systems with unknown context distribution and heterogeneous costs. To the best of our knowledge, this is the first work that shows how to achieve logarithmic regret in constrained contextual bandits. Moreover, this work also sheds light on the study of computationally efficient algorithms for general constrained contextual bandits.

Wiener-Granger causality is a widely used framework of causal analysis for temporally resolved events. We introduce a new measure of Wiener-Granger causality based on kernelization of partial canonical correlation analysis with specific advantages in the context of large high-dimensional data. The introduced measure is able to detect non-linear and non-monotonous signals, is designed to be immune to noise, and offers tunability in terms of computational complexity in its estimations. Furthermore, we show that, under specified conditions, the introduced measure can be regarded as an estimate of conditional mutual information (transfer entropy). The functionality of this measure is assessed using comparative simulations where it outperforms other existing methods. The paper is concluded with an application to climatological data.