Energy disaggregation, the task of taking a whole home electricity signal and decomposing it into its component appliances, has been proved to be essential in energy conservation research. One powerful cue for breaking down the entire household's energy consumption is user's daily energy usage behavior, which has so far received little attention: existing works on energy disaggregation mostly ignored the relationship between the energy usages of various appliances across different time slots. To model such relationship, we combine topic models with Hawkes processes, and propose a novel probabilistic model based on marked Hawkes process that enables the modeling of marked event data. The proposed model seeks to capture the influence from the occurrence and the marks of one usage event to the occurrence and the marks of subsequent usage events in the future. We also develop an inference algorithm based on variational inference for model parameter estimation. Experimental results on both synthetic data and three real world data sets demonstrate the effectiveness of our model, which outperforms state-of-the-art approaches in decomposing the entire consumed energy to each appliance. Analyzing the influence captured by the proposed model provides further insights into numerous interesting energy usage behavior patterns.

Bursty topics discovery in microblogs is important for people to grasp essential and valuable information. However, the task is challenging since microblog posts are particularly short and noisy. This work develops a novel probabilistic model, namely Bursty Biterm Topic Model (BBTM), to deal with the task. BBTM extends the Biterm Topic Model (BTM) by incorporating the burstiness of biterms as prior knowledge for bursty topic modeling, which enjoys the following merits: 1) It can well solve the data sparsity problem in topic modeling over short texts as the same as BTM; 2) It can automatical discover high quality bursty topics in microblogs in a principled and efficient way. Extensive experiments on a standard Twitter dataset show that our approach outperforms the state-of-the-art baselines significantly.

We are concerned with modeling the strength of links in networks by taking into account how often those links are used. Link usage is a strong indicator of how closely two nodes are related, but existing network models in Bayesian Statistics and Machine Learning are able to predict only wether a link exists at all. As priors for latent attributes of network nodes we explore the Chinese Restaurant Process (CRP) and a multivariate Gaussian with fixed dimensionality. The model is applied to a social network dataset and a word coocurrence dataset.

Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively low-dimensional problems. We introduce Hamiltonian ABC (HABC), a set of likelihood-free algorithms that apply recent advances in scaling Bayesian learning using Hamiltonian Monte Carlo (HMC) and stochastic gradients. We find that a small number forward simulations can effectively approximate the ABC gradient, allowing Hamiltonian dynamics to efficiently traverse parameter spaces. We also describe a new simple yet general approach of incorporating random seeds into the state of the Markov chain, further reducing the random walk behavior of HABC. We demonstrate HABC on several typical ABC problems, and show that HABC samples comparably to regular Bayesian inference using true gradients on a high-dimensional problem from machine learning.

The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, since no closed-form solution exists. Adopting a decision-theoretic perspective, this article provides a formal and experimental analysis of different approaches for maximizing the F-measure. We start with a Bayes-risk analysis of related loss functions, such as Hamming loss and subset zero-one loss, showing that optimizing such losses as a surrogate of the F-measure leads to a high worst-case regret. Subsequently, we perform a similar type of analysis for F-measure maximizing algorithms, showing that such algorithms are approximate, while relying on additional assumptions regarding the statistical distribution of the binary response variables. Furthermore, we present a new algorithm which is not only computationally efficient but also Bayes-optimal, regardless of the underlying distribution. To this end, the algorithm requires only a quadratic (with respect to the number of binary responses) number of parameters of the joint distribution. We illustrate the practical performance of all analyzed methods by means of experiments with multi-label classification problems.

We demonstrate that a popular class of nonparametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI. Consequently, accurate estimation of MI between two strongly dependent variables is possible only for prohibitively large sample size. This important yet overlooked shortcoming of the existing estimators is due to their implicit reliance on local uniformity of the underlying joint distribution. We introduce a new estimator that is robust to local non-uniformity, works well with limited data, and is able to capture relationship strengths over many orders of magnitude. We demonstrate the superior performance of the proposed estimator on both synthetic and real-world data.

Optimising black-box functions is important in many disciplines, such as tuning machine learning models, robotics, finance and mining exploration. Bayesian optimisation is a state-of-the-art technique for the global optimisation of black-box functions which are expensive to evaluate. At the core of this approach is a Gaussian process prior that captures our belief about the distribution over functions. However, in many cases a single Gaussian process is not flexible enough to capture non-stationarity in the objective function. Consequently, heteroscedasticity negatively affects performance of traditional Bayesian methods. In this paper, we propose a novel prior model with hierarchical parameter learning that tackles the problem of non-stationarity in Bayesian optimisation. Our results demonstrate substantial improvements in a wide range of applications, including automatic machine learning and mining exploration.

We introduce local expectation gradients which is a general purpose stochastic variational inference algorithm for constructing stochastic gradients through sampling from the variational distribution. This algorithm divides the problem of estimating the stochastic gradients over multiple variational parameters into smaller sub-tasks so that each sub-task exploits intelligently the information coming from the most relevant part of the variational distribution. This is achieved by performing an exact expectation over the single random variable that mostly correlates with the variational parameter of interest resulting in a Rao-Blackwellized estimate that has low variance and can work efficiently for both continuous and discrete random variables. Furthermore, the proposed algorithm has interesting similarities with Gibbs sampling but at the same time, unlike Gibbs sampling, it can be trivially parallelized.

Many machine learning tasks can be formulated in terms of predicting structured outputs. In frameworks such as the structured support vector machine (SVM-Struct) and the structured perceptron, discriminative functions are learned by iteratively applying efficient maximum a posteriori (MAP) decoding. However, maximum likelihood estimation (MLE) of probabilistic models over these same structured spaces requires computing partition functions, which is generally intractable. This paper presents a method for learning discrete exponential family models using the Bethe approximation to the MLE. Remarkably, this problem also reduces to iterative (MAP) decoding. This connection emerges by combining the Bethe approximation with a Frank-Wolfe (FW) algorithm on a convex dual objective which circumvents the intractable partition function. The result is a new single loop algorithm MLE-Struct, which is substantially more efficient than previous double-loop methods for approximate maximum likelihood estimation. Our algorithm outperforms existing methods in experiments involving image segmentation, matching problems from vision, and a new dataset of university roommate assignments.

Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and covering-based rough sets provide a systematic approach to this type of representation. In this paper, we study the connectedness of graphs through covering-based rough sets and apply it to connected matroids. First, we present an approach to inducing a covering by a graph, and then study the connectedness of the graph from the viewpoint of the covering approximation operators. Second, we construct a graph from a matroid, and find the matroid and the graph have the same connectedness, which makes us to use covering-based rough sets to study connected matroids. In summary, this paper provides a new approach to studying graph theory and matroid theory.