This paper provides new insight into maximizing F1 scores in the context of binary classification and also in the context of multilabel classification. The harmonic mean of precision and recall, F1 score is widely used to measure the success of a binary classifier when one class is rare. Micro average, macro average, and per instance average F1 scores are used in multilabel classification. For any classifier that produces a real-valued output, we derive the relationship between the best achievable F1 score and the decision-making threshold that achieves this optimum. As a special case, if the classifier outputs are well-calibrated conditional probabilities, then the optimal threshold is half the optimal F1 score. As another special case, if the classifier is completely uninformative, then the optimal behavior is to classify all examples as positive. Since the actual prevalence of positive examples typically is low, this behavior can be considered undesirable. As a case study, we discuss the results, which can be surprising, of applying this procedure when predicting 26,853 labels for Medline documents.

A standard technique for understanding underlying dependency structures among a set of variables posits a shared conditional probability distribution for the variables measured on individuals within a group. This approach is often referred to as module networks, where individuals are represented by nodes in a network, groups are termed modules, and the focus is on estimating the network structure among modules. However, estimation solely from node-specific variables can lead to spurious dependencies, and unverifiable structural assumptions are often used for regularization. Here, we propose an extended model that leverages direct observations about the network in addition to node-specific variables. By integrating complementary data types, we avoid the need for structural assumptions. We illustrate theoretical and practical significance of the model and develop a reversible-jump MCMC learning procedure for learning modules and model parameters. We demonstrate the method accuracy in predicting modular structures from synthetic data and capability to learn influence structures in twitter data and regulatory modules in the Mycobacterium tuberculosis gene regulatory network.

Much recent research has been conducted in the area of Bayesian learning, particularly with regard to the optimization of hyper-parameters via Gaussian process regression. The methodologies rely chiefly on the method of maximizing the expected improvement of a score function with respect to adjustments in the hyper-parameters. In this work, we present a novel algorithm that exploits notions of confidence intervals and uncertainties to enable the discovery of the best optimal within a targeted region of the parameter space. We demonstrate the efficacy of our algorithm with respect to machine learning problems and show cases where our algorithm is competitive with the method of maximizing expected improvement.

Our winning submission to the 2014 Kaggle competition for Large Scale Hierarchical Text Classification (LSHTC) consists mostly of an ensemble of sparse generative models extending Multinomial Naive Bayes. The base-classifiers consist of hierarchically smoothed models combining document, label, and hierarchy level Multinomials, with feature pre-processing using variants of TF-IDF and BM25. Additional diversification is introduced by different types of folds and random search optimization for different measures. The ensemble algorithm optimizes macroFscore by predicting the documents for each label, instead of the usual prediction of labels per document. Scores for documents are predicted by weighted voting of base-classifier outputs with a variant of Feature-Weighted Linear Stacking. The number of documents per label is chosen using label priors and thresholding of vote scores. This document describes the models and software used to build our solution. Reproducing the results for our solution can be done by running the scripts included in the Kaggle package. A package omitting precomputed result files is also distributed. All code is open source, released under GNU GPL 2.0, and GPL 3.0 for Weka and Meka dependencies.

Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models in many branches of science they have not been the focus of systematic statistical analysis until recently. In this work we propose a general approach to estimate the parameters of systems of differential equations measured with noise. Our methodology is based on the maximization of the penalized likelihood where the system of differential equations is used as a penalty. To do so, we use a Reproducing Kernel Hilbert Space approach that allows to formulate the estimation problem as an unconstrained numeric maximization problem easy to solve. The proposed method is tested with synthetically simulated data and it is used to estimate the unobserved transcription factor CdaR in Steptomyes coelicolor using gene expression data of the genes it regulates.

The continuous time Bayesian network (CTBN) is a probabilistic graphical model that enables reasoning about complex, interdependent, and continuous-time subsystems. The model uses nodes to denote subsystems and arcs to denote conditional dependence. This dependence manifests in how the dynamics of a subsystem change based on the current states of its parents in the network. While the original CTBN definition allows users to specify the dynamics of how the system evolves, users might also want to place value expressions over the dynamics of the model in the form of performance functions. We formalize these performance functions for the CTBN and show how they can be factored in the same way as the network, allowing what we argue is a more intuitive and explicit representation. For cases in which a performance function must involve multiple nodes, we show how to augment the structure of the CTBN to account for the performance interaction while maintaining the factorization of a single performance function for each node.

We report the results of an empirical evaluation of structural simplification of Bayesian networks by removing weak arcs. We conduct a series of experiments on six networks built from real data sets selected from the UC Irvine Machine Learning Repository. We systematically remove arcs from the weakest to the strongest, relying on four measures of arc strength, and measure the classification accuracy of the resulting simplified models. Our results show that removing up to roughly 20 percent of the weakest arcs in a network has minimal effect on its classification accuracy. At the same time, structural simplification of networks leads to significant reduction of both the amount of memory taken by the clique tree and the amount of computation needed to perform inference.

Contrastive divergence (CD) is a promising method of inference in high dimensional distributions with intractable normalizing constants, however, the theoretical foundations justifying its use are somewhat shaky. This document proposes a framework for understanding CD inference, how/when it works, and provides multiple justifications for the CD moment conditions, including framing them as a variational approximation. Algorithms for performing inference are discussed and are applied to social network data using an exponential-family random graph models (ERGM). The framework also provides guidance about how to construct MCMC kernels providing good CD inference, which turn out to be quite different from those used typically to provide fast global mixing.

Developing feature selection algorithms that move beyond a pure correlational to a more causal analysis of observational data is an important problem in the sciences. Several algorithms attempt to do so by discovering the Markov blanket of a target, but they all contain a forward selection step which variables must pass in order to be included in the conditioning set. As a result, these algorithms may not consider all possible conditional multivariate combinations. We improve on this limitation by proposing a backward elimination method that uses a kernel-based conditional dependence measure to identify the Markov blanket in a fully multivariate fashion. The algorithm is easy to implement and compares favorably to other methods on synthetic and real datasets.

This paper proposes an online tree-based Bayesian approach for reinforcement learning. For inference, we employ a generalised context tree model. This defines a distribution on multivariate Gaussian piecewise-linear models, which can be updated in closed form. The tree structure itself is constructed using the cover tree method, which remains efficient in high dimensional spaces. We combine the model with Thompson sampling and approximate dynamic programming to obtain effective exploration policies in unknown environments. The flexibility and computational simplicity of the model render it suitable for many reinforcement learning problems in continuous state spaces. We demonstrate this in an experimental comparison with least squares policy iteration.