Since there are 25 long haired women and 2 long haired men, guessing that the ticket owner is a woman is a safe bet. To lay our foundation, we need to quickly mention four concepts: probabilities, conditional probabilities, joint probabilities and marginal probabilities. The probability of a thing happening is the number of ways that thing can happen divided by the total number of things that can happen. Combining these by multiplication gives the joint probability, P(woman with short hair) P(woman) * P(short hair woman).

Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which contains Student-t distributions as family members and thus allows us to handle noisy data well. However, since the t-exponential family is denied by the deformed exponential, we cannot derive an efficient learning algorithm for the t-exponential family such as expectation propagation (EP). In this paper, we borrow the mathematical tools of q-algebra from statistical physics and show that the pseudo additivity of distributions allows us to perform calculation of t-exponential family distributions through natural parameters. We then develop an expectation propagation (EP) algorithm for the t-exponential family, which provides a deterministic approximation to the posterior or predictive distribution with simple moment matching. We finally apply the proposed EP algorithm to the Bayes point machine and Student-t process classication, and demonstrate their performance numerically.

We introduce a new family of graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. We show that these models are suitable for representing causal models with additive error terms. We provide a set of sufficient graphical criteria for the identification of arbitrary causal effects when the new models contain directed and undirected edges but no bidirected edge. We also provide a necessary and sufficient graphical criterion for the identification of the causal effect of a single variable on the rest of the variables. Moreover, we develop an exact algorithm for learning the new models from observational and interventional data via answer set programming. Finally, we introduce gated models for causal effect identification, a new family of graphical models that exploits context specific independences to identify additional causal effects. Keywords: Acyclic directed mixed graphs; causal models; answer set programming.

In this paper, we consider an infinite dimensional exponential family, $\mathcal{P}$ of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, $H$ and show it to be quite rich in the sense that a broad class of densities on $\mathbb{R}^d$ can be approximated arbitrarily well in Kullback-Leibler (KL) divergence by elements in $\mathcal{P}$. The main goal of the paper is to estimate an unknown density, $p_0$ through an element in $\mathcal{P}$. Standard techniques like maximum likelihood estimation (MLE) or pseudo MLE (based on the method of sieves), which are based on minimizing the KL divergence between $p_0$ and $\mathcal{P}$, do not yield practically useful estimators because of their inability to efficiently handle the log-partition function. Instead, we propose an estimator, $\hat{p}_n$ based on minimizing the \emph{Fisher divergence}, $J(p_0\Vert p)$ between $p_0$ and $p\in \mathcal{P}$, which involves solving a simple finite-dimensional linear system. When $p_0\in\mathcal{P}$, we show that the proposed estimator is consistent, and provide a convergence rate of $n^{-\min\left\{\frac{2}{3},\frac{2\beta+1}{2\beta+2}\right\}}$ in Fisher divergence under the smoothness assumption that $\log p_0\in\mathcal{R}(C^\beta)$ for some $\beta\ge 0$, where $C$ is a certain Hilbert-Schmidt operator on $H$ and $\mathcal{R}(C^\beta)$ denotes the image of $C^\beta$. We also investigate the misspecified case of $p_0\notin\mathcal{P}$ and show that $J(p_0\Vert\hat{p}_n)\rightarrow \inf_{p\in\mathcal{P}}J(p_0\Vert p)$ as $n\rightarrow\infty$, and provide a rate for this convergence under a similar smoothness condition as above. Through numerical simulations we demonstrate that the proposed estimator outperforms the non-parametric kernel density estimator, and that the advantage with the proposed estimator grows as $d$ increases.

The Bayesian community should really start going to ICLR. They really should have started going years ago. For too long we Bayesians have, quite arrogantly, dismissed deep neural networks as unprincipled, dumb black boxes that lack elegance. We said that highly over-parametrised models fitted via maximum likelihood can't possibly work, they will overfit, won't generalise, etc. We touted our Bayesian nonparametric models instead: Chinese restaurants, Indian buffets, Gaussian processes. And, when things started looking really dire for us Bayesians, we even formed an alliance with kernel people, who used to be our mortal enemies just years before because they like convex optimisation.

Innovation diffusion has been studied extensively in a variety of disciplines, including sociology, economics, marketing, ecology, and computer science. Traditional literature on innovation diffusion has been dominated by models of aggregate behavior and trends. However, the agent-based modeling (ABM) paradigm is gaining popularity as it captures agent heterogeneity and enables fine-grained modeling of interactions mediated by social and geographic networks. While most ABM work on innovation diffusion is theoretical, empirically grounded models are increasingly important, particularly in guiding policy decisions. We present a critical review of empirically grounded agent-based models of innovation diffusion, developing a categorization of this research based on types of agent models as well as applications. By connecting the modeling methodologies in the fields of information and innovation diffusion, we suggest that the maximum likelihood estimation framework widely used in the former is a promising paradigm for calibration of agent-based models for innovation diffusion. Although many advances have been made to standardize ABM methodology, we identify four major issues in model calibration and validation, and suggest potential solutions.

The majority of medical documents and electronic health records (EHRs) are in text format that poses a challenge for data processing and finding relevant documents. Looking for ways to automatically retrieve the enormous amount of health and medical knowledge has always been an intriguing topic. Powerful methods have been developed in recent years to make the text processing automatic. One of the popular approaches to retrieve information based on discovering the themes in health & medical corpora is topic modeling, however, this approach still needs new perspectives. In this research we describe fuzzy latent semantic analysis (FLSA), a novel approach in topic modeling using fuzzy perspective. FLSA can handle health & medical corpora redundancy issue and provides a new method to estimate the number of topics. The quantitative evaluations show that FLSA produces superior performance and features to latent Dirichlet allocation (LDA), the most popular topic model.

Process mining techniques focus on extracting insight in processes from event logs. Process mining has the potential to provide valuable insights in (un)healthy habits and to contribute to ambient assisted living solutions when applied on data from smart home environments. However, events recorded in smart home environments are on the level of sensor triggers, at which process discovery algorithms produce overgeneralizing process models that allow for too much behavior and that are difficult to interpret for human experts. We show that abstracting the events to a higher-level interpretation can enable discovery of more precise and more comprehensible models. We present a framework for the extraction of features that can be used for abstraction with supervised learning methods that is based on the XES IEEE standard for event logs. This framework can automatically abstract sensor-level events to their interpretation at the human activity level, after training it on training data for which both the sensor and human activity events are known. We demonstrate our abstraction framework on three real-life smart home event logs and show that the process models that can be discovered after abstraction are more precise indeed.

More than 100 years ago, the invention of the internal combustion engine revolutionized automotive travel, and with it gave birth to a new industrial economy. Just as internal combustion once did, the proliferation of data science and analytics is once again reshaping the information economy and transforming how we interact with technology. Business analytics, in particular, is playing a pivotal role in improving operations at large-scale organizations. For example--UPS, a shipping service, saved $30 million in fuel by using predictive analytics. These kinds of cost savings are mouthwatering if you're a C-suite executive.

The volume of data generated by internet and social networks is increasing every day, and there is a clear need for efficient ways of extracting useful information from them. As those data can take different forms, it is important to use all the available data representations for prediction. In this paper, we focus our attention on supervised classification using both regular plain, tabular, data and structural information coming from a network structure. 14 techniques are investigated and compared in this study and can be divided in three classes: the first one uses only the plain data to build a classification model, the second uses only the graph structure and the last uses both information sources. The relative performances in these three cases are investigated. Furthermore, the effect of using a graph embedding and well-known indicators in spatial statistics is also studied. Possible applications are automatic classification of web pages or other linked documents, of people in a social network or of proteins in a biological complex system, to name a few. Based on our comparison, we draw some general conclusions and advices to tackle this particular classification task: some datasets can be better explained by their graph structure (graph-driven), or by their feature set (features-driven). The most efficient methods are discussed in both cases.